MLB Home versus Away
Win Proportions
This post considers the test for a difference in home vs.
away win proportions for all MLB teams in the 2015 regular season.
Question: Test whether the home win proportion differs
from the away win proportion for all MLB teams during the 2015 regular
season.
What can we say about the null hypothesis that the
difference between the home and away win proportion is zero for all MLB teams
during the 2015 regular season?
Can we conclude that home field advantage is equally
important for all MLB teams?
Can we conclude that most teams are significantly more
likely to win at home than away?
Analysis: We conduct a ttest on the hypothesis that
the home win proportion was identical to the road win proportion for all MLB teams. The Excel based calculator used in this
ttest was developed in a previous post.
All one has to in order to run this calculator is input the
four home/away win loss numbers and copy the formulas. The calculator results for the American
League East are presented below.
AL East Results


Label

Toronto

New York

Baltimore

Tamp Bay

Boston

Observed Win/Home

53

45

47

42

43

Observed Lose/Home

28

36

31

42

38

Observed Win Away

40

42

34

38

35

Observed Lose Away

41

39

50

40

46

Total Home

81

81

78

84

81

Total Away

81

81

84

78

81

Win Probability Home

0.654

0.556

0.603

0.500

0.531

Win Probability Away

0.494

0.519

0.405

0.487

0.432

Diff Win Probabilities

0.160

0.037

0.198

0.013

0.099

Pooled Variance

0.238

0.248

0.240

0.250

0.247

Standard Error

0.077

0.078

0.077

0.079

0.078

tstatistic

2.093

0.473

2.567

0.163

1.264

pvalue

0.036

0.636

0.010

0.870

0.206

The difference in proportions and the pvalue for test
results of the hypothesis that the homewin proportion is equal to the awaywin
proportion for all majorleague teams are presented below.
Results of Test for
Hypothesis that Home and Away Win
Probabilities are Identical  Regular
Season 2015


Team

Diff Probability Home Win
 Probability Away Win

pvalue

Toronto

0.160

0.0363

New York

0.037

0.6362

Baltimore

0.198

0.0103

Tamp Bay

0.013

0.8704

Boston

0.099

0.2062

Kansas City

0.086

0.2623

Minnesota

0.111

0.1546

Cleveland

0.031

1.3062

Chicago

0.049

0.5284

Detroit

0.019

0.8075

Texas

0.025

1.2477

Houston

0.247

0.0012

Los Angeles

0.160

0.0382

Seattle

0.049

1.4716

Oakland

0.000

1.0000

New York

0.099

0.2037

Washington

0.111

0.1546

Miami

0.136

0.0787

Atlanta

0.210

0.0055

Philadelphia

0.136

0.0734

Saint Louis

0.123

0.1032

Pittsburgh

0.099

0.1962

Chicago

0.012

0.8726

Milwaukee

0.000

1.0000

Cincinnati

0.049

0.5198

Los Angeles

0.222

0.0034

San Francisco

0.123

0.1131

Arizona

0.012

1.1249

San Diego

0.049

0.5276

Colorado

0.049

0.5237

Discussion of Test
Results:
·
If the null hypothesis of no difference in home
versus road win percentage was actually true for all major league teams the
difference in probabilities would be positive around half the time and negative
around half the time. This clearly is
not the case. The difference between
the probability of winning at home and the probability of winning on the road
is greater than zero for twentyfour teams and less or equal to zero for six
teams.
·
If the null hypothesis of no difference in the
home and away win probability was true for all 30 teams we would expect to
reject the null hypothesis for 3 teams if we choose a significance level of
0.10. Furthermore, half of the
significant rejections would be in the left tail and half in the right
tail. We reject the null hypothesis for
eight teams. All eight teams where the
null hypothesis was rejected were in the right tail meaning their probability
of winning at home was greater than their probability of wining on the road. There was no team with a significantly
greater win proportion on the road than at home.
·
The eight teams with a significant difference in
home versus road win proportion are over 26 percent of the sample, a lot more
than the expected 10 percent.
·
Note that for 22 of the 30 teams the difference
between the home and road win proportion was not significantly different from
zero.
Final Thoughts:
We reject the null hypothesis of no difference between home and away win
proportions for over 26 percent of MLB teams in the 2015 regular season. This is a lot higher than what would have
occurred if the null hypothesis of no difference was true for all teams.
However, the likelihood of winning at home versus winning on
the road did not significantly differ for most teams. Analysis based on pooled winloss data across
all teams would often overstate the importance of the home field advantage for
many teams. More on what these results
suggest about whether we should build models on pooled or team specific models
in subsequent posts.
Authors Note: If you enjoyed this post you might also get some use out of my old book Statistical Applications of Baseball, available on Kindle.
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