This thesis examines the effects of penalties in the NFL on violent strategies and the probability of injuries. It presents a theoretical model that focuses on the offense's decision to pass or run, and the defense's decision to blitz or not. The model considers players' strategy sets and payoffs, and how penalties may alter payoffs and incentives. Defensive penalties for fouls on passing plays could increase the incentive to pass more often, potentially offsetting the goal of reducing injuries. The thesis will test this theoretical framework empirically and analyze how different penalty structures affect the probability of injury.
The Economic Impact of Hearing Loss in AustraliaSophiaJohn12
Hearing loss affects around one in six Australians and is projected to increase to one in four by 2050 due to an aging population. It reduces the ability to communicate and participate in education, employment, and relationships. In 2005, the total financial cost of hearing loss in Australia was estimated at $11.75 billion or 1.4% of GDP, including both direct health costs and indirect costs like lost productivity. While devices like hearing aids and cochlear implants can help, the majority (85%) of those with hearing loss do not have such devices. The study aimed to quantify the full economic impacts of hearing loss in Australia for the first time.
Report wall street bank involvement with physical commodities (11-18-14)Ruslan Sivoplyas
The Permanent Subcommittee on Investigations has scheduled a two-day hearing, “Wall Street Bank Involvement With Physical Commodities,” on Thursday, November 20 and Friday, November 21, 2014.
After a two-year bipartisan investigation, the subcommittee will hold a hearing examining the extent to which banks and their holding companies own physical commodities like oil, natural gas, aluminum and other industrial metals, as well as own or control businesses like power plants, oil and gas pipelines, and commodity warehouses.
This document proposes the Virtual Integrated Planning and Execution Resource System (VIPERS) to achieve information supremacy for US air forces in 2025. It outlines requirements for future force support, including synchronized support for dispersed forces and collaborative parallel planning. VIPERS would provide commanders with battlespace awareness and the ability to rapidly plan and execute operations. It would integrate data from multiple sensors using fusion and decision support technologies, and use holographic displays for intuitive 3D visualization during planning and execution. The document describes potential technologies that could enable VIPERS and provides an example concept of operations.
This document provides a summary of a research report on security management and operations conducted through a survey of 315 security professionals. Key findings include:
1) Most large organizations have significant shortcomings in security management and operations, with only 19% considered "leaders" based on criteria like staffing, testing, and visibility.
2) New technologies like cloud, mobile, and remote work are making security management much more difficult for over half of organizations.
3) Information security is becoming more aligned with business processes and corporate culture, though regulatory compliance and data protection remain top priorities.
4) Effectiveness of security depends on collaboration between security and other IT teams like networking and operations.
This document provides an overview of child safety and security in K-12 schools in India. It is divided into four parts.
Part One examines the current state of safety in schools through data on reported crimes against children, student perceptions of safety, and unique safety challenges in schools. It finds that schools are generally considered safer for children than other environments like streets or even homes.
Part Two provides key policy recommendations to improve safety based on input from child experts. Part Three discusses the legal framework around school safety. It outlines the rights of children and the obligations and standards of care required of schools.
Part Four presents a toolkit for schools to implement safety, including essential policies, documentation, a student safety policy template,
Proves that Money Laundering statutes are being abused by corrupted government as a means to compel financial institutions to become the equivalent of federal employment recruiters against their business associates.
Comprehensive Multi-year Plan - Universal Immunization Program -
In India Universal Immunization Program - (UIP) is bring forward by the Government, UIP ( Universal Immunization Program) in India is among the most successful vaccination program and cost-effective public health interventions.
Routine Immunization Program in India, Immunization Technical Support, routine immunization services in India, Ministry of Health and Family Welfare, Adverse Event Following Immunization Secretariat, Vaccine logistics and supply chain,Universal Immunization Program in India
The Economic Impact of Hearing Loss in AustraliaSophiaJohn12
Hearing loss affects around one in six Australians and is projected to increase to one in four by 2050 due to an aging population. It reduces the ability to communicate and participate in education, employment, and relationships. In 2005, the total financial cost of hearing loss in Australia was estimated at $11.75 billion or 1.4% of GDP, including both direct health costs and indirect costs like lost productivity. While devices like hearing aids and cochlear implants can help, the majority (85%) of those with hearing loss do not have such devices. The study aimed to quantify the full economic impacts of hearing loss in Australia for the first time.
Report wall street bank involvement with physical commodities (11-18-14)Ruslan Sivoplyas
The Permanent Subcommittee on Investigations has scheduled a two-day hearing, “Wall Street Bank Involvement With Physical Commodities,” on Thursday, November 20 and Friday, November 21, 2014.
After a two-year bipartisan investigation, the subcommittee will hold a hearing examining the extent to which banks and their holding companies own physical commodities like oil, natural gas, aluminum and other industrial metals, as well as own or control businesses like power plants, oil and gas pipelines, and commodity warehouses.
This document proposes the Virtual Integrated Planning and Execution Resource System (VIPERS) to achieve information supremacy for US air forces in 2025. It outlines requirements for future force support, including synchronized support for dispersed forces and collaborative parallel planning. VIPERS would provide commanders with battlespace awareness and the ability to rapidly plan and execute operations. It would integrate data from multiple sensors using fusion and decision support technologies, and use holographic displays for intuitive 3D visualization during planning and execution. The document describes potential technologies that could enable VIPERS and provides an example concept of operations.
This document provides a summary of a research report on security management and operations conducted through a survey of 315 security professionals. Key findings include:
1) Most large organizations have significant shortcomings in security management and operations, with only 19% considered "leaders" based on criteria like staffing, testing, and visibility.
2) New technologies like cloud, mobile, and remote work are making security management much more difficult for over half of organizations.
3) Information security is becoming more aligned with business processes and corporate culture, though regulatory compliance and data protection remain top priorities.
4) Effectiveness of security depends on collaboration between security and other IT teams like networking and operations.
This document provides an overview of child safety and security in K-12 schools in India. It is divided into four parts.
Part One examines the current state of safety in schools through data on reported crimes against children, student perceptions of safety, and unique safety challenges in schools. It finds that schools are generally considered safer for children than other environments like streets or even homes.
Part Two provides key policy recommendations to improve safety based on input from child experts. Part Three discusses the legal framework around school safety. It outlines the rights of children and the obligations and standards of care required of schools.
Part Four presents a toolkit for schools to implement safety, including essential policies, documentation, a student safety policy template,
Proves that Money Laundering statutes are being abused by corrupted government as a means to compel financial institutions to become the equivalent of federal employment recruiters against their business associates.
Comprehensive Multi-year Plan - Universal Immunization Program -
In India Universal Immunization Program - (UIP) is bring forward by the Government, UIP ( Universal Immunization Program) in India is among the most successful vaccination program and cost-effective public health interventions.
Routine Immunization Program in India, Immunization Technical Support, routine immunization services in India, Ministry of Health and Family Welfare, Adverse Event Following Immunization Secretariat, Vaccine logistics and supply chain,Universal Immunization Program in India
This document provides a detailed policy analysis and rebuttal of the U.C.C. redemption approach. It introduces some of the main proponents of redemption theories and provides a high-level summary of the redemption approach. The bulk of the document systematically rebuts common redemption arguments, citing legal authorities. It concludes that redemption theories are factually and legally invalid and warns those associated with SEDM against using redemption processes or materials.
This document discusses how individuals can defend themselves against demands from the government by asserting their right to be left alone and requiring the government to prove any claims or obligations. It argues that the only ways the government can create obligations are through common law violations that injure others or through contractual agreements. To win in court against the government, an individual must force the government to produce either an injured party or a valid contract showing the individual agreed to obligations. The document provides principles and examples for how to extract oneself from legal entanglements by requiring the government to meet its burden of proof in establishing obligations or claims against an individual.
This document discusses an individual's exclusive right to declare or establish their own civil status. It begins by noting that it is a state's duty to protect the civil status of its citizens and forbid interference by other states. It then provides definitions of civil status and discusses the main methods states use to control inhabitants by attaching obligations to property or civil statuses. Several legal authorities are cited that establish an individual's right to declare their own civil status, including international law, U.S. court cases, and constitutional provisions. The document concludes that individuals have remedies available if a government improperly changes or challenges their self-declared civil status.
The National Science and Technology Council's Task Force on Identity Management was established to assess the current state of identity management (IdM) across the U.S. government and develop a vision for the future. The Task Force found that over 3,000 federal systems currently utilize personally identifiable information (PII) in an inconsistent and duplicative manner. The Task Force proposed a new framework that includes: 1) A "network of networks" to securely manage common PII elements across agencies; 2) Strong security, privacy and auditability standards; and 3) Ubiquitous yet controlled access to verified identity data. This proposed approach aims to improve accuracy, availability, privacy and coordination of IdM across the federal government.
This document proposes concepts and technologies for counterspace operations in 2025, including space detection, anti-satellite weapons, space interdiction nets, miniaturized satellites, satellite cloaking, kinetic and directed energy weapons. It outlines offensive and defensive counterspace architectures and recommends further analysis of miniaturization, stealth, detection and targeting concepts as well as kinetic and directed energy weapons. The goal is to maintain US space superiority as space becomes increasingly vital to national security and more countries and commercial entities access space.
This document provides a summary of health indicators in OECD countries. It begins with an introduction that describes the document as the 2013 edition of Health at a Glance, which presents recent comparable data on key health indicators across 34 OECD countries. The data is drawn from contributions of national health agencies and aims to monitor health status, determinants, health workforce, health care activities, and quality of care.
