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Wednesday, December 22, 2010

Testing Matchup Myth #2: the Rivalry

Myth #2: You can throw out the records for a rivalry game

Beck to Harline, 2006
BYU beats Utah 33-31
Most college football fans and experts seem to accept at face value the notion that the outcome of a rivalry game is more random than other games - you can throw out the records. Why might this be? First, to be rivals the programs must be on relatively equal footing. Therefore, the gap in talent on the sidelines is generally not as large as the gap in records between the two teams. For example, Auburn may have had the better rank and record going in to the 2010 Iron Bowl but no one doubted that Alabama had as much physical talent as Auburn. 

Second, the underdog in a rivalry game is not going to be intimidated. Like I said before, the two programs have a lot in common. The two teams know each other intimately. The opposing players and coaches are humans, not ubermensch in fancy uniforms. And every rivalry highlights upsets from past seasons that coaches can draw on to inspire their team.

On the other hand, rivalries seem to erase the one potential advantage underdogs have. A team can only circle so many games on its schedule. Bad teams circle games against good teams; good teams circles games against better teams. But better teams will circle a game against a bad team if that team is a rival. The underdog can pull off the upset if they are preparing for the super bowl but their opponent is just preparing for another game, but both teams should be looking forward to rivalry games. 

Hall to Collie on 4th and 18, 2007
BYU beats Utah 17-10
What do the numbers say? I've picked 36 rivalry games, games with names like the Red River Shootout and the Duel in the Desert, the Apple Cup and Egg Bowl, the Backyard Brawl, Bedlam, Clean, Old-Fashioned Hate, the Civil War, the Holy War, the Game and the Big Game. These 36 pairings have played 1052 times since 1950. I have established expected results using scores from the rest of the season - the method I have used is well-tested and the results relatively reliable.

In these rivalry games, favorites have won 73% of the time; they have won 98% of games when favored by 21 or more, 81% when favored by 7 to 21, and 54% when favored by less than 7. This last result is notable, because in all 13,800 or so games since 1950, teams favored by less than 7 points have won 60% of the time. In all, underdogs have won about 25 more games (of 1,052) than expected.

Hall to George in overtime, 2009
BYU beats Utah 26-23
On average, underdogs do about 3/4 of a point better than expected, but almost 2 points better when they are expected to lose by less than 7. To offset that, they do 1.5 points worse on average when 21 point dogs or more. I would guess this is because players find it easier to keep the motor running when blowing out a rivalry than in a typical blowout.

The two charts below show the performance of teams in rivalry games compared to all games by the odds/expected score margin. The first chart, the x-axis (moving right to left) is the odds of teams winning and the y-axis (moving up and down) is the winning percentage of teams with those odds. With all games, you see that as the odds of winning increase, the winning percentage increases in a straight line. In rivalry games the relationship isn't exactly linear. When one team is favored by a lot of points, the results are as expected (that 1.5 points worse than average for the underdog doesn't dramatically affect their odds of winning when they are 30 point dogs). But when the odds are tight, the underdogs win more games than expected and, conversely, favorites lose more games than expected. 

In the second chart, the x-axis is the expected score margin and the y-axis is the difference between the actual margin and the expected margin. Consistent with the first chart, slight underdogs outperformed expectations, but big underdogs underperformed expectations.

Can we throw out records in rivalry games? Of course not. Better teams still win the majority of the time, and heavy favorites almost always win. But when the teams are close, the results are more random than we would otherwise expect.

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