Analytics Edge: Unit 2 - Moneyball
Sulman Khan
October 26, 2018
Moneyball
The Story
- Moneyball tells the story of the Oakland A’s in 2002
- One of the poorest teams in baseball
- But they were improving every year
The Problem
Rich teams can afford the all-star players
How do the poor teams compete?
A Different Approach
The A’s started using a different method to select players
- The traditional way was through scouting
- Scouts would go watch high school and college players
- Report back about their skills
- A lot of talk about speed and athletic build
The A’s selected players based on their statistics, not on their looks
The Goal of a Basketball Team
Making it to the Playoffs
The A’s calculated that they needed to score 155 more runs than they allowed during the regular season to expect to win 95 games
Now, let’s verify this statement with Linear Regression
Scoring Runs
How does a team score more runs?
The A’s discovered that two baseball statistics were significantly more important than anything else
- On-Base Percentage (OBP)
- Percentage of time a player gets on base (including walks)
- Slugging Percentage (SLG)
- How far a player gets around bases on his turn (measures power)
- On-Base Percentage (OBP)
Most teams focused on Batting Average (BA)
- The A’s claimed that
- OBP was the most important
- SLG was important
- BA was overvalued
Runs Allowed
- Use pitching statistics to predict runs allowed
- Opponents On-Base Percentage (OOBP)
- Opponents Slugging Percentage (OSLG)
- We get the following linear regression model
\[RunsAllowed = -837.38 + 2913.60(OOBP) + 1514.29(OSLG)\]
Predicting Runs and Wins
Can we predict how many games the 2002 Oakland A’s will win using our models
The models for runs use team statistics
- We need to estimate the new team statistics using past player performances
- Assumes past performances correlates with future performance
- Assume few injuries
We can estimate the team statistics for 2002 by using the 2001 player statistics
Predicting Runs Scored
- Using the 2001 regular season statistics for these players
- Team OBP is 0.339
- Team SLG is 0.430
- Our regression equation was
\[RunsScored = -804.63 + 2737.77(OBP) + 1584.91(SLG)\]
- Our 2002 prediction for the A’s is
\[RunsScored = -804.63 + 2737.77(0.339) + 1584.91(0.430) = 805\]
Predicting Runs Allowed
- Using the 2001 regular season statistics for these players
- Team OOBP is 0.307
- Team OSLG is 0.373
- Our regression equation was
\[RunsAllowed = -837.38 + 2913.60(OOBP) + 1514.29(OSLG)\]
- Our 2002 prediction for the A’s is
\[RunsAllowed = -837.38 + 2913.60(0.307) + 1514.29 (0.373) = 622\]
Predicting Wins
- Regression equation to predict wins
\[Wins = 80.8814 + 0.1058(RS - RA)\]
\[Wins = 80.8814 + 0.1058(805 - 622) = 100\]
Results
The Analytics Edge
Models allow managers to more accurately value players and minimize risk
Relatively simple models can be useful
Moneyball in R
Linear Regression
Read in data
# Load the dataset
baseball = read.csv("baseball.csv")
# Output the string
str(baseball)