This 2013 edition of Health at a Glance – OECD Indicators presents the most recent comparable
data on key indicators of health and health systems across the 34 OECD member countries. Where
possible, it also reports comparable data for Brazil, China, India, Indonesia, the Russian Federation,
and South Africa, as key emerging countries
Dr Dev Kambhampati | World Bank - Fish to 2030- Prospects for Fisheries and A...Dr Dev Kambhampati
This document discusses projections for the global fisheries and aquaculture sector from 2013 to 2030 using the International Model for Policy Analysis of Agricultural Commodities and Trade (IMPACT) model. It aims to improve upon previous World Bank projections from 2000 to 2020 by enhancing the IMPACT model's structure and data. The document describes updates made to the model's data inputs, parameter specifications, and regional and commodity details. It then presents baseline projections for production, consumption, trade, and fishmeal/oil to 2030, along with alternative scenarios examining faster aquaculture growth, disease outbreaks, and climate change impacts. The analysis finds that aquaculture will continue to be the main driver of supply growth to meet rising demand
This document contains a physical education exam paper with multiple choice and short answer questions testing knowledge of physical education concepts. The questions cover topics like cardiovascular fitness, benefits of exercise, healthy active lifestyles, sports injuries, fitness components, and muscle function.
This document recommends expanding federally qualified health center (FQHC) services in greater Detroit to improve access to quality healthcare. It identifies several high need areas that currently lack FQHC sites based on factors like poverty rates, uninsured populations, and health status indicators. New FQHC sites are recommended in specific zip codes to help address gaps. Expansion strategies include opening new access points, expanding medical services, and pursuing practice acquisitions or partnerships to better serve communities in greatest need. Cooperative efforts are suggested to help overcome challenges to development like capital needs.
Montana Videoconferencing Strategic Plan Final Report June 12 ...Videoguy
The Montana Videoconferencing Strategic Plan provides recommendations for the future of videoconferencing services in Montana. It recommends continuing to support current METNET services while establishing H.323 as the future standard and accelerating the transition to IP-based SummitNet II. It also suggests aggressively pursuing partnerships with other providers through a trial program with the Courts and evaluating long-term outsourcing options. Additionally, it proposes revising the METNET chargeback model and implementing stronger supplier management and marketing initiatives to increase utilization.
Evaluation of medicines_shortages_in_europe_by_birglibirgli ag
We have published our first industry report. Commissioned by the EAEPC, birgli put together an independent report on the causes of shortages of medicines in Europe with a more in depth look at France, Greece, Poland, Spain, and the United Kingdom. We would like to thank the EAEPC for commissioning the report and to everyone who contributed and provided support.
Attached is the report and in a separate post (I am unable to load the two reports on one post) the EAEPC contribution to the report. Each document represents our independent views on shortages.
Use this form to prove to those you are submitting any kind of application to that you are not eligible for Social Security. Present it only if they argue about your eligibility and ask them to rebut the pamphlet and especially the questions at the end to prove they are right.
This document contains a physical education exam with multiple choice and short answer questions covering topics like cardiovascular fitness, benefits of exercise, healthy lifestyles, nutrition, injuries, fitness and the skeletal system. It tests knowledge of these concepts and their application to examples like designing a personal exercise program.
The document summarizes a project to design a welding fixture with active positioning functions. It provides background on robotic welding, benefits over manual welding. It discusses HUST's current fixture which allows only 1 degree of freedom. The project aims to give the fixture increased versatility with 2 degrees of freedom to weld more complex parts without repositioning. Background research covered the history of robotics, benefits of automated manufacturing and welding. Current solutions were examined, including adaptive fixturing and robot controllers.
The Effect of an Ageing Population on British DietsAlexander Lewzey
This document analyzes how population aging in the UK will impact British diets through examining household food consumption and nutrient intake over the lifecycle. Using data from the Living Costs and Food Survey from 2008-2013, the author controls for cohort and time effects and estimates age curves showing the nonlinear relationship between age and food/nutrient expenditure and intake. Projections incorporating these age effects and UK population projections forecast the potential impacts of an aging population on food purchases and nutrient consumption, which could significantly affect health outcomes and healthcare costs associated with diet-related diseases.
This report summarizes the program plans and funding for each of the major acquisition programs included in the SAR and four additional programs. The Air Force’s Long Range Strike-Bomber (LRS-B), Long Range Standoff Missile (LRSO), and Ground Based Strategic Deterrent (GBSD), the future replacement for the Minuteman III, and the Navy’s Ohio-Class Replacement are not yet reported in the SAR, but enough is known about each program to construct a reasonable cost estimate. These programs are among the largest acquisition programs in DoD’s portfolio, and any discussion of major acquisitions would be incomplete without them. The programs included in this report represent 36 percent of the total acquisition budget in the FY 2016 FYDP. The remaining 64 percent of funding is used for hundreds of smaller acquisition programs not reported in the SAR or other programs too early in development to be included in the SAR.
This document provides information on correcting erroneous information returns, such as Forms W-2, 1099, and 1042, that were submitted to the IRS. It discusses why certain returns need to be corrected, the procedures for correcting returns administratively, and how to avoid penalties when submitting corrected returns. The document also addresses rebutting false information used for IRS collection or in criminal prosecution and answers frequently asked questions about correcting erroneous returns.
The report summarizes the findings of a survey of 5 segments of the US supply chain regarding counterfeit electronics from 2005-2008. It found that 39% of respondents encountered counterfeits, with incidents rising from 3,868 in 2005 to 9,356 in 2008. Weaknesses were identified in inventory management, procurement, recordkeeping, testing, and communication within and across organizations. The report provides general findings on the impacts and issues identified, and recommends best practices for organizations to curb counterfeits, such as clear guidance for personnel, detection/reporting procedures, and traceability in the supply chain.
The document reports on Charles Bwlaya Chisanga's training at the Centre for Development of Advanced Computing in India from January 17th to March 11th, 2011, where he learned about Geographic Information Systems (GIS) and remote sensing software like ArcGIS, ERDAS Imagine, and MapInfo, as well as gaining hands-on experience through practical exercises.
This document is a dissertation that examines the determinants of NHL goalies' salaries. It aims to extend previous research by considering factors related to a player's popularity in addition to on-ice performance statistics. The author argues that after the 2004-2005 NHL lockout, which increased league profitability and popularity, goalies' wages became dependent on both on-ice production and off-ice popularity measures. Using regression analysis, the paper finds that including variables related to popularity significantly improves the model's ability to explain variation in goalies' salaries compared to only using performance statistics. The document provides context on previous literature, discusses the impact of the lockout, and outlines the data and methodology used in the empirical analysis.
Recovery in Soccer Part I – Post-Match Fatigue and Time Course of RecoveryFernando Farias
This document discusses post-match fatigue in soccer players and the time course of recovery. It finds that a soccer match leads to fatigue due to dehydration, glycogen depletion, muscle damage, and mental fatigue. The magnitude of fatigue depends on intrinsic player factors and the match itself. Recovery of physical performance, cognitive function, and biochemical markers takes approximately 3 days, though individual markers may recover at different rates. Managing rehydration, glycogen restoration, and muscle damage response is important for optimal recovery when matches are spaced close together.
This document provides a detailed policy analysis and rebuttal of the U.C.C. redemption approach. It introduces some of the main proponents of redemption theories and provides a high-level summary of the redemption approach. The bulk of the document systematically rebuts common redemption arguments, citing legal authorities. It concludes that redemption theories are factually and legally invalid and warns those associated with SEDM against using redemption processes or materials.
This document discusses how individuals can defend themselves against demands from the government by asserting their right to be left alone and requiring the government to prove any claims or obligations. It argues that the only ways the government can create obligations are through common law violations that injure others or through contractual agreements. To win in court against the government, an individual must force the government to produce either an injured party or a valid contract showing the individual agreed to obligations. The document provides principles and examples for how to extract oneself from legal entanglements by requiring the government to meet its burden of proof in establishing obligations or claims against an individual.
This document discusses an individual's exclusive right to declare or establish their own civil status. It begins by noting that it is a state's duty to protect the civil status of its citizens and forbid interference by other states. It then provides definitions of civil status and discusses the main methods states use to control inhabitants by attaching obligations to property or civil statuses. Several legal authorities are cited that establish an individual's right to declare their own civil status, including international law, U.S. court cases, and constitutional provisions. The document concludes that individuals have remedies available if a government improperly changes or challenges their self-declared civil status.
The National Science and Technology Council's Task Force on Identity Management was established to assess the current state of identity management (IdM) across the U.S. government and develop a vision for the future. The Task Force found that over 3,000 federal systems currently utilize personally identifiable information (PII) in an inconsistent and duplicative manner. The Task Force proposed a new framework that includes: 1) A "network of networks" to securely manage common PII elements across agencies; 2) Strong security, privacy and auditability standards; and 3) Ubiquitous yet controlled access to verified identity data. This proposed approach aims to improve accuracy, availability, privacy and coordination of IdM across the federal government.
This document proposes concepts and technologies for counterspace operations in 2025, including space detection, anti-satellite weapons, space interdiction nets, miniaturized satellites, satellite cloaking, kinetic and directed energy weapons. It outlines offensive and defensive counterspace architectures and recommends further analysis of miniaturization, stealth, detection and targeting concepts as well as kinetic and directed energy weapons. The goal is to maintain US space superiority as space becomes increasingly vital to national security and more countries and commercial entities access space.
This document provides a summary of health indicators in OECD countries. It begins with an introduction that describes the document as the 2013 edition of Health at a Glance, which presents recent comparable data on key health indicators across 34 OECD countries. The data is drawn from contributions of national health agencies and aims to monitor health status, determinants, health workforce, health care activities, and quality of care.
This 2013 edition of Health at a Glance – OECD Indicators presents the most recent comparable
data on key indicators of health and health systems across the 34 OECD member countries. Where
possible, it also reports comparable data for Brazil, China, India, Indonesia, the Russian Federation,
and South Africa, as key emerging countries
Dr Dev Kambhampati | World Bank - Fish to 2030- Prospects for Fisheries and A...Dr Dev Kambhampati
This document discusses projections for the global fisheries and aquaculture sector from 2013 to 2030 using the International Model for Policy Analysis of Agricultural Commodities and Trade (IMPACT) model. It aims to improve upon previous World Bank projections from 2000 to 2020 by enhancing the IMPACT model's structure and data. The document describes updates made to the model's data inputs, parameter specifications, and regional and commodity details. It then presents baseline projections for production, consumption, trade, and fishmeal/oil to 2030, along with alternative scenarios examining faster aquaculture growth, disease outbreaks, and climate change impacts. The analysis finds that aquaculture will continue to be the main driver of supply growth to meet rising demand
This document contains a physical education exam paper with multiple choice and short answer questions testing knowledge of physical education concepts. The questions cover topics like cardiovascular fitness, benefits of exercise, healthy active lifestyles, sports injuries, fitness components, and muscle function.
