This document discusses advanced baseball statistics that can be calculated using MongoDB's aggregation pipeline. It provides examples of how to calculate statistics like batting average, on-base percentage, runs created, weighted on-base average, and wins above replacement using the aggregation stages of $match, $project, $group, $sort, and $limit. It also discusses where to find more information on baseball statistics and factors used in calculations.

1. David Hoerster
2014

2.  C# MVP (Since April 2011)
 Sr. Director of Web Solutions at RGP
 Conference Director for Pittsburgh TechFest
 Co-Founder of BrainCredits (braincredits.com)
 Past President of Pittsburgh .NET Users Group and organizer of recent
Pittsburgh Code Camps and other Tech Events
 Twitter - @DavidHoerster
 Blog – http://geekswithblogs.net/DavidHoerster
 Email – david@agileways.com

3. +

4.  Basic understanding of document databases, like Mongo
 Familiarity of querying (non-aggregate pipeline) in Mongo
 General understanding of baseball

5.  Basics of AVG, OBP, ERA have been around
 Underground of advanced statistics been growing since early 70s
 Bill James is probably most well known
 Society for American Baseball Research (SABR)
 Fosters the research of baseball statistical history
 Stats like wOBA, wRAA, WAR, DIPS, NERD and more
 Lends itself to computer modeling and big data

6.  Document database
 A “NoSQL” solution
 Wide range of querying and manipulation capabilities

7.  Issue a JSON document
 find and findOne like LINQ Select and First/Single methods
 Basic cursor functionality (think DataReader)

8.  Download as a NuGet package
 Actively worked on and contributed to
 There is an “official” client, along with several community clients

9.  MongoDB’s data aggregation solution
 Modeled on the concept of data processing pipelines
 Operations are performed in stages
 Results from one stage “piped” to the next stage
$match
$project
$sort

10.  Number of operations available
 $group, $match, $project, $sort, $limit, $skip, $redact, $out, …
 Essentially replaces the older mapReduce functionality
 Aggregation Pipeline provides better performance, generally
 mapReduce is more flexible
 Aggregation combines a number of operations in order to produce a result set

11.  Maximum size of a returned document is 16 MB
 Aggregation Pipeline now returns results using cursor (as of 2.6)
 Each stage of a pipeline has a maximum limit of 100MB of RAM
 Enable allowDiskUse in order to write to disk and avoid this limitation
 MongoDB will also optimize the pipeline, if possible

12.  Count

13.  Batting Average (Hits / At Bats)

14.  Batting Average

15.  Batting Average in C#

16.  Part of Mongo C# Driver
 Implements find and findOne
 Other grouping and projecting done client-side
 Do you want all that data before manipulating it?

17.  Add a $match pipeline operation

18.  Now need to sort

19.  But wait…we have incorrect results for top Batting Average
 Need to enhance $match to include those with 3.1 PA for 162 games

20.  In C# Using LINQ

21.  Not truly aggregation pipeline in C#
 Done on client, not server
 Materialize on client with LINQ
 Must use BsonDocument for aggregation pipeline
 Yikes!

22.  Creating the $match BsonDocument
var match = new BsonDocument{
{"$match", new BsonDocument{
{"Year", 2013},
{"AtBats", new BsonDocument{
{"$gte", 502}
}}
}}
};

23.  Create the $project operation
var project = new BsonDocument {
{"$project", new BsonDocument{
{"PlayerId", 1},
{"Year", 1},
{"TeamId", 1},
{"AVG", new BsonDocument{
{"$cond", new BsonDocument{
{"if", new BsonDocument{
{"$eq", new BsonArray{"$AtBats", "0"}}
}},
{"then", 0},
{"else", new BsonDocument{
{"$divide", new BsonArray{"$Hits", "$AtBats"}}
}}
}}
}}
}}
};

