## Friday, January 15, 2016

### Does the home court impact the Golden State Warriors?

Question:  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

Analysis:

There are several ways to test this hypothesis.  I will use the Chi-Square test for difference in two proportions.

The test statistic for the chi-square test is

Chisquare= sum over all cells (fo-fe)2/fe

Here fo is the observed outcomes win/losses at home/away.

fe is the expected number of wins/losses at home/away under the null hypothesis that the win loss percentage does not depend on whether the game is home or way.

The overall win percentage is 36/39 or 0.923.

The overall loss percentage is 3/39 or 0.077.

Multiply the overall win/loss percentage by the number of home/away games to get the expected wins/loss at home/away.   The calculation of fe is presented below.

 Calculation of Expected Outcomes fe fe calculation Win/Home 16.62 (0.923*18) Win/Away 19.38 (0.923*21) Lose/Home 1.38 (0.076*18) Lose/Away 1.62 (0.076*21)

The chi-square statistic is calculated in the table below.

 Calculation of ChiSquare Statistic fo fe (fo-fe)2/fe Win/Home 18 16.62 0.12 Win/Away 18 19.38 0.10 Lose/Home 0 1.38 1.38 Lose/Away 3 1.62 1.19 Total Chi-Square Statistic 2.79 p-value 0.09511

The test statistic is chi squared with 1 degree of freedom.  Excel allows for the calculation of the p-value for the chi square statistic with the CHIDIST function.

The p-value of 0.0951 is marginally significant for a two-tailed test.  However, it might be reasonable to use a one-tailed test for this problem.

This book, which is on line, is a good reference fort this type of problem.

The home court or home field issue can be used to illustrate a bunch of statistical problems or questions.

Why might some sports have higher home court advantages than other sports?

Why would home court advantage be a more important factor for some baseball teams and not other teams?

Why might home court advantage be less important for NFL wildcard games than for subsequent playoff games?  (Should this question be addressed with a one or two tailed test?)

More problems teaching hypothesis tests on proportions and sometimes on means based on the home field issue will follow.

My most popular book on Kindle is Statistical Applications of Baseball.   It is a bit dated as it was written in 1996 and it has some typos but it got a good review in the Journal Chance and it has numerous word problems, which can reduce lesson planing time for teachers.   I hope it provides some use to you.

http://www.amazon.com/Statistical-Applications-Baseball-Statistics-Sports-ebook/dp/B006M3PQWQ

Go Back to the Seven Home-Field Advantage Hypothesis Testing Problems:

http://www.dailymathproblem.com/p/home-field-hypothesis-testing-problems.html