Superbowl XLIV Onside Kick and Game Theory
Articles
The Play that Turned the Superbowl: http://blogs.wsj.com/dailyfix/2010/02/08/the-play-that-turned-the-super-bowl/
The Count: Payton’s Gutsy Calls Were the Safer