This document recommends expanding federally qualified health center (FQHC) services in greater Detroit to improve access to quality healthcare. It identifies several high need areas that currently lack FQHC sites based on factors like poverty rates, uninsured populations, and health status indicators. New FQHC sites are recommended in specific zip codes to help address gaps. Expansion strategies include opening new access points, expanding medical services, and pursuing practice acquisitions or partnerships to better serve communities in greatest need. Cooperative efforts are suggested to help overcome challenges to development like capital needs.
Montana Videoconferencing Strategic Plan Final Report June 12 ...Videoguy
The Montana Videoconferencing Strategic Plan provides recommendations for the future of videoconferencing services in Montana. It recommends continuing to support current METNET services while establishing H.323 as the future standard and accelerating the transition to IP-based SummitNet II. It also suggests aggressively pursuing partnerships with other providers through a trial program with the Courts and evaluating long-term outsourcing options. Additionally, it proposes revising the METNET chargeback model and implementing stronger supplier management and marketing initiatives to increase utilization.
Evaluation of medicines_shortages_in_europe_by_birglibirgli ag
We have published our first industry report. Commissioned by the EAEPC, birgli put together an independent report on the causes of shortages of medicines in Europe with a more in depth look at France, Greece, Poland, Spain, and the United Kingdom. We would like to thank the EAEPC for commissioning the report and to everyone who contributed and provided support.
Attached is the report and in a separate post (I am unable to load the two reports on one post) the EAEPC contribution to the report. Each document represents our independent views on shortages.
Use this form to prove to those you are submitting any kind of application to that you are not eligible for Social Security. Present it only if they argue about your eligibility and ask them to rebut the pamphlet and especially the questions at the end to prove they are right.
This document contains a physical education exam with multiple choice and short answer questions covering topics like cardiovascular fitness, benefits of exercise, healthy lifestyles, nutrition, injuries, fitness and the skeletal system. It tests knowledge of these concepts and their application to examples like designing a personal exercise program.
The document summarizes a project to design a welding fixture with active positioning functions. It provides background on robotic welding, benefits over manual welding. It discusses HUST's current fixture which allows only 1 degree of freedom. The project aims to give the fixture increased versatility with 2 degrees of freedom to weld more complex parts without repositioning. Background research covered the history of robotics, benefits of automated manufacturing and welding. Current solutions were examined, including adaptive fixturing and robot controllers.
The Effect of an Ageing Population on British DietsAlexander Lewzey
This document analyzes how population aging in the UK will impact British diets through examining household food consumption and nutrient intake over the lifecycle. Using data from the Living Costs and Food Survey from 2008-2013, the author controls for cohort and time effects and estimates age curves showing the nonlinear relationship between age and food/nutrient expenditure and intake. Projections incorporating these age effects and UK population projections forecast the potential impacts of an aging population on food purchases and nutrient consumption, which could significantly affect health outcomes and healthcare costs associated with diet-related diseases.
This report summarizes the program plans and funding for each of the major acquisition programs included in the SAR and four additional programs. The Air Force’s Long Range Strike-Bomber (LRS-B), Long Range Standoff Missile (LRSO), and Ground Based Strategic Deterrent (GBSD), the future replacement for the Minuteman III, and the Navy’s Ohio-Class Replacement are not yet reported in the SAR, but enough is known about each program to construct a reasonable cost estimate. These programs are among the largest acquisition programs in DoD’s portfolio, and any discussion of major acquisitions would be incomplete without them. The programs included in this report represent 36 percent of the total acquisition budget in the FY 2016 FYDP. The remaining 64 percent of funding is used for hundreds of smaller acquisition programs not reported in the SAR or other programs too early in development to be included in the SAR.
This document provides information on correcting erroneous information returns, such as Forms W-2, 1099, and 1042, that were submitted to the IRS. It discusses why certain returns need to be corrected, the procedures for correcting returns administratively, and how to avoid penalties when submitting corrected returns. The document also addresses rebutting false information used for IRS collection or in criminal prosecution and answers frequently asked questions about correcting erroneous returns.
The report summarizes the findings of a survey of 5 segments of the US supply chain regarding counterfeit electronics from 2005-2008. It found that 39% of respondents encountered counterfeits, with incidents rising from 3,868 in 2005 to 9,356 in 2008. Weaknesses were identified in inventory management, procurement, recordkeeping, testing, and communication within and across organizations. The report provides general findings on the impacts and issues identified, and recommends best practices for organizations to curb counterfeits, such as clear guidance for personnel, detection/reporting procedures, and traceability in the supply chain.
The document reports on Charles Bwlaya Chisanga's training at the Centre for Development of Advanced Computing in India from January 17th to March 11th, 2011, where he learned about Geographic Information Systems (GIS) and remote sensing software like ArcGIS, ERDAS Imagine, and MapInfo, as well as gaining hands-on experience through practical exercises.
This document is a dissertation that examines the determinants of NHL goalies' salaries. It aims to extend previous research by considering factors related to a player's popularity in addition to on-ice performance statistics. The author argues that after the 2004-2005 NHL lockout, which increased league profitability and popularity, goalies' wages became dependent on both on-ice production and off-ice popularity measures. Using regression analysis, the paper finds that including variables related to popularity significantly improves the model's ability to explain variation in goalies' salaries compared to only using performance statistics. The document provides context on previous literature, discusses the impact of the lockout, and outlines the data and methodology used in the empirical analysis.
Recovery in Soccer Part I – Post-Match Fatigue and Time Course of RecoveryFernando Farias
This document discusses post-match fatigue in soccer players and the time course of recovery. It finds that a soccer match leads to fatigue due to dehydration, glycogen depletion, muscle damage, and mental fatigue. The magnitude of fatigue depends on intrinsic player factors and the match itself. Recovery of physical performance, cognitive function, and biochemical markers takes approximately 3 days, though individual markers may recover at different rates. Managing rehydration, glycogen restoration, and muscle damage response is important for optimal recovery when matches are spaced close together.
NH Sport Concussion Advisory Council Consensus statement version 2.1Andrew Cannon
This document provides guidance from the New Hampshire State Advisory Council on Sport-Related Concussion for managing concussions in school and youth sports. It defines concussion, outlines prevention strategies like proper equipment usage and rules enforcement, and describes protocols for baseline testing, recognizing concussions, ongoing assessment, and graduated return to learning and sports. Special considerations are given to pediatric athletes and the roles of various medical professionals. The Council recognizes resource variability but stresses supporting best practices to safely manage concussions.
Global Medical Cures™ | NEW YORK STATE- Percutaneous Coronary InterventionsGlobal Medical Cures™
Global Medical Cures™ | NEW YORK STATE- Percutaneous Coronary Interventions
DISCLAIMER-
Global Medical Cures™ does not offer any medical advice, diagnosis, treatment or recommendations. Only your healthcare provider/physician can offer you information and recommendations for you to decide about your healthcare choices.
Fill-us-in: Information Asymmetry, Signals and The Role of Updates in Crowdfu...CamWebby
In this empirical study, I examine the role of updates for projects listed on crowdfunding platform (CFP), Kickstarter.com. Using a novel dataset and fixed-effects (FE) regression, I corroborate existing research that updates do encourage future project support. Extant research uses this stylised fact to help support the hypothesis that funders are responding to signals of quality (Mollick, 2014). However, results from this study suggest that funders discriminate negatively on the objectivity of updates - a measure of update quality. Further analysis also reveals that updates mask a day-of-the-week effect that has been previously demonstrated (Vismara, 2018). This paper finds evidence that updates may mitigate reduced support experienced by projects on weekends. Limitations and implications to CFPs and fundraisers are also discussed.
The document evaluates football helmet testing standards and recommends including rotational acceleration testing. It analyzes different helmet testing methods, including linear drop tests, linear impact tests, and the football and hockey STAR methods. The hockey STAR method uses a pendulum to strike helmets at adjustable angles, allowing tests of both linear and rotational acceleration. The document concludes the hockey STAR method is the most realistic and versatile for testing impacts involving rotational acceleration, which are common in football and contribute significantly to brain injuries. Rotational acceleration testing should be incorporated into football helmet standards.
This document is the thesis of Jose Luis Contreras Biekert for obtaining a Doctorate in Economics. It consists of three essays in microeconomics. The first essay empirically analyzes the impact of hosting the Summer Olympic Games on a country's future performance and finds no lasting legacy for sports. The second essay develops a general equilibrium model to analyze mitigation of negative externalities through public good production and income taxes. It finds conditions for a Pareto optimal equilibrium and that eco-friendly technological changes may reduce welfare. The third essay considers coalition formation and models how it reduces rivalry in consumption, finding it can impact inequality.
В 2008 году JASON, группа научных советников Министерства обороны США, опубликовала доклад «Human Performance» (Возможности человеческого организма), в котором обсуждаются виды и способы биомедицинских усовершенствований.
Human Performance Human Performance Human PerformanceKarlos Svoboda
This document summarizes a report on the potential for adversaries to exploit advances in human performance modification and create threats to national security. It evaluates the present capabilities in areas like pharmaceutical cognitive enhancement and brain-computer interfaces, and considers how future developments could be used. Key areas discussed include the effects of sleep deprivation on military effectiveness, brain plasticity and new neuropharmaceuticals, and non-invasive and invasive brain-computer interfaces. The report provides findings and recommendations for monitoring these fields and maintaining expertise to evaluate potential threats.
The literature review summarizes previous research on the relative age effect (RAE) in the following areas:
1. The RAE refers to differences in development between players born in different quartiles of an annual age grouping, with early born players tending to be physically more mature.
