Testing for a difference in average team home and road wins
Previous posts used tests on proportions to assess the
importance of home field advantage in MLB.
This post examines and tests for a difference in average home and away
wins across all MLB teams.
Question: 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: The table below contains the mean and
standard deviation for wins at home, wins on the road and the paired
differences of wins at home and on the road.
Summary Statistics on
Wins at Home and on the Road
2015 Regular Season MLB


Wins at Home

Wins at Road

Difference


Average

43.833

37.133

6.700

STD

6.587

5.563

6.587

We need to consider whether the variances from the home and
away samples are identical or different.
If we fail to reject the null hypothesis of identical variances we can
use a standard error based on the pooled variance.
The ratio of the estimators of the variance is 1.4.
The critical value for tests on the ratio of variances is
obtained from the
FINV function =F INV(0.05,29,
29)=1.86.
We cannot reject the null hypothesis of equal variances so I
will use a pooled variance estimator.
Pooled Variance = (43.4+30.9)/2 = 37.2
The tests statistic for the difference in two means is
Z = (AVG(HW) –AVG(RW))/((STD_pooled x 2/30)^{0.5}
Here HW is home wins and RW is road wins.
Z = 6.7/(37.2 x (1/15))^{0.5}
=4.2.
We reject the null hypothesis mean wins on the road is equal
to mean wins at home.
Results are even stronger when we use the paired difference
procedure.
The test statistic for the paired mean test is
Z = AVG(Diff)/ (Var(Diff)/n)^{0.5}
=5.57
Again we reject the null hypothesis that the difference in
means is zero.
Would results differ if we divided the mean wins by 81 the
number of home and away games?
No.
The test statistics for the numerator and denominator are
both divided by 81. The Z scores are
unchanged. The critical values are
unchanged.
Test results on the mean of wins are identical to test
results on means of proportions of wins.
How do the results presented here differ from results in
previous posts that looked at proportion of games won?
The questions asked and answered differ as do the samples
used to address the issue.
One post considers whether the proportion of all MLB games
won by the home team is larger than the proportion of games won by the away
team. The sample covers all games
played in the major leagues. There are
81 x 30 regular season games in a season.
The second post tests for home field advantage for each team
in MLB. The sample size is the number of
home games for each team. Each team
plays 81 games.
This post looks at average home and road wins. The sample size is the number of teams in
the league, 30 teams.
How would size of samples differ if we looked at home field
advantage in college basketball or baseball?
Authors Note: Please consider my book Statistical
Applications of Baseball.
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