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.