2. Studies show the RAE persists from youth through professional levels, with early born players making up a larger percentage of cohorts at each stage.
3. Areas shown to be affected by the RAE include selection for talent pathways, physical development advantages, and potentially psychological traits, though research on the latter is limited.
Morgan Estimating the Risk of Brain Tumors 4-7-09Lloyd Morgan
This article reviews and analyzes published case-control studies on the risk of brain tumors from cellphone use. It finds that the industry-funded Interphone studies reported no increased risk in most cases, while the independently-funded Swedish studies led by Dr. Hardell reported numerous findings of increased brain tumor risk. The article identifies 11 flaws in the Interphone studies' design and methodology that could explain their incredulous findings. In contrast, the Swedish studies' data are consistent with an increased tumor risk from cellphone use and have fewer flaws. Given the potential for a large public health impact if a risk exists, the article argues for applying the precautionary principle and reducing cellphone radiation exposure.
This document provides a summary of the Colorado HJR07-1050 Behavioral Health Task Force Report from January 2008. It includes 11 recommendations to reform and integrate Colorado's behavioral health system. The recommendations call for establishing a leadership structure, adopting shared outcomes, aligning service areas, increasing joint budget planning and auditing across agencies, integrating policies and regulations, and promoting workforce development and consumer involvement. The report is based on research conducted by the Task Force, including stakeholder surveys and agency interviews, to assess priorities and themes within Colorado's existing behavioral health system.
To Explore Whether the Financial Impacts of the Football-Media-Sponsorship 'A...David Risebrow
This document summarizes a student's final year project on exploring whether the financial impacts of the football-media-sponsorship alliance in England only benefit Premier League clubs. The project aims to establish the main media companies in the alliance, explore if the alliance has caused financial discrepancies between the Premier League and Football League, and analyze if the FA is doing enough to help Football League clubs. It outlines the objectives, justification, and research methods to be used, which will include analyzing academic sources and secondary data on the alliance and its impacts on different levels of English football clubs.
An Empirical Investigation of The Impact of Reviews on Movie Revenues.pdfKristen Carter
This thesis investigates the impact of critics' reviews on movie revenues. It examines key factors such as production budget, genre, MPAA ratings, and critics' reviews that influence movie success. The dependent variables are total domestic gross, total foreign gross, and domestic opening weekend. Regression analysis will be used to analyze the relationship between these variables and determine the predictive power of critics' reviews on box office performance.
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1. VIOLENT STRATEGIES
AN INQUIRY INTO THE EFFECTS OF
PENALTIES IN THE NFL
____________________________________
A Thesis
Presented to the
Faculty of
California State University, Fullerton
____________________________________
In Partial Fulfillment
of the Requirements for the Degree
Master of Arts
in
Economics
____________________________________
By
Dana Shapiro
Approved by:
Dr. David Wong, Committee Chair Date
Department of Economics
Dr. Andrew Gill, Member Date
Department of Economics
Dr. Robert Mead, Member Date
Department of Economics
2. ii
ABSTRACT
The actions taken by the National Football League (NFL) to mitigate the threat of injuries to quarterbacks were constructed using an inappropriate framework. By failing to take into account the incentives of the offense, policy makers are exacerbating the problem–altering the game in such a way that increasingly violent strategies prevail as optimal. It appears both theoretically and empirically that defensive yardage penalties, assessed for fouls typically committed during passing plays, augment payoffs in such a way that the intention of decreasing injuries is offset by increased passing frequency. In contrast, offensive yardage penalties assessed for feigning illegal contact or being intentionally reckless decrease the probability of injury. Finally research and education regarding the long-term effects of injuries, which allow players to more accurately project the expected costs of violence, have the potential to reduce the probability of injury, and depend on the relative magnitudes of the players’ reactions.
3. iii
TABLE OF CONTENTS
ABSTRACT ................................................................................................................... ii
LIST OF TABLES ......................................................................................................... iv
LIST OF FIGURES ....................................................................................................... v
LIST OF EQUATIONS ................................................................................................. vi
ACKNOWLEDGMENTS ............................................................................................. vii
Chapter
1. INTRODUCTION ................................................................................................ 1
2. RELEVANT LITERATURE ................................................................................ 4
3. THEORETICAL MODEL .................................................................................... 9
Players ................................................................................................................... 10
Strategy Sets ......................................................................................................... 10
Payoffs .................................................................................................................. 11
Penalties ................................................................................................................ 13
4. EMPIRICAL MODEL .......................................................................................... 21
5. DATA ................................................................................................................... 26
6. RESULTS ............................................................................................................. 28
7. CONCLUSIONS AND CAVEATS ..................................................................... 33
REFERENCES ............................................................................................................. 38
4. iv
LIST OF TABLES
Table Page
1. Summary of the Theoretical Model ..................................................................... 20
2. Summary Statistics .............................................................................................. 27
3. Estimation of Equation 12 ................................................................................... 29
4. Estimation of Equation 13. .................................................................................. 30
5. Joint Significance F Tests for Select Dummies and Interactions. ....................... 32
5. v
LIST OF FIGURES
Figure Page
1. Summary of Game ............................................................................................... 10
6. vi
LIST OF EQUATIONS
Equation Page
1. P* Derivation of probability of a pass ............................................................... 13
2. Q* Derivation of probability of a blitz ............................................................... 13
3. Effect of changes in defensive payoff on probability of a pass .................... 13
4. Effect of changes in offensive payoff on probability of a blitz .................... 13
5. Pʀ(Injury) Probability of Injury .......................................................................... 14
6. Effect of changes in defensive yardage penalties on injury .......................... 15
7. Effect of changes in offensive yardage penalties on injury .......................... 17
8. Effect of changes in education on probability of injury ............................... 18
9. Ω Offensive reaction to education .................................................................... 18
10. Δ Defensive reaction to education .................................................................... 18
11. Effect of changes in education of probability of injury ................................ 18
12. Passoiws Empirical estimation of probability of a pass ........................................ 22
13. Sackoiws Empirical estimation of probability of a sack ........................................ 24
7. vii
ACKNOWLEDGMENTS
Indispensable to the completion of this analysis were: Dr. David Wong for his attention to eloquence, Dr. Andrew Gill and the creative process which he employs, and Dr. Robert Mead for his awareness of, and ability to account for, the countless nuances of football.
8. 1
CHAPTER 1
INTRODUCTION
The problem of players sustaining career-threatening injuries while playing professional football has become an issue of growing concern for both players and league officials. Rules such as defensive yardage penalties have been employed with the intent of protecting quarterbacks who have been deemed defenseless and thus more susceptible to injury. Often, the intentions of rules that attempt to regulate risk, such as seatbelt laws, are offset by individuals acting more carelessly, such as driving more recklessly. The questions become: are the regulations imposed by the NFL susceptible to what game theorists refer as strategic offsetting behavior due to the increased expected profitability of passing, and to what degree will this offsetting change the probability that the players in question sustain injuries.
These questions are important because a 2011 report by the NFL Players Association (NFLPA) found that players’ injuries are becoming both more frequent and more severe. In particular, the number of players on the injured reserve list increased dramatically from 250 to 350 between the 2009 and 2010 seasons. 1 In addition, the percentage of players who sustained at least one concussion rose 300% between 2006 and
1 National Football League Players Association, “Dangers of the Game,” Edgeworth Economics, accessed December 12, 2012, http://www.esquire.com/cm/esquire/data/Dangers-of-the-Game-Report- Esquire.pdf .
9. 2
2010.2 Moreover, the medical literature is beginning to show that concussions pose a far greater long-term threat than previously believed. Specifically, findings suggest that the onset of dementia-related syndromes may be initiated by repetitive cerebral concussions. 3 Further compounding the problem has been the perceived innocuousness of minor head trauma by NFL players exemplified by the decision made by Peyton Manning, then the quarterback of the Indianapolis Colts, to openly test low on baseline concussion diagnosis tests in order to be cleared to play after sustaining mild concussions. 4
Recently, the NFL made it public that it intends to discourage violent behavior in the hope of reducing its comparative negligence in lawsuits brought by players who suffer from the long-term effects of concussions. Increases in defensive yardage penalties, implemented as a means of increasing the marginal cost of risky play, are thought to impose a tax on the supply of violent behavior thus reducing the equilibrium quantity. However, this analysis fails to account for the reaction of the offense. The policies being employed by the NFL to regulate the risks of the game are being strategically offset in the same way that seatbelt laws, which attempt to reduce fatalities, cause drivers to drive less carefully and offset the intention of reducing risk. The aim of this study is to analyze the effects that the actions taken by the NFL have on the
2 National Football League Players Association, “Dangers of the Game,” Edgeworth Economics, accessed December 12, 2012, http://www.esquire.com/cm/esquire/data/Dangers-of-the-Game-Report- Esquire.pdf .
3 Kevin Guskiewicz, et al., “Association between Recurrent Concussion and Late-Life Cognitive Impairment in Retired Professional Football Players,” Neurosurgery. 57, no. 3 (2005): 719.
4 Mike Florio, “Peyton Manning Admits to Tanking Baseline Concussion Tests,” NBC Sports, last modified April 27, 2011, http://profootballtalk.nbcsports.com/2011/04/27/peyton-manning-admits-to- tanking-baseline-concussion-tests/.
10. 3
incentives of the players and how one might expect the probability of injury to change as a result. The study employs a simplified model of the game and narrows the scope of the analysis to a specific type of risky play in order to anticipate the effects that various regulations will have on the probability that the quarterback sustains an injury. Specifically, it will be shown theoretically and empirically that increased severity and enforcement of defensive yardage penalties, for fouls typically committed during passing plays, leads to an increase in the probability of injury.
