## Tuesday, December 14, 2010

### Overtime Revisited

by Denis O'Regan.

With nine seconds remaining in the 4th during week 14 Washington were a point adrift of Tampa Bay with the extra point to come. Redskins had two options.They could kick the extra point and take their chances in almost certain overtime or go for the 2 point conversion and try to win the game there and then.

In researching the post "A Game of two Halves",posted last year,I looked at how teams fared in overtime.I specifically looked to see if the pregame chances of the teams carried over into overtime.This involved producing pre game probabilties for over 300 games that have gone to overtime since 1989.I then grouped the games into batches where the home team had a similar probability of winning the game at the outset.

For example there were 42 OT games where the home side had about a 59% chance of winning the game before a ball was kicked.Of those 42 games the pre game favourite went on to win the game in overtime on 23 occasions.Just under 55%.Similarly,home teams having a pregame win probability of just 25% who managed to take the game to OT went on to win 33% of the time in sudden death.

I repeated the process over a wide range of pre game probabilities and plotted pregame probability against overtime winning percentage to see if there was a correlation.

Results.
There appears to be a positive,moderate to strong correlation between a team's pre game chances and their chance of winning that game should it go to overtime.
If P is the pregame probability of the home side winning,then the probability of that team winning should the game go to overtime is given by

OT win probability =(P multiplied by 0.732) + 0.124

To summarise, favourites are still favoured in overtime,but not by as much.Underdogs are still more likely to lose,but they do see their chances increase in OT compared to pre game.

Tampa at Washington.
Pregame estimates of Washington's chances of winning the game varied.Efficiency based models had the Redskins as narrow favourites,the model I used gave the Redskins a 0.56 probability of winning the game.

The probabilty of Washington winning in OT becomes.

(0.56*0.732)+0.124 = 0.53

The success rates for 2 point conversions is in the region of 48%.Therefore given the almost automatic outcome for a extra point kick and assuming the accuracy of the pre game probabilty,Washington made the correct decision in attempting the kick,even though they missed it!

As an aside,the Vegas line made Tampa the 2 point favourites.If we instead use this figure as a reflection of the pre game odds,we find now that Washington should have gone for 2.Their pregame win probability would have been about 0.46.This would increase by a very small amout if they took the game to OT,but not by enough to pass the 48% chance they probably had to make the two point conversion.

As a general point in similar circumstances,pre game favourites should kick the extra point and pregame dogs should go for two.