## 'data.frame': 1232 obs. of 15 variables:
## $ Team : Factor w/ 39 levels "ANA","ARI","ATL",..: 2 3 4 5 7 8 9 10 11 12 ...
## $ League : Factor w/ 2 levels "AL","NL": 2 2 1 1 2 1 2 1 2 1 ...
## $ Year : int 2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 ...
## $ RS : int 734 700 712 734 613 748 669 667 758 726 ...
## $ RA : int 688 600 705 806 759 676 588 845 890 670 ...
## $ W : int 81 94 93 69 61 85 97 68 64 88 ...
## $ OBP : num 0.328 0.32 0.311 0.315 0.302 0.318 0.315 0.324 0.33 0.335 ...
## $ SLG : num 0.418 0.389 0.417 0.415 0.378 0.422 0.411 0.381 0.436 0.422 ...
## $ BA : num 0.259 0.247 0.247 0.26 0.24 0.255 0.251 0.251 0.274 0.268 ...
## $ Playoffs : int 0 1 1 0 0 0 1 0 0 1 ...
## $ RankSeason : int NA 4 5 NA NA NA 2 NA NA 6 ...
## $ RankPlayoffs: int NA 5 4 NA NA NA 4 NA NA 2 ...
## $ G : int 162 162 162 162 162 162 162 162 162 162 ...
## $ OOBP : num 0.317 0.306 0.315 0.331 0.335 0.319 0.305 0.336 0.357 0.314 ...
## $ OSLG : num 0.415 0.378 0.403 0.428 0.424 0.405 0.39 0.43 0.47 0.402 ...Subset to only include moneyball years
# Subset to the moneyball team
moneyball = subset(baseball, Year < 2002)
# Output the string
str(moneyball)
## 'data.frame': 902 obs. of 15 variables:
## $ Team : Factor w/ 39 levels "ANA","ARI","ATL",..: 1 2 3 4 5 7 8 9 10 11 ...
## $ League : Factor w/ 2 levels "AL","NL": 1 2 2 1 1 2 1 2 1 2 ...
## $ Year : int 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
## $ RS : int 691 818 729 687 772 777 798 735 897 923 ...
## $ RA : int 730 677 643 829 745 701 795 850 821 906 ...
## $ W : int 75 92 88 63 82 88 83 66 91 73 ...
## $ OBP : num 0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
## $ SLG : num 0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
## $ BA : num 0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
## $ Playoffs : int 0 1 1 0 0 0 0 0 1 0 ...
## $ RankSeason : int NA 5 7 NA NA NA NA NA 6 NA ...
## $ RankPlayoffs: int NA 1 3 NA NA NA NA NA 4 NA ...
## $ G : int 162 162 162 162 161 162 162 162 162 162 ...
## $ OOBP : num 0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
## $ OSLG : num 0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...Compute Run Difference
# Compute Run Differences
moneyball$RD = moneyball$RS - moneyball$RA
# Output the string
str(moneyball)
## 'data.frame': 902 obs. of 16 variables:
## $ Team : Factor w/ 39 levels "ANA","ARI","ATL",..: 1 2 3 4 5 7 8 9 10 11 ...
## $ League : Factor w/ 2 levels "AL","NL": 1 2 2 1 1 2 1 2 1 2 ...
## $ Year : int 2001 2001 2001 2001 2001 2001 2001 2001 2001 2001 ...
## $ RS : int 691 818 729 687 772 777 798 735 897 923 ...
## $ RA : int 730 677 643 829 745 701 795 850 821 906 ...
## $ W : int 75 92 88 63 82 88 83 66 91 73 ...
## $ OBP : num 0.327 0.341 0.324 0.319 0.334 0.336 0.334 0.324 0.35 0.354 ...
## $ SLG : num 0.405 0.442 0.412 0.38 0.439 0.43 0.451 0.419 0.458 0.483 ...
## $ BA : num 0.261 0.267 0.26 0.248 0.266 0.261 0.268 0.262 0.278 0.292 ...
## $ Playoffs : int 0 1 1 0 0 0 0 0 1 0 ...
## $ RankSeason : int NA 5 7 NA NA NA NA NA 6 NA ...
## $ RankPlayoffs: int NA 1 3 NA NA NA NA NA 4 NA ...
## $ G : int 162 162 162 162 161 162 162 162 162 162 ...
## $ OOBP : num 0.331 0.311 0.314 0.337 0.329 0.321 0.334 0.341 0.341 0.35 ...
## $ OSLG : num 0.412 0.404 0.384 0.439 0.393 0.398 0.427 0.455 0.417 0.48 ...
## $ RD : int -39 141 86 -142 27 76 3 -115 76 17 ...Scatterplot to check for linear relationship
# Scatterplot
plot(moneyball$RD, moneyball$W)
Regression model to predict wins
# Linear Regression model
WinsReg = lm(W ~ RD, data=moneyball)
# Output the summary
summary(WinsReg)
##
## Call:
## lm(formula = W ~ RD, data = moneyball)
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.2662 -2.6509 0.1234 2.9364 11.6570
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 80.881375 0.131157 616.67 <2e-16 ***
## RD 0.105766 0.001297 81.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.939 on 900 degrees of freedom
## Multiple R-squared: 0.8808, Adjusted R-squared: 0.8807
## F-statistic: 6651 on 1 and 900 DF, p-value: < 2.2e-16Regression model to predict runs scored
# Linear Regression model
RunsReg = lm(RS ~ OBP + SLG + BA, data=moneyball)
# Output the summary
summary(RunsReg)
##
## Call:
## lm(formula = RS ~ OBP + SLG + BA, data = moneyball)
##
## Residuals:
## Min 1Q Median 3Q Max
## -70.941 -17.247 -0.621 16.754 90.998
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -788.46 19.70 -40.029 < 2e-16 ***
## OBP 2917.42 110.47 26.410 < 2e-16 ***
## SLG 1637.93 45.99 35.612 < 2e-16 ***
## BA -368.97 130.58 -2.826 0.00482 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 24.69 on 898 degrees of freedom
## Multiple R-squared: 0.9302, Adjusted R-squared: 0.93
## F-statistic: 3989 on 3 and 898 DF, p-value: < 2.2e-16