Effects of Rivalry game
Criticism: “You can’t predict a rivalry game, anything can happen.”
Ok, fair enough. But what does that mean mathematically?
Does it mean that the standard deviation for a rivalry game is higher than a non-rivalry game? Thus, the favorite has a lower probability of winning independent of the expected game margin.
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However, there is another possibility. What if one team always performs better in a rivalry game?
West Liberty vs West Branch
expected = (West Branch – West Liberty)
(+) positive if West Branch is favored
(-) negative if West Liberty is favored
actual = (West Branch – West Liberty)
(+) positive if West Branch wins
(-) negative if West Liberty wins
resid = actual – expect
(+) postive if West Branch performs better than expected
(-) negative if West Liberty performs better than expected
1993-1995 unknown 1998-1999 unknown 2006-2009 did not play date WB WL residual expected actual 08/30/1991 21 6 -10.24 25.24 15 09/11/1992 34 15 -0.06 19.06 19 10/25/1996 14 6 -19.74 27.74 8 10/24/1997 14 12 -14.15 16.15 2 09/01/2000 @ 23 15 -3.33 11.33 8 08/31/2001 7 @ 48 -20.15 -20.85 -41 09/06/2002 @ 2 14 -11.21 -0.79 -12 09/05/2003 25 @ 7 -5.82 23.82 18 09/03/2004 7 @ 14 -5.14 -1.86 -7 09/02/2005 @ 19 12 -7.08 14.08 7 08/27/2010 27 @ 13 -10.07 24.07 14 average 17.6 14.7 -9.73 12.54 2.82
So for the last 20 years of known data, West Branch underperform by an average of 9.73 points per game against West Liberty.
Using the Open Office Cal Paired Student’s T-test (expected vs actual), we arrive at a test statistic of -5.05, with a 0.0001 probability that this is due to chance.
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Conclusions:
For this time period and the available data, West Liberty performs better than expected when playing West Branch. West Liberty performs about 9.7 points better than expected. It very unlikely that this result is due solely to chance.