11. 4
CHAPTER 2
RELEVANT LITERATURE
As mentioned above, the present analysis belongs to the subcategory of Game Theory that is concerned with the strategic offsetting of policies that are intended to regulate risk by the perverse incentives they create. This effect was first rigorously studied by Peltzman who found that following the implementation of seat belt laws increased accident frequency fully offset the effect of increased safety–resulting in no net change to the death rate associated with car accidents. 5 More recently, work has been done studying the effect of a policy instituted by the NCAA in men’s collegiate basketball which moved the three-point line further from the hoop in an attempt to spread out the defense, and thus increase two-point shooting percentage. It is hypothesized that because three-point shots are made harder, offenses tend to value them less–causing the defense to defend more against two-point shots, thus partially defeating the intention of the policy to spread out the defense. 6 This phenomenon appears in football in much the same way as in other contexts with the intent of the defensive yardage penalties, to
5 Sam Peltzman, “The Effects of Automobile Safety Regulation,” Journal of Political Economy 83, no. 4 (1975): 677.
6 Bryan McCannon, “Strategic Offsetting Behavior: Evidence From National Collegiate Athletic Association Men’s Basketball,” Contemporary Economic Policy 29, no. 4 (2011): 550.
12. 5
reduce injuries, being offset by the offense putting itself in precarious situations more often due to the increased profitability of these situations.
The problem that the NFL and its players face is similar in nature to that which all employers and employees face in hazardous occupations. However, there is a stark asymmetry between how the NFL attempts to regulate risks and how other hazardous occupations, such as boxing, attempt to regulate risks. Arguments have been advanced contending that football should be considered more of a combative sport than it has traditionally been considered. For example, Daniel Goldberg notes that the model of health delivery currently endorsed by every NFL team is ethically suboptimal. 7 Specifically, there exists a principal-agent problem between the team owners, medical staff, and the players stemming from the asymmetry between their respective utility functions. While attempting to maximize profits, owners coerce medical staff to return injured players to the game prematurely, effectively disregarding the disutility that such premature clearance will ultimately have on players. Due to this asymmetry, Goldberg argues that prevention of, and liability for, injury should be dealt with in a way similar to that of boxing with more objective return to play guidelines. This would then reduce the asymmetry between the utility of the player and the payoff to the owner by more tightly tying the profitability of players to their health.
7 Daniel Goldberg, “Concussions, Professional Sports, and Conflicts of Interest: Why the National Football League’s Current Policies are Bad for Its (Players’) Health,” HEC Forum (2008): 337.
13. 6
The decision to commit a foul that would result in a penalty can be analyzed in light of the Becker Model of Crime and Punishment. 8 In the arena of professional sports, fouls may be regarded as akin to criminal activity. Because the sanctioning bodies of professional sports saliently assign various penalties to fouls and players are able to estimate their potential gains, it follows naturally that players will allocate time between “criminal” and reputable behavior in the form of a mixed strategy of lawful and unlawful plays. Authors have used a similar line of reasoning to estimate a demand curve for physically aggressive behavior in the Barclays Premier League of soccer. By considering aggressive behavior as an input into the production of potential league points, an empirical estimation of the demand for aggression yields own price elasticities for all teams in the sample. The findings suggest that although entirely inelastic, the demand curves of the best and worst teams in terms of skill are proportionately less responsive to changes in the price of misconduct as measured by an index of consequences, with certain teams having an infinitely inelastic demand for violent play. 9
Professional sports and the myriad data they produce also lend themselves naturally to game theoretic and applied econometric analysis. Competitive games of skill can serve as analogues for other, less accessible, yet nontrivial economic phenomena. Once the immaterial has been discarded from the structure of both the sport and the phenomenon, similarities to classic game theoretic situations are often discovered. For
8 Gary Becker, “Crime and Punishment: An Economic Approach,” Journal of Political Economy 76, no. 2 (1968): 169.
9 Todd Jewell, “Estimating Demand for Aggressive Play: The Case of English Premier League Football,” International Journal of Sport Finance 4, no. 3 (2009): 192.
14. 7
example, the decisions to call a passing or a running play, given that the star quarterback has sustained an injury, has been modeled in the framework of a zero-sum matching pennies game. Findings suggest that given a decrease in the productivity of an input (in this case passing), there exist situations where the players will have no incentive to alter their strategies. 10 That is, if the second-string quarterback is as equally lacking in passing ability as he is in his capacity to capitalize on the defensive error, the players will adopt the same mixed strategies as before the injury occurred. The inadequacy of data on infrequent yet significant events typified by classic games makes it difficult to infer whether or not players actually follow mixed strategies, however it may be argued that if those who play the pass/run game adopted a mixed strategy, then similar behavior may occur in comparable circumstances that are less easily illuminated empirically.
The contributions of the present study to the existing body of literature, which uses professional sports to analyze economic phenomena, are three-fold. First, it shows that, the regulations employed by the NFL are flawed. Gaining a better perspective on the way strategic interactions evolve in response to costs and benefits of potentially injurious behavior may allow policies to be put in place that more efficiently curtail violence. Second, it shows that by understanding the way penalties affect the players in football, one may more accurately predict how the regulation of risk will affect other pseudo-zero-sum games (games where reductions in the payoff to one player amount to increases in the payoff to the other). Finally, this analysis contributes to the growing
10 Joseph McGarrity and Brian Linnen, “Pass or Run: An Empirical Test of the Matching Pennies Game Using Data from the National Football League,” Southern Economic Journal 76, no. 3 (2010): 791- 810.
15. 8
body of empirical work that seeks to expand the implications of game theoretic constructs by lending evidence in favor of the hypothesis that players follow mixed strategies.
16. 9
CHAPTER 3
THEORETICAL MODEL
The game of football as whole is far too intricate to analyze in any one all- encompassing model. The sheer magnitudes of the different strategies sets that are available to the players make a comprehensive model of the entire game impossibly complex. A solution to the game of football would be so nuanced and would require such an intimate knowledge of every possible detail that it quickly becomes unattainable. However, upon narrowing the scope of analysis and constructing a set of plausible assumptions, it becomes possible to analyze the specific situations that are relevant to the concerns that the NFL has regarding injuries to its quarterbacks.
Because the aim of the analysis is to determine how quarterbacks and defenders will respond to regulation, the theoretical model focuses on the decision that the offense faces of how frequently to pass, the decision that the defense faces of how often to defend against a pass, and how regulations will augment the payoffs of both sides in this context.
Unlike basketball and soccer, which are played in an essentially continuous fashion, football is naturally broken up into non-arbitrary, discrete time intervals, or plays. It seems natural therefore, to model each play as a separate stage game.
17. 10
Players
Let the Home and Away teams be Players 1 and 2, respectively. The team as a whole is considered one strategic decision-making unit. At any stage one player is of the type–Offense and the other Defense. Players make decisions simultaneously.
Strategy Sets
The offensive strategy set is partitioned by passing plays and running plays; kicking plays can safely be omitted due to their being strictly dominated or dominating in most stages.
The defensive strategy set is more complex. Given that the offense will attempt to advance the football by either passing or running (rushing) down the field, it can be assumed that the defense will focus on either defending against a pass or a run. One effective strategy to defend is with the use of a blitz. There are broadly three types of blitzes: pass, run, and zone. In a pass-blitz, the defense devotes more than the usual amount of defenders to targeting the quarterback, increasing pressure with the intent of tackling (sacking) the quarterback, or causing an interception or fumble. The run-blitz is designed in much the same way as the pass-blitz, but with the intent of devoting more than the usual amount of defenders to tackling a runner. The zone-blitz is different in that it seeks to cause an offensive error with the use of confusion rather than with the use of increased pressure. For the purpose of this analysis it may be instructive to partition the defensive strategy set between the pass-blitz, and other forms of defense, as the pass- blitz poses the greatest risk of injury to the quarterback. In addition to reduce confusion, a pass-blitz will henceforth be referred to simply as a blitz.
18. 11
Payoffs
Each team seeks to win a championship. The result of each game alters the probability of winning a championship. Each play changes the context of the game, and thus changes the probability of winning. Payoffs are therefore defined as the marginal change in the probability of winning a championship given: any yards gained or lost on each play, game context, which teams are playing, at what point in the season the game is taking place, etc. In other words, players are always thinking about how each action they take will change the chance that they win the championship. For example, the expected utility from attempting a pass that wins the Super Bowl is large compared to one that simply gets a first down in an otherwise uneventful blowout during the season.
Although the payoffs differ among stages, their relative magnitudes are assumed to remain constant throughout all stages. It is assumed that the offense would rather run against a blitz, and the defense would rather blitz against a pass. The game is summarized in Figure 1.
Where: A< B
C > D
E > F G < H
Figure 1. Summary of Game
Defense
Q
(1 – Q)
Blitz
Other
Offense
P
Pass
(A,E)
(C,F)
(1 – P)
Run
(B,G)
(D,H)
19. 12
The elements {A,…,H} of the bi-matrix are the payoffs to the offense and the defense from each of the four strategy combinations or states of nature. By convention the first element of the parenthetic pair in each square is the payoff to the offense, and the second is the payoff to the defense. For example, given that the offense attempts a pass while the defense attempts a blitz, the payoffs will be A and E to offense and defense, respectively.
The bold and underlined payoffs are the highest payoff that can be expected given the other players choice of action. In other words, given a blitz, the payoff to the offense from passing (A) will always be lower than that of running (B). In addition, given a pass, the payoff to the defense from a blitz (E) will be higher than other forms of defense (F).
The assumptions imply that no pure-strategy Nash equilibrium exists, i.e. no strategy is dominant in all situations. Thus, it may be assumed that the players mix their play between their respective strategies according to a probability distribution that makes their opponent indifferent between their choices, a method known as employing mixed strategies. Given this indifference, there will be no incentive for either player to alter their chosen probability distribution, and equilibrium will be reached. The mixed strategies are calculated in Equations 1 and 2, where the + and – indicate the sign of the terms below them. Subsequent equations are numbered in ascending order.
