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### Home Field Advantage

Home Field Hypothesis Testing Problems

This page teaches hypothesis testing procedures with eight questions on home field advantage in three sports.

Question One:  The table below has the home and away record for the Golden State Warriors as of 1/14/26.   Test the null hypothesis that the win percentage of the Warriors is the same both home and away.

 Golden State Home and Away as of 1/14/2016 Home Away Total Win 18 18 36 Loss 0 3 3 Total 18 21 39

Question Two:  The table below contains information on games won by the home team and games won by the road team in three professional sports.

 Home Wins and Losses Across Sports Games Won by Home Team Games Won By Away Team Baseball 1315 1114 Football 138 118 Basketball 707 523

Questions:

·      What percent of all games played did the home team win in each sport?

·      Create a 95% confidence interval for the home-win proportion in each sport?

·      Explain why it is unnecessary to conduct an evaluation of the home-loss percentage in each sport if one has already conducted an analysis of the home-win percentage?

·      Test the hypothesis that the home-win proportion for each team is greater than 0.5 in each sport

·      Explain how the number of games played impacts the estimated standard error used in the t-test for the hypothesis that the home-win proportion differs from O.5.

Question Three:   The New England Patriots had a 7-1 record at home and a 5-3 record on the road during the 2015 regular season.   Was the New England home win proportion significantly higher than the road-win proportion?

Question Four:  The table below has regular-season won/loss records for the opponent of the Carolina Panthers and the Denver Broncos.    Is the total win percentage of the opposition to Carolina significantly different from the total win percentage of the opposition to the Denver Broncos?  Discuss the limitations of this test and other things a statistician might do to assess the strength of schedule for the two Super Bowl Teams.

 Strength of Schedule Carolina Denver Opposition Wins Losses Wins Losses Jacksonville 5 11 Baltimore 5 11 Houston 9 7 Kansas City 10 5 New Orleans 7 9 Detroit 7 9 Tampa Bay 6 10 Minnesota 11 5 Seattle 10 6 Oakland 7 9 Philadelphia 7 9 Cleveland 3 13 Indianapolis 8 8 Green Bay 10 6 Green Bay 10 6 Indianapolis 8 8 Tennessee 3 13 Kansas City 10 5 Washington 9 7 Chicago 6 10 Dallas 4 12 New England 12 4 New Orleans 7 9 San Diego 4 12 Atlanta 8 8 Oakland 7 9 New York Giants 6 10 Pittsburgh 10 6 Atlanta 8 8 Cincinnati 12 4 Tampa Bay 6 10 San Diego 4 12 Total 113 143 Total 126 128

Question Five:  Below we have data on the win-loss record at home and on the road for the Toronto Blue Jays.

 Toronto Blue Jay Record Home and Away 2015 Home Away Win 53 40 93 Loss 28 41 69 81 81 162

Use the large sample t-test comparing two proportions and the chi-square test on difference between actual and expected proportions to determine whether home field advantage was important to the Toronto Blue Jays in 2015.

Question Six:    Below is information on the home win-loss record for all major league teams in the 2015 regular season.   What percent of games played in the major leagues during the 2015 regular season did the home team win?

Is this percent significantly different from 0.50?

What do we learn from this test compared to tests for individual teams?

 Win Loss Records in Home Games 2015 MLB Regular Season Team Observed Win/Home Observed Lose/Home Toronto 53 28 New York 45 36 Baltimore 47 31 Tamp Bay 42 42 Boston 43 38 Kansas City 51 30 Minnesota 46 35 Cleveland 39 41 Chicago 40 41 Detroit 38 43 Texas 43 38 Houston 53 28 Los Angeles 49 32 Seattle 36 45 Oakland 34 47 New York 49 32 Washington 46 35 Miami 41 40 Atlanta 42 39 Philadelphia 37 44 Saint Louis 55 26 Pittsburgh 53 28 Chicago 49 32 Milwaukee 34 47 Cincinnati 34 47 Los Angeles 55 26 San Francisco 47 34 Arizona 39 42 San Diego 39 42 Colorado 36 45

Question Seven:   Test the hypothesis that the home win percentage is larger than the away win percentage for each team in MLB baseball during the regular season.  How important is home field advantage in MLB baseball? Compare and contrast test results from individual teams to a single test based on pooled data from all teams in the league.

Question Eight:   Below is data on home wins, road wins and the difference between home and road wins for all MLB teams during the 2015 regular season.   Test the null hypothesis that the difference in the mean number of home wins and road wins is identical.  Barring some fart in the schedule each team plays 81 games on the road and 81 games at home.   What happens if we test the hypothesis that mean of the percent of games won at the home is equal to the mean percent of games on the road?How do the tests on differences in mean home/away wins compare to tests on differences in proportion of home/away games?

 Home and Road Wins 2015 Regular Season b.y Team Team Wins at Home Wins on Road Difference (Home - Road) Toronto 53 40 13 New York 45 42 3 Baltimore 47 34 13 Tamp Bay 42 38 4 Boston 43 35 8 Kansoas City 51 44 7 Minnesota 46 37 9 Cleveland 39 42 -3 Chicago 40 36 4 Detroit 38 36 2 Texas 43 45 -2 Houston 53 33 20 Los Angeles 49 36 13 Seattle 36 40 -4 Oakland 34 34 0 New York 49 41 8 Washington 46 37 9 Miami 41 30 11 Atlanta 42 25 17 Philadelphia 37 26 11 Saint Louis 55 45 10 Pittsburgh 53 45 8 Chicago 49 48 1 Milwaukee 34 34 0 Cinncinatti 34 30 4 Los Angeles 55 37 18 San Francisco 47 37 10 Arizona 39 40 -1 San Diego 39 35 4 Colorado 36 32 4