Monday, January 18, 2016

MLB Home versus Away Win Proportions

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 t-test 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 t-test 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
t-statistic
2.093
0.473
2.567
0.163
1.264
p-value
0.036
0.636
0.010
0.870
0.206


The difference in proportions and the p-value for test results of the hypothesis that the home-win proportion is equal to the away-win proportion for all major-league 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
p-value
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 twenty-four 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 win-loss 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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