E(Blitz) = E(Other) E(Pass) = E(Run)
PE + (1 – P)G = PF + (1 – P)H QA + (1 – Q)C = QB + (1 – Q)D
PE + G – PG = PF + H – PH QA + C – QC = QB + D – QD
PE – PF – PG + PH = H – G QA – QB – QC – QD = D – C
P(E – F – G + H) = H – G Q(A – B – C + D) = D – C
20. 13
+ –
0 < P* = < 1 (1) 0 < Q* = < 1 (2)
+ + – –
where P* is the probability that the offense will pass, (1 – P*) is the probability that the offense will run, Q* is the probability that the defense will blitz, and (1 – Q*) is the probability that the defense will not blitz. Note:
+
= − < 0 (3)
+
and,
–
= − > 0 (4)
+
Equation 3 implies that decreases in the defensive payoff of the pass/blitz situation (E↓) cause the offense to pass more often (P*↑). Equation 4 implies that increases of the offensive payoff of the pass/blitz situation (A↑) cause the defense to blitz more frequently (Q*↑).
Penalties
The aim of this theoretical analysis is to determine how penalties change the probability that the quarterback sustains an injury. To do this, it must first be established how penalties change the payoffs of each player, then a link between the payoffs and the probability of injury can be formed to shed light on the consequences of specific policies.
21. 14
A typical way penalties are given is by taking yards from the team that committed a foul and awarding them to the other team in a zero-sum fashion. 11 However, since payoffs are in terms of changes in the probability of winning a championship, the yards gained and lost do not necessarily increase and decrease the payoffs symmetrically. Therefore, changes in payoffs from penalties are pseudo-zero sum in that they necessarily cause an opposing award, but not necessarily of the same magnitude. For instance, if the top ranked team were to be penalized for a foul committed against a team that is in need of a win to remain in contention, the decrease in the probability of the top ranked team winning the championship would be much smaller than the increase in the probability of the mid-level team winning the championship.
Let ϑ represent a penalty such that > 0 and < 0.
characterizes the typical defensive yardage penalty that only affects the payoffs in the pass/blitz situation, such as roughing the passer, as defenses cannot commit such a foul when the offense attempts a running play. This penalty accrues as a net loss to the defense (E↓), and a net gain to the offense (A↑).
To establish a link between the players’ strategies and injuries, let the probability that the quarterback sustains and injury be given by,
Pʀ(Injury) = ƒ(P*,Q*, X) (5)
where X is a vector of exogenous determinants of Pʀ(Injury).
11 National Football League, “Official Playing Rules.” 2012 Rule Book, http://www.nfl.com/rulebook (accessed Dec 12, 2012).
22. 15
Assume , > 0. In other words, if the offense attempts more passing plays (P*↑) or the defense attempts to blitz more frequently (Q*↑), then the probability that the quarterback will sustain an injury will increase (Pʀ(Injury) ↑) due to his exposure to situations conducive to injury.
Consider the marginal effect of a penalty, ϑ, on the probability that the quarterback sustains an injury, where the signs are indicated above each term:
+ + – – + + +
= • • + • • > 0 (6)
Note that if other factors are held constant, increases in the severity of this type of defensive penalty (ϑ↑) unambiguously increases the probability of injury (ƒ↑).
To show the merit of this conclusion, consider a stylized rule change that increases the severity of the penalty for roughing the passer from 5 to 15 yards, in a situation where the expected payoff gained from 15 yards is high, but that gained from 5 yards is low–i.e. when a first down is crucial. Due to the pseudo-zero-sum nature of the game, the increased severity of the penalty (ϑ↑) raises the expected payoff from drawing a foul (A↑), causing the offense to value passing more through , which in turn makes the defense attack the quarterback more frequently (Q*↑) through . Moreover, the penalty (ϑ↑) decreases the expected value of attempting a blitz (E↓), causing the defense to value attacking the quarterback less through , which in turn makes the offense able to pass more (P*↑) through . Since both the offense is passing more (P*↑) and the
23. 16
defense is blitzing more (Q*↑), the probability that the quarterback will get injured increases ( ↑) due to his exposure through and respectively.
Since payoffs are simply expectations, decreases in the variability of expectations act in much the same way as increases in severity. For instance, in 2005 the NCAA removed all references to the word “intent” from the definition of helmet-to-helmet contact in an effort to reduce traumatic head injuries. 12 This omission reduces the variability of attempting to draw a helmet-to-helmet foul, making plays where such fouls may be drawn more valuable to the offense. This causes a string of events similar to that described above, resulting in an increase in the likelihood that the quarterback sustains an injury.
Consider now an offensive yardage penalty.
Let Γ represent a penalty such that < 0 and > 0.
Γ characterizes the typical offensive yardage penalty that accrues as a net loss in expected utility to the offense (A↓) and as a net gain in expected utility to the defense (E↑), and typically only effects the pass/blitz situation. In addition to penalties for offensive misconduct typical to this state of nature such as holding, other types of offensive penalties exist. For example, in soccer, and more recently in basketball, the offense has been penalized for attempting to draw a foul by feigning illegal defensive contact, colloquially known as flopping. Although this exact type of conduct does not yet
12 National Collegiate Athletics Association, “A Primer on NCAA Rules for Football Safety,” Latest News, last modified October 20, 2010, http://www.ncaa.org/wps/wcm/connect/public/NCAA/Resources/Latest+News/2010+news+stories/October/A+primer+on+NCAA+rules+for+football+safety.
24. 17
exist in football, a penalty that awards yards to the defense in response to an offensive attempt to initiate contact would act in much the same way.
Consider the marginal effect of Γ on the probability that the quarterback sustains an injury.
– + – + + + –
= • • + • • < 0 (7)
The Γ penalty works in the opposite direction as the ϑ penalty. An increase in Γ decreases the expected value of attempting a pass (A↓) through , thereby making the defense necessitate the blitz less often (Q*↓) through . In addition, due to the pseudo- zero-sum nature of the game, the Γ penalty increases the expected value of attempting a blitz (E↑) through , thereby making the offense less able to attempt passing plays (P*↓) through . Since both the defense is blitzing less (Q*↓) and the offense is passing less (P*↓), the probability that the quarterback will sustain an injury decreases ( ↓) through and .
This type of offensive yardage penalty manages violent behavior by reducing the exposure of the quarterback to potentially injurious situations (P*↓), while reducing the frequency with which the defense attempts to blitz (Q*↓), thus reducing the probability of injury ( ↓).
Finally, consider how making players aware of the research being done regarding the long-term effects of the injuries in question lowers the expected payoff from plays where said injuries are most likely to occur.
25. 18
In this specific context, the research and education proposed pertains to injuries typically suffered when the offense attempts to pass and the defense attempts to blitz, such as head trauma to the linebackers and quarterbacks. The education affects the offense and the defense in the same way, by decreasing the payoff of attempting a pass and blitz respectively, but not necessarily to the same degree.
Let Ʈ represent an increased awareness by players of the long term effects of injuries such that < 0 and < 0.
Consider the marginal effect of Ʈ on the probability that the quarterback sustains an injury:
+ – – + + –
= • • + • • (8)
+ – –
Let Ω = • • > 0 (9)
+ + –
and Δ = • • < 0 (10)
Ω and Δ can broadly be interpreted as the offensive and defensive reactions to the penalty, and the effect those reactions have on the probability of injury respectively. Then,
< 0 if Ω < Δ (11)
In contrast to the defensive yardage penalty, the penalty (Ʈ↑) decreases the payoff expected by the offense from passing (A↓) through , which encourages the defense to blitz less frequently (Q*↓) through , ultimately decreasing the probability of injury
26. 19
( ↓) through . The effect of the penalty (Ʈ↑) on the offense is exactly the same as above, reducing the expected payoff for the defense (E↓) through , thus increasing the frequency of passing (P*↑) through and the probability of injury ( ↑) through .
To speculate about the magnitudes of Ω and Δ is not a simple task as each has three components that change with context of the game and the abilities each team. They are, (1) the degree to which the education reduces the payoff of the opposing team, (2) the degree to which that reduction increases passing and decreases blitzing, and (3) the degree to which the increase in passing and decrease in blitzing change with the probability of injury. For example, consider an offense that specializes in passing against a low ability defense. The change in the frequency that the offense passes in response to the change in payoff, , may be large because of their ability to capitalize by passing more. However, the change in the frequency that defense blitzes in response to the change in payoff, , may be small, because they may blitz very infrequently to begin with due to their low ability. This could result in an increase in the probability of injury because the increased passing drowns out the effect of the decreased blitzing. It is important however, to keep in mind that within this framework the defense does not reduce the frequency with which they blitz out of concern for their own players’ wellbeing, but instead do so in response to the decreased value placed on the pass by the offense.
Changing the perception of injuries, that have traditionally been considered benign in the long-term, effectively increases expected costs, thereby lowering the net
27. 20
expected payoff for both offense (A↓) and defense (E↓). A net reduction in the probability of injury ( ↓) will occur when the total effect of the penalty on the defense (Δ) is greater in magnitude than the effect on the offense (Ω).
By using a simplified model of a generic situation encountered by teams in an average football game, combined with a set of plausible assumptions, the following conclusions have been derived. First, defensive yardage penalties, assessed for fouls typically committed within the pass/blitz situation, unambiguously increase the probability that the quarterback sustains an injury. Second, offensive yardage penalties, assessed for fouls typically committed within the pass/blitz situation, unambiguously decrease the probability that the quarterback sustains an injury by decreasing the quarterback’s exposure and by reducing the probability that the defense attempts to blitz. Finally, research and education of the long term effects of concussions, that increase the marginal cost of the pass/blitz situation for both offense and defense, can decrease the probability that the quarterback sustains an injury if the way that the defense responds to the penalty outweighs the way that the offense responds, as summarized in Table 1.
Table 1. Summary of the Theoretical Model
E
P*
A
Q*
Pr(Injury)
Defensive Penalty
↓
↑
↑
↑
↑
E
P*
A
Q*
Pr(Injury)
Offensive Penalty
↑
↓
↓
↓
↓
E
P*
A
Q*
Pr(Injury)
Research and Education
↓
↑
↓
↓
↓ or ↑
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CHAPTER 4
EMPIRICAL MODEL
The primary theoretical conclusion that: defensive yaradge penalties–assessed for fouls typically commited during the pass/blitz situation–unambiguously increase the probability that the quarterback sustains an injury, hinges on the comparative statics of the mixed strategies. Specifically,
< 0 and > 0.
