Home Field Hypothesis Testing Problems


Home Field Hypothesis Testing Problems

This page teaches hypothesis testing procedures with seven 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

Answer is Here:


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.



Answer is Here:




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?

Answer is Here:

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


See Answer Here:



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


Answer Below:



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.

Partial Answer Here:


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

Answer Here:
http://www.dailymathproblem.com/2016/01/testing-for-difference-in-average-team.html

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