24.  Create the $sort and $limit operations and then combine them all in an Array
var sort = new BsonDocument{
{"$sort", new BsonDocument{
{"AVG", -1}
}
}
};
var limit = new BsonDocument{
{"$limit", 25}
};
return new[] { match, project, sort, limit };

25.  All the { } with BsonDocument and BsonArray reminds me of…

26. A measure of how often a batter reaches base for any reason other than a fielding
error, fielder's choice, dropped/uncaught third strike, fielder's obstruction, or
catcher's interference.
- Wikipedia (http://en.wikipedia.org/wiki/On-base_percentage)
Usually a better measure of batter’s performance than straight average
(H + BB + HBP) / (AB + BB + HBP + SF)

27. (Hits + BB + HBP) / (AB + BB + HBP + SF)
db.batting.aggregate([
{$match: { Year: 2013, AtBats: {$gte: 502} }},
{$project: {
PlayerId: 1, Year: 1, TeamId: 1,
OBP: { $cond: { if: {$eq: ["$AtBats", 0] },
then: 0,
else: { $divide: [
{$add:["$Hits","$BaseOnBalls","$HitByPitch"]},
{$add:["$AtBats","$BaseOnBalls","$HitByPitch","$SacrificeFlies"]}
]}
}}
}},
{$sort: {OBP: -1}}, {$limit: 25}
])

28. $match
$project
$sort
$limit

29. Early SABRmetric type of stat, invented by Bill James
With regard to an offensive player, the first key question is how many runs have resulted from
what he has done with the bat and on the basepaths. Willie McCovey hit .270 in his career,
with 353 doubles, 46 triples, 521 home runs and 1,345 walks -- but his job was not to hit
doubles, nor to hit singles, nor to hit triples, nor to draw walks or even hit home runs, but
rather to put runs on the scoreboard. How many runs resulted from all of these things?
- Bill James (James, Bill (1985). The Bill James Historical Baseball Abstract (1st ed.), pp. 273-4.
Villard. ISBN 0-394-53713-0)
((H + BB) x TB) / (AB + BB)
Aggregated across a team, RC is usually within 5% of a team’s actual runs

30. (Hits + Walks) * Total Bases / (At Bats + Walks)
db.batting.aggregate([
{$match: {Year:2013, AtBats:{$gte:502}}},
{$project: {
PlayerId: 1,
Year: 1,
TeamId: 1,
RC: { $divide: [
{$multiply:
[ {$add: ["$Hits","$BaseOnBalls"]},
{$add: ["$Hits","$Doubles","$Triples","$Triples",
"$HomeRuns","$HomeRuns","$HomeRuns"] }]
},
{ $add: ["$AtBats","$BaseOnBalls"] }]
}
}},
{$sort: {RC:-1}}, {$limit: 25}
])

31. $match
$project
$sort
$limit

32. db.batting.aggregate([
{$match: {Year:2013}},
{$group: {
_id: "$TeamId",
Hits: {$sum: "$Hits"},
Walks: {$sum: "$BaseOnBalls"},
Doubles: {$sum: "$Doubles"},
Triples: {$sum: "$Triples"},
HR: {$sum: "$HomeRuns"},
AtBats: {$sum: "$AtBats"}
}},
{$project: {
RC: { $divide: [
{$multiply:
[ {$add: ["$Hits","$Walks"]},
{$add: ["$Hits","$Doubles","$Triples","$Triples","$HR","$HR","$HR"] } ]},
{ $add: ["$AtBats","$Walks"] }]
} }},
{$sort: {RC: -1}}
])

33. $match
$group
$project
$sort

34.  Babe Ruth highest paid player in 20’s ($80K in ‘30/’31)
 Babe and Ty Cobb were highest paid in 1920 at $20K
 Joe DiMaggio highest paid in 1950 ($100K)
 Nolan Ryan made $1M in 1980 (1st time)
 Albert Belle made $10M in 1997
 In 1999, made ~$12M (more than entire Pirates payroll)
 2001 – ARod made $22M
 2009 – ARod made $33M

35.  Hoerster copyrighted statistic
 Compares the value each base produced by a hitter
 Who are the most expensive players?

