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Brewers Regression ECN


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Constructed an econometrics model for the Milwaukee Brewers Demand in the 2010 regular season

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Brewers Regression ECN

  1. 1. The Milwaukee Brewers<br />Regression Analysis of 2010 Season<br />Performed By:<br />Adam Benson & Tecwyn Roberts Analysis Corp. LLC<br />Executive Summary:The Milwaukee Brewers are a Major League Baseball team located in Milwaukee, Wisconsin. The Brewers have seen a very faithful crowd throughout the years; however, during a single year this crowd shows many inconsistencies. As a result, an econometric model was constructed to estimate the various determinants of Milwaukee Brewers attendance at Miller Park in the 2010 regular season.Previous statistics and literature for MLB demand was found and was useful in this econometric study. Statistics and factors collected that provided useful for this study included: time of day the game was played (day vs evening as well as weekday vs weekend), whether or not the opponent made the postseason the previous year, Brewers games behind the division leader, whether or not there was a promotion run a certain day, opponent percentage record, and whether or not Wisconsin schools where let out for summer break. These variables all were expected to have a significant positive impact on the attendance at Miller Park except Brewers games behind division leader and opponent record.Upon specifying the model, estimations of all variables were correct except evening games and days when there was a promotion both had negative impacts on attendance. We believe this is because the length of evening games might deter those who have to work the next day. To reason for the decrease in attendance during a promotion can be equated to the Brewers already running an econometrics model and promoting on days they feel attendance would be lower. Significant observations recorded in this study include:<br />Games played in Fridays, Saturdays and Sundays experienced an  impact of 5,632 people compared to games played on Monday—Thursday.<br />When Wisconsin public schools are out of session for the summer there is a positive impact of 1,457 people at Miller Park.<br />As the Milwaukee Brewers fell back in the division they lost 184 fans per game they fell behind. The Brewers in the future must look at the revenue lost from these fans and compare that to the cost of acquiring talented players or resigning existing talent to be closer to the top of the division and thusly having more fans attend the game.<br />In the future the Milwaukee Brewers must look at these variables as well as find more significant variables to enact a pricing strategy that would maximize profits and fill Miller Park to full attendance. The Brewers must also look at their current promotions and determine if each is actually successful in accomplishing their end goal of gaining attendance. By having a better understanding of the demand for each game the Brewers can have a better strategy to maximize profits and attendance.<br />Introduction:<br />The Milwaukee Brewers are a significant part of the culture in and around the Milwaukee area. The Brewers are one of two major professional sports in Milwaukee, the other being the National Basketball Association’s (NBA) Milwaukee Bucks. These major professional sports along with the college sports in Milwaukee fuel many businesses in the Milwaukee area. Because the Brewers play mostly during the summer months, both when the NBA and colleges are out of session, the Brewers home games draw many people into the Milwaukee area. The fact that the Milwaukee Brewers are the main attraction in Milwaukee during the MLB season has lead them to record the 11th best attendance in the 2010 season with an average of 34,278 people at each game. Having such a high attendance rate is a very positive things for the Brewers; however, full capacity at Miller Park is 41,900 people so there is improvements that can be made ( 2010). <br />While the attendance for Miller Park is one of the highest in the MLB, game attendance from day to day widely varies and there was only 6 out of 81 recorded sell outs. Below is a graph showing game to game attendance for the 2010 attendance at Miller Park.<br />Review of Literature:<br />Demand for professional sports has been a widely reviewed topic and econometrics models are created frequently for specific teams. HG Demmert is recognized by most as the founder of demand models for sports attendance (Demmert 1973).