The first comparative static result reached in the theoretical model deals with how the offense will react to reductions in the defense’s payoffs. Specifically, < 0. Once again this implies that decreases in the payoff to the defense of a pass/blitz situation cause the offense to pass more frequently. In the theoretical model each play is modeled individually, so it follows that an emprical model designed to test the implications of the theory should be modeled at the same level. The following linear probability model of an offenseo passing on a given playi in a given weekw during a given seasons, is proposed:
29. 22
Passoiws = α + β1ln(average sacks per gameos) + β2field goal rangeoiws + β3can’t puntoiws + β4score differentialoiws + β5yards to gooiws + β6yard lineoiws+ β7quarteroiws + β8downoiws + β9defenseows + β10offenseows + β11weekows + β12biseasonos + β13offenseows*weekows + β14offenseows*biseasonos + β15weekows*biseasonos + β16offenseows*weekows*biseasonos + uoiws (12)
where uiows is assumed to be normally distributed with zero mean, and bold face parameters and variables denote vectors.
Equation 12 is an attempt to model empirically the choice faced by the offense of how frequently to pass. Since this choice is in theory dependent on the payoffs to the defense, which are in turn dependent on such things as: game context, which teams are playing, at what point in the season the game is taking place, etc., variables to account for such variation have been included in the empirical model. The score differential, the number of yards to go for a first down or touchdown, the yard line where the play begins, whether the offense is in field goal range, and whether punting is a dominated strategy have been included to account for how the game context will affect the probability that the offense attempts a pass. The average number of sacks per game for the defense in a given play, as well as a dummy for each defense have been included to account for variation due to which teams are playing. In addition dummy variables for the quarter and down have been included as passing is thought to bear some correlation to both. Offense dummies are included to account for the time invariant team characteristics. Week dummies are included to account for the point during the season at which the game is played. Dummies indicating every other season (biseason) are included to account for
30. 23
season to season variation such as rule changes. Finally, a set of interactions are included to account for the variation in team makeup and thus ability over the course of, and between seasons. This set of interactions is crucial to account for the most classic example of omitted variables, that which is due to ability.
In the empirical analysis, the parameter of interest is β1, which can be interpreted as the change in the probability that the offense will pass (P*), given a one percent increase in average number of sacks per game held by the defense against which they are attempting to pass. The main point of the analysis is to test the null hypothesis that β1 < 0. In other words, the average number of sacks per game is used as a proxy for variation in the expected payoff to the defense of a pass/blitz situation (E). It is assumed that defenses with more sacks on average will expect higher payoffs from blitzing (E↑). Therefore, β1 approximates , qualitatively. From this estimate, inferences can be made regarding what effect a penalty to the defense will have on the offensive strategy.
From the theory and our understanding of the game, a priori predictions as to the signs of select coefficients in the model can be made. Specifically, it is expected that increases in the number of yards to go for a first down or touch down, and positive score differentials will increase the probability of a pass on any given play. In addition it is expected that situations where punting is dominated would increase the likelihood of passing, while situations where attempting a field goal dominates would lead to decreases in the probability of passing. For the other parameters in this model, no a priori predictions are made.
31. 24
The second comparative static result reached by the theory is that > 0. Once again this implies that increases in the payoff to the offense of the pass/blitz situation cause the defense to blitz more. Following a similar line of reasoning, the following linear probability model of a defensed sacking the quarterback on a given playi in a given weekw during a given seasons is proposed to test this conclusion:
Sackoiws = α + λ1ln(average team incompletionsos) + λ2field goal rangeoiws + λ3can’t puntoiws + λ4score differentialoiws + λ5yards to gooiws + λ 6yardlineoiws + λ7quarteroiws + λ 8downoiws + λ9offenseows + λ10defenseows + λ11weekows + λ12biseasonos + λ13defenseows*weekows + λ14defenseows*biseasonos + λ15weekows*biseasonos + λ16defenseows*weekows*biseasonos + uoiws (13)
where uoiws is assumed to be standard normal and bold face denote vectors.
Equation 13 is an attempt to model the choice faced by the defense of how frequently to defend against a pass. Since this choice is in theory dependent on the payoffs to the offense, which are in turn dependent on such things as: game context, which teams are playing, at what point in the season the game is taking place, etc., variables to account for such variation have been included in the empirical model. Again, the score differential, the number of yards to go for a first down or touchdown, the yard line where the play begins, whether the offense is in field goal range, and whether punting is a dominated strategy have been included to account for how the game. The average number of team incompletions per game for the offense in a given play, as well as a dummy for each offense have been included to account for variation due to which teams are playing. Once again, week dummies are included to account for the point
32. 25
during the season at which the game is played, and the biseason dummies are included to account for season to season variation, and defense dummies are included to account for time invariant team characteristics. In addition a similar set of interactions are included to account for the time varying ability of the defense over time.
Here, the parameter of interest is λ1, which may be interpreted as the effect that an increase of one incompletion per game on average of the offense will have on the probability that the defense accomplishes a sack of the quarterback. The main point of this analysis is to test the null hypothesis that -λ1 > 0. In other words, fewer incompletions are assumed to be indicative of less ineptitude on the part of the offense, causing them to expect higher payoffs from the pass/blitz situation (A↑) due to their increased ability to survive a blitz. If it can be assumed that more sacks are indicative of more attempts to sack (Q*), then, since incompletions proxy decreases in expected payoff (A↓), - λ1 can be used to approximate qualitatively. From this estimate, inferences can be made regarding the effect of a defensive penalty on the defensive strategy. Other than this prediction, no other a priori predictions are made about the parameters.
33. 26
CHAPTER 5
DATA
Play-by-play data from the 2003-2010 regular seasons have been compiled by a team of statisticians and football enthusiasts headed by Brain Burke, founder of Advanced NFL Stats - a website dedicated to analysis of the NFL and vetted by the community of analysts. 13 Each observation includes the following: a unique game identification; the quarter, minute, and second at the start of the play; the teams on offense and defense; the down, line of scrimmage (ydline), and how many yards to go for either a first down or touchdown (togo); the season; the scores of the offense and the defense; and a description of the play. The score differential (diff) is generated by taking the difference between the scores of the defense and offense, with a positive value indicating that the offense is losing. Dummy variables for an attempted pass (pass) or a sack (sack) are set equal to one if somewhere within the description variable the word “pass” or “sack”, respectively, appear. A dummy indicating if the offense is within field goal range (fgrange) is equal to one if it is fourth down and ydline is less than 50. A dummy indicating that the offense can expect little to no value from punting (cantpunt) is equal to one if the play occurs in the last minute of the fourth quarter, it is fourth down,
13 Brian Burke, “Play-by-Play Data,” Advanced NFL Stats, last modified June 6, 2010, http://www.advancednflstats.com/2010/04/play-by-play-data.html.
34. 27
and the score differential is positive. In addition, dummy variables indicating the offense, defense, quarter, down, week and every other season (biseason) were created.
Finally, average team statistics were gathered from Team Rankings, a website composed of various sports data. 14 In particular, average team incompletions (avtminc) and average sacks per game (avskpgm) were collected at the season level, and appended to the dataset. Table 2 provides summary statistics for select variables
Table 2. Summary Statistics
Variable
Observations
Mean
St. Dev.
Min
Max
Natural log of average sacks per game of the defense
310083
0.752
0.237
0.51
1.31
Average team incompletions of the offense
310083
12.92
1.98
0
17.7
Score differential (defense - offense)
310083
0.7
10.67
-59
59
Yards to go for a first or touch down
310083
7.77
4.59
0
90
Yard line
310083
48.92
25.51
0
100
Pass (binary)
310083
0.422
0
1
Sack (binary)
310083
0.028
0
1
4th Down on the 50 yardline or closer (binary)
310083
0.02
0
1
4th Down in 4th quarter with less than a minute left (binary)
310083
0.002
0
1
14 Team Rankings, “Team Stats,” NFL Stats, last modified February 2, 2013, http://www.teamrankings.com/nfl/stats
35. 28
CHAPTER 6
RESULTS
The empirical model seeks to test the validity of the conclusion that defensive yardage penalties, assesed for fouls typically committed in a pass/blitz situation (which amount to A↑ and E↓), tend to increase the probability that quarterbacks will sustain injuries. Equation 6 states mathematically the above hypothesis:
+ – – + + +
= • • + • • > 0
hinges on the two intermediate conclusions: (1) that decreases in the payoff to the defense of the pass/blitz situation (E) increase the probability that the offense passes (P*), or < 0; and (2) that increases in the payoff to the offense of the pass/blitz situation (A) increase the probability that the defense attempts a blitz (Q*), or > 0.
Equation 12 seeks to estimate the change in the probability that the offense attempts a pass (P*) given a one percent increase in the average number of sacks of the defense against whom they are playing. Table 3 presents the results of the estimation of Equation 12, with standard errors clustered by offense.
Table 3 shows that holding week, season, defense, and game context constant, the natural log of the average number of sacks held by the defense has a statistically
36. 29
significant negative effect on the probability that the offense attmepts a pass (P*). This supports the conclusion that < 0 because the ineptitude indicated by fewer sacks
Table 3. Estimation of the Probability of Pass
Independent Variables
Coefficient
P Value
Natural log of average sacks per game of the defense
-0.0295
0.001
4th Down on the 50 yardline or closer
-0.0756
0.000
4th Down in 4th quarter less than a minute and diff > 0
0.5551
0.000
Score differential (defense - offense)
0.0080
0.000
Yards to go for a first or a touch down
0.0129
0.000
Yardline
0.0003
0.000
This supports the conclusion that < 0 because the ineptitude indicated by fewer sacks on average reduces the expected payoff to defense in a similar way to that of a defensive yardage penalty, and causes the offense to pass more. Therefore, one may infer that the defensive yardage penalties would elicit similar behavior, and cause a marginal increase in the probability that the quarterback sustains an injury through his increased exposure, thereby offsetting to some extent the intention of the policy to reduce injuries.