36.  Takes total bases
 Hits + Doubles + (Triples x 2) + (HR x 3) + SB + BB + HBP – CS
 Divides salary into it
 Definitely not predictive
 More of a value statistic

37. Is a statistic, created by Tom Tango and based on linear regression, designed to
measure a player's overall offensive contributions per plate appearance.
- Wikipedia (http://en.wikipedia.org/wiki/Weighted_on-base_average)
Weighs each component of offensive with a factor
((wBB*BB)+(wHBP*HBP)+(wH*Hits)+(w2B*2B)+(w3B*3B)+(wHR*HR)+(wSB*SB)+(wCS*CS))
(AB+BB+HBP+SF-IBB)

38. var woba = db.WOBALookup.findOne({_id:2013});
db.batting.aggregate([
{$match: {Year: woba._id}},
{$redact: {
$cond: { if: { $gte: ["$AtBats",502] },
then: "$$KEEP",
else: "$$PRUNE“ } }},
{$project: {
Year: 1,
PlayerId: 1,
TeamId: 1,
WOBA: {
$divide: [
{$add: [{$multiply:[woba.wBB,"$BaseOnBalls"]}, {$multiply:[woba.wHBP,"$HitByPitch"]},
{$multiply:[woba.w1B,"$Hits"]}, {$multiply:[woba.w2B,"$Doubles"]},
{$multiply:[woba.w3B,"$Triples"]}, {$multiply:[woba.wHR,"$HomeRuns"]},
{$multiply:[woba.runSB,"$StolenBases"]}, {$multiply:[woba.runCS,"$CaughtStealing"]}
]},
{$add: "]}]}
]
}
}},
{$limit:25}, {$sort: {WOBA:-1}}, {$out: "2013TopWOBA"}
])

39. $match
$redact
$project
$limit
$sort
$out
wOBA_Factors
2013TopWOBA

40.  Calculates, on average, how many more runs a player generates than the average
player in the league
 Uses wOBA as a primary factor in calculation
 This then gets figured in for the over WAR of a player
 Good description here:
http://www.baseball-reference.com/about/war_explained_wraa.shtml

41. var woba = db.WOBALookup.findOne({_id:2013});
db.TopWOBA2013.aggregate([
{$match: {Year: woba._id}},
{$project: {
Year: 1, PlayerId: 1, TeamId: 1,
wRAA: {
$multiply: [
{$divide: [{$subtract: ["$WOBA",woba.wOBA]}, woba.wOBAScale]},
{$add: ["$AtBats","$BaseOnBalls","$HitByPitch",
"$SacrificeFlies","$SacrificeHits"]}
]
}
}},
{$sort: { wRAA: -1 }}, {$out: 'TopWRAA013'}
]);

42. $match
$project
$sort
$out
wOBA_Factors
'TopWRAA013

43.  Much of aggregate pipeline in Mongo can be done with LINQ
 But it will be client-side, not in Mongo!
 Take advantage of $out for intermediary tables during processing
 Stage your operations
 Maybe intermediary tables can be reused for other calcs
 $group id’s can be multi-valued
 Ends up as a sub-document and must be referenced accordingly

44.  Sean Lahman’s Baseball Database
http://seanlahman.com/baseball-archive/statistics/
 Society for American Baseball Research
http://sabr.org/
 wOBA Annual Factors
http://www.beyondtheboxscore.com/2011/1/4/1912914/custom-woba-and-linear-
weights-through-2010-baseball-databank-data
 Tom Tango’s Blog
http://espn.go.com/blog/statsinfo/tag/_/name/tom-tango
 Annual Salary Leaders, 1874 – 2012
http://sabr.org/research/mlbs-annual-salary-leaders-1874-2012