<br />More closely related to our project however, was a model of more significance. Hall, Madura and Zuber created a short-run demand model in 1977 of the entire MLB(Hill ). They collected data on all the 2013 games in the 1977 regular season and sorted determined variables from four major areas: Location, Expected Quality Variable, Time Variables and Special Conditions Variables. We used their results and formulated variable that meet these variable excluded the location variables due to the nature of our project. <br />The Milwaukee Brewers must also make an econometrics model showing demand for tickets at Miller Park however they do not make this public for many reasons. One can see the actions taken by management after reviewing their econometrics model from the pricing change in certain marquee games as well as promotions they run during certain times. <br />Based on our review of these literatures we found it imperative that we include variables that encompass expected quality, time, and special conditions variables.<br />Expectations<br />Listed below are the variables, as well as their abbreviations, we are considering for our analysis and the impact we expect them to have on the attendance to Milwaukee Brewers home games.<br />Independent VariableExpected Sign<br />Promotion (PROM)+<br />Weekend (WKND)+<br />Home Record Percentage (HREC)+<br />Home Pitcher Wins Minus Loses (HPWML)+<br />Opponent Record Percentage (OREC)+<br />Opponent Pitcher Wins Minus Loses (APWML)+<br />Marquee Games (MQ)+<br />Evening (EVN)+<br />Conference (CON01)+<br />Home Team Games Behind Division Leader (HGBL)-<br />Visitor Team Games Behind Division Leader (VGBL)-<br />Bobble Head (BBL)+<br />Opponent Previous Year Post Season (OPPS)+<br />Opening Day (OD)+<br />Public School Out for Summer (NOSCHOOL)+<br />Variables<br />Attendance (ATT): Our dependent variable. That is the variable we have used to show the attendance at all Miller Park home games for the 2010 season. Since this is the dependent variable, it is known and we will use this to determine the coefficients for each independent variable.<br />Promotional games (PROM): This is a dummy variable, either a 1 or 0 value, for games with special promotions. A game that does not have a special promotion would be represented by a 0 in our model and any game with promotions would have a rating of 1. We would expect a positive value for this coefficient because the promotions should bring more people into the game than would have come without the promotion.<br />Games Played on the Weekend (WKND): This variable signifies if the game was played on a weekend. Weekends consist of any game played on a Friday, Saturday, or Sunday. This variable is also a dummy variable, so for any game on a weekday a 0 would be entered into the equation and any weekend game would have a 1. We would expect this variable to be positive because people tend to have more free time on the weekends to be able to attend events, like sports.<br />Home Team Record (HREC): Also known as winning percentage. This variable is found by dividing the number of wins the home team, the Milwaukee Brewers, had by the total number of games before the start of the selected home game. This number will always be between 0 and 1. We would expect this to have a positive correlation because we would expect more people to want to watch the Brewers when they are doing better versus when they are not.<br />Opponent Record (OREC): This variable is the opponent or visiting team record in terms of winning percentage. To find this percentage we divided the number of wins the visiting team had coming into the game by the total number of games they had finished to that point in the season. This number will also be between 0 and 1. We expect this to have a positive correlation because we would expect a better opponent to bring in larger crowds.<br />National League Games (NL): Games played against other teams in the National League. We would expect these to be positively correlated because these are the teams they are competing for the trip to the world series with. For this we used a dummy variable, where the games that were against other teams in the National League we gave them a value of 1, otherwise they were 0.<br />Specific Bobble-head Promotional Games (BBL): This is a variable for any game when a bobble-head was handed out at the game. It is a separate promotional tool that is used less frequently than other promotions and we felt it might be more significant than the normal promotions. We expected this to have a positive correlation there are fans who collect the bobble-heads.<br />Visiting Team Games Behind Division Leader (VGBL): this variable measures how far the visiting team is behind the division leader or how far ahead of the closest team they were. We expect this to have a negative correlation because fans want to see a better game between better opponents.<br />Opening Day (OD): This dummy variable is equal to 1 at only the opening day at Miller Park. All other games are a 0. Opening day has the highest attendance of all games played in 2010, so we thought it would be wise to account for that in our equation. We expect this to have a positive correlation because there are many people who want to attend opening day.<br />Division Games (CON01): This variable is a 1 when the Brewers play another National League Central Division Team (the Astros, the Cardinals, the Pirates, the Cubs, and the Reds). This is a dummy variable where the variable is 1 for all games between division teams, and a 0 for all non division teams. We expect a positive correlation because these are the teams they are competing with the closest for a spot in the post season.<br />Home Team Games behind Division Leader (HGBL): This variable measures how far behind the division leader or how far ahead of the closest team they were. We expect this to have a negative correlation because the further back they get from the leader, the less likely the chances the team is playing well enough to move into the post season.<br />Marquee Games (MQ): These are usually played between rival teams and due to the rivalry between these two teams these are the only games of the season with a higher ticket price. This variable is a dummy variable, so when playing a marquee game our variable is equal to 1, all others are 0. We expect these to have a positive correlation because these games are more popular.<br />Opponent in the 2009 Post Season (OPPS): This is a dummy variable to show when the Brewers played a team that went to the post season in the 2009 season. It is shown with either a 1 for played in the post season, or 0 if they didn't. We expect this to be positively correlated because these are the teams who fans would expect to be doing better because of their success in the previous year.<br />Away Pitcher Wins minus Losses (APWML): To find this number we subtracted the number of losses from the number of wins for the away teams starting pitcher before the start of the game. For this we expected a positive correlation because fans want to see better pitching.<br />Evening games starting after 6:00pm Central Time (EVE): This is a dummy variable that is equal to 1 for any game starting after 6pm, and 0 for any other time. We expect this to have a positive correlation because we thought people would have a greater opportunity to go to the evening games opposed to going to an afternoon game.<br />Public Schools Out For Summer (NOSCHOOL): A dummy variable used to show when public schools are out of session. When public schools are in session value is 0, when kids are out of school it is 1. We expect this to have a positive correlation because we think more parents will want to go to a Brewers game when they can take their kids with them.<br />Home Pitcher Wins minus Losses (HPWML): For this variable we subtracted the number of losses from the number of wins for the home teams starting pitcher before the start of the game. We expect these to have a positive affect because fans are going to want to watch the better pitchers and also would want their team to win.<br />Theoretical Equation<br />ATT = C + β1(PROM) + β2(WKND) + β3(HPWML) + β4(HREC) + β5(OREC) + β6(APWML) + β7(MQ) + β8(CON01) + β9(OD) – β10(HGBL) – β11(VGBL) + β12(OPPS) + β13(BBL) + β14(EVE) + β15(SCHOL) + β16(NL)<br />Possible Violations<br />There are a few possible violations in our model while using all of our data. Division games are also games played within the National League which could lead to covariance. Another possible violation is the fact that a Bobble-head is a promotional product, it is simply a specified promotion and could also be covariance. We could also see some correlation between the home team record and the home pitcher record, and the same for the visiting team.<br />Results<br />ATT = 40,054.77 – 2,541.917(EVE) + 5,626.913(WKND) + 4,935.077(OPPS) – 358.0912(HGBL) – 2,836.386(PROM) - 8,362.085(OREC) + 2,532.826(NOSCHOOL)<br />Dependent Variable: ATTMethod: Least SquaresDate: 04/21/11 Time: 19:03Sample: 1 81Included observations: 81VariableCoefficientStd. Errort-StatisticProb.  