In addition Table 3 shows that being within field goal range on a fourth down decreases the probility of passing. It can also be seen that situations where a punt is a dominated strategy (4th down at the end of the fourth quarter and trailing in points) increase the probability of passing. Finally, in line with a priori expectation, the greater the number of yards to go for a first or touch down, the greater the probability that the offense will pass.
Equation 13 seeks to test the less inuitive portion of the theory, that increases in the offensive payoff in a pass/blitz situtation similar to that of a defensive yardage
37. 30
penalty, cause the defense to blitz more often. Specifically it estimates the effect that an increase of one team incompletion per game on average has on the probability that the defenses sacks the quarterback. The results are presented in Table 4, with standard errors clustered by defense.
Table 4. Estimation of Probability of Sack
Independent Variables
Coefficient
P Value
Average team incompletions of the offense
-4.2 x 10-4
0.30
4th Down on the 50 yardline or closer
0.0110
0.00
4th Down in 4th quarter with less than a minute and diff > 0
0.0362
0.09
Score differential (defense - offense)
5.5 x 10-4
0.00
Yards to go for a first or a touch down
0.0014
0.00
Yardline
5.6 x 10-5
0.00
Table 4 shows that the average number of incompletions of the offense has no statiscally significant effect on the frequency that the quarterback gets sacked that. If it can be assumed that sacks are indicative of blitzes, then since the high quality of a team with low incompletions raises the expected payoff to the offense of attempting a pass in a similar manner as a defensive yardage penalty, it may be inferred that such penalties would have no effect on the number of sacks as well, and therefore no effect on the number of blitzes, or that
= 0.
Recall the expression for Equation 6 is,
+ – – + + +
= • • + • • > 0
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if we can assume that the more often the offense chooses to pass, the more often quarterbacks will get injured, then it has been shown empirically that decreases in the expected defensive payoff of a pass/blitz situation similar to those created by a defensive yardage penalty raise the probability that the offense will pass, thus increasing the marginal probability that the quarterback will sustain an injury. In addition, if we can assume that the more often defenses choose to blitz, the more often they will get a sack, then it has been shown empirically that variation in the expected offensive payoff of a pass/blitz situation similar to that created by a defensive yardage penalty has no effect on the marginal probability that the quarterback sustains an injury. It should be noted that, although the defense does not contribute to the problem by blitzing more frequently, the probability of injury still increases due to the actions of the offense.
To test whether the interaction terms are necessary in the two preceding estimations, joint significance tests were performed on the team, week, and season dummies, and all of the interactions. The results of these tests are presented in Table 5, and lend overwhelming evidence for their inclusion in the model.
First, the joint significance of the offense and defense in the pass and sack models respectively suggests that team specific fixed effects are important. In other words, there exists some time-invariant heterogeneity between teams that significantly affects both
39. 32
Table 5. Joint Significance F Tests for Select Dummies and Interactions
Pass
Significance
Sack
Significance
Offense
0.000
Defense
0.000
Week
0.000
Week
0.000
Biseason
0.000
Biseason
0.000
Offense*Week
0.000
Defense*Week
0.000
Week*Biseason
0.000
Week*Biseason
0.000
Offense*Biseason
0.000
Defense*Biseason
0.000
Offense*Week*Biseason
0.000
Defense*Week*Biseason
0.000
passing and sacking. In addition the week and biseason variables have been shown to be jointly significant. This suggests that the point during the season (earlier or later) and the season play a significant role in both passing and sacking. Also, all the interactions in both models exhibit joint significance. This suggests that the changing make up of the team over the course of, and between seasons plays a role in passing and sacking repsectively. Finally the joint significance of the triple interactions imply that the match up between two teams, which two teams are playing against each other, is an important factor to include in the model.
40. 33
CHAPTER 7
CONCLUSIONS AND CAVEATS
It has become apparent that the argument regarding what actions should be taken by the NFL to reduce the number of injuries suffered by its players is being conducted within an inappropriate framework. By failing to account for the perverse incentives that defensive yardage penalties assessed for violence create, policies are being employed that act in the exact opposite direction to that intended.
Defensive yardage penalties for fouls typically committed while defending against a pass, are intended to curb injury, and are designed to decrease the payoff that the defense expects from blitzing. Theoretically, offenses will capitalize on this by increasing the frequency with which they pass and by doing so, increase the probability that quarterbacks sustain injuries, thus offsetting the intention of the policy. In addition, due to the pseudo-zero-sum nature of the game, these penalties increase the payoff that the offense expects from passing. Theoretically, defenses will react to this by increasing the frequency with which they blitz, and by doing so, increase the probability that quarterbacks sustain injuries, further offsetting the intention of the policy.
Alternatively, offensive yardage penalties, that decrease the expected value of passing, which have typically not been implemented to protect quarterbacks from injury, do just that. In theory, defenses will react to the decreased value placed passing by the offense by decreasing the frequency with which they blitz, while offenses will react to the
41. 34
increased valuation place on the blitzing by decreasing the frequency with which they pass. Since both players are engaging in potentially injurious behavior less frequently, the probability that the quarterback sustains an injury is reduced. Although this result is appealing, it must be noted that it pushes the game to be more one dimensional, centered on running plays, a far less exciting game to watch.
On the other hand, research and education, regarding the unknown effects of injuries typically sustained in the pass/blitz situation effectively raise costs for both players. Theoretically, offenses will capitalize on this in the same way as a defensive yardage penalty by increasing the frequency with which they pass, thus increasing the probability that the quarterback sustains an injury. Defenses however, will react to the decreased value placed on passing by the offense by reducing the frequency with which they blitz, thus reducing the probability that the quarterback sustains an injury. If the total effect of the increased awareness of the defense (the degree to which the education augments the payoff to the offense, how that changes the frequency of blitzing, and how it all taken together reduces the probability of injury) outweighs the total effect of the increased awareness of the offense (the degree to which the education augments the payoff to the defense, how that changes the frequency of passing, and how it all taken together increases the probability of injury), there will be a net reduction in the probability that quarterbacks sustain injuries.
Empirically, it has been show that there is a statistically significant negative relationship between the probability that the offense will pass and the relative sacking ability of the defense against whom they are playing. Since relative sacking ability changes the expected value of a blitz in a similar way as the possibility of a defensive
42. 35
yardage penalty, it may be reasonable to expect that offenses will react to changes in penalties similarly to how they react to changes in sacking ability. Additionally, the data show that the probability that the defense will sack the quarterback is unaffected by the average number incompletions of the offense. Since average incompletions changes the expected value of a pass in a similar way as the possibility of a defensive yardage penalty, it may be reasonable to expect that defenses will react to changes in penalties similarly to how they react to changes in the ineptitude of the offense.
In total, even though the defensive reaction to the change in offensive payoff, , has been shown to be nearly zero, if it can be assumed that by passing more frequently the quarterback is more prone to injury, then the empirical evidence supports the hypothesis that the offenses are offsetting the intention of the policy to reduce injuries by passing more frequently. In other words, in the absence of a defensive reaction, the probability of injury still increases due solely to the choice made by the offense to pass more often.
Since the coefficients of both empirical models were estimated using a linear probability model, and such models do not allow the probabilities in question to be nonlinear functions of the independent variables, it may be unwise to use them to make quantitative predictions, since both models fail to account for nonlinearities such as diminishing marginal returns. Moreover, the use of a linear probability model poses problems because the values that the dependent variables (pass and sack) can take are limited to the interval [0,1], thus predictions outside this interval make no sense. Since the dependent variables in Equations 12 and 13 are not limited to this interval, the above models may result in such erroneous predictions. Although the use of probit estimation
43. 36
may be more appropriate to predict marginal effects in a limited dependent variable model, given the nature of the question (to sign coefficients), using a linear probability model adequately answers this question.
Another caveat to the empirical estimation of Equation 13 is that regarding the asymmetry between the value of losses and gains. Since average team incompletions proxy ineptitude which amounts to a net decrease in expected utility of a pass (A↓), and the theory deals with an increase in expected utility of a pass (A↑), quantitative approximations may be misleading. In other words, the players may react more dramatically to decreases in their expected payoff than they do to increases. It is however, not the intention of this analysis to make quantitative predictions regarding the effect of penalties, but to show that they are working in the wrong direction. The qualitative conclusions derived from the theory and shown in the empirics can be expected to be consistent in the face of diminishing return and the asymmetry of the value function.
In addition, it must be noted that educating players about the long term effects of their choices to engage in potentially injurious activity changes the present value of certain costs as they will not come to light for many years. It is therefore worthwhile to note that such awareness has the potential to change not only perceived cost, but also players’ discount rates, and the time frame that the consequences will manifest within. For example, game situations create very high discount rates, but by making players aware that concussions pose a higher long term threat than previously believed, players may weigh such costs more heavily in the decision making process, effectively lowering their discount rates. Moreover, the discovery that such costs may be felt sooner in the
44. 37
long term than previously believed may decrease the number of periods that players discount such costs back. It must be noted however, that the qualitative conclusions derived in the theory are robust to this deconstruction of the cost function, and the reader is urged to perform the comparative statics for themselves, for they are beyond the scope of the present analysis.
To conclude, football is an inherently violent game. If violence is considered to be an economic good, efficient allocations are possible given the right market conditions. Attempts to regulate risk, however, which distort the incentives of the players, only lead to inefficiency. A wider understanding of the long-term effects of concussions and other injuries can in theory reduce the frequency of injury while not materially altering the game. Further lines of research may include the effect that such education will have on the demand for quality medical diagnoses by players in the NFL. An increased awareness of costs will presumably make more apparent the principal-agent problem stemming from a doctor who is paid by an owner and not the player. In other words, it is plausible that encouraging players to employ their own medical staff may also decrease the probability that players will allow themselves and others to be put in situations conducive to injury.
45. 38
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