C40054.772276.74417.593010.0000EVE-2541.917844.1586-3.0111840.0036WKND5626.913853.73906.5909050.0000OPPS4935.0771118.3464.4128360.0000HGBL-358.0912153.7336-2.3292970.0226PROM-2836.3861149.985-2.4664550.0160OREC-8362.0853717.519-2.2493730.0275NOSCHOOL2532.8261359.6391.8628660.0665R-squared0.511114    Mean dependent var34278.16Adjusted R-squared0.464235    S.D. dependent var4855.008S.E. of regression3553.671    Akaike info criterion19.28289Sum squared resid9.22E+08    Schwarz criterion19.51938Log likelihood-772.9571    Hannan-Quinn criter.19.37777F-statistic10.90273    Durbin-Watson stat2.225440Prob(F-statistic)0.000000<br />Interpretation<br />In our model, we have eliminated the variables with probability above 10%. In doing so, we have found that the most statistically relevant variables are: Weekend Games, Evening Games, if the opponent went to the post season in 2009, how many games the Brewers were behind the division leader, the opponents record, whether there was a promotion at the game, and if kids were off of school for the summer. We can also tell there is some missing data that could be considered highly significant since our r2 and adjusted r2 are both below .55, suggesting we are only accounting for 55% of the data needed to perfectly calculate and account for the attendance. We also have a .05 gap between our r2 and adjusted r2 which can be explained by our number of variables (too many) and lack of at least 40% of the information required to more accurately predict attendance.<br />Forecasting<br />Ex-Ante Forecast:<br />Given the scenario of a normal day game when kids our out of school on the weekend against a team that did not go to the post season the year before but has a perfect .5 winning percentage when they are 3 games behind the division leader with a promotion we would use the following equation to find that the attendance is projected to be 40,122.8069.<br />ATT = 40,054.77 – 2,541.917(0) + 5,626.913(1) + 4,935.077(0) – 358.0912(3) – 2,836.386(1) – 8,362.085(.5) + 2,532.826(1)<br />Given the scenario of an evening game during the week against a team that went to the postseason the year before and currently has a .72 winning percentage with a lead of 2 games on the division, no promotion and kids still in school we would have a projected attendance of 37,143.41 with the following equation:<br />ATT = 40,054.77 – 2,541.917(1) + 5,626.913(0) + 4,935.077(1) – 358.0912(-2) – 2,836.386(0) – 8,362.085(.72) + 2,532.826(0)<br />Variables Not Accounted For In Final Model<br />One major variable not accounted for in this model is weather. Historical weather data does cost money to obtain, and we were not given the resources to have that information available to us. We would have used a dummy variable of 1 when there was bad weather and would have expected a negative correlation because we would expect less people to go to a baseball game when there is bad weather.<br />Another major variable only taken partly into consideration is that of ticket price. Since we used only one season, the price remained constant except for marquee games, which we accounted for.<br />One other variable we could have included in our model was the season. Having a different dummy variable for each season may have helped a little bit, but we saw it as interfering with the NOSCHOOL variable.<br />Another factor often taken into account, but left out in our model, is the unemployment rate of the surrounding area. We have made the assumption that this number, as it is possible to record, remained constant over the course of our test.<br />Other factors that were removed in the final analysis because of statistical insignificance and multi-coliniarity include: Home Team Record, National League Games, Bobble-head Promotional Games,Visiting Team Games Behind Division Leader, Opening Day, Divisional Games, Marquee Games, Away Pitcher Wins minus Losses, and Home Pitcher Wins minus Losses. When these variables were removed we were left with the most statistically relevant variables to attendance.<br />Conclusion<br />The best thing that can happen for Brewers attendance would be for them to be leading the division, playing against an opponent that went to the post season but has a bad record this year on a weekend afternoon when kids are out of school and no promotion at the game. While we found that promotional games negatively affected the attendance, it can be assumed that without the promotions attendance would be down further than what our model predicts. Also, looking at the model logically we can assume that the best games are games that the Brewers are likely to win on a warm sunny day when kids are out of school and people are off work for the weekend.<br />Works Cited<br />Demmert, H. G. (1973). The economics of professional team sports. Lexington,MA:Lexington Books.<br />Hill, James, Jeff Madura, and Richard Zuber. "The short run demand for major league baseball." Atlantic Economic Journal. 10.2 (1982): 31-35. Print.<br />"Milwaukee Brewers." Yahoo Sports . Yahoo, 2010. Web. 26 Feb 2011. <>.<br />"MLB Attendance Report - 2010." N.p., 2010. Web. 26 Feb 2011. <>.<br />"2010 Milwaukee Brewers." Baseball Reference. Baseball Reference, 2010. Web. 26 Feb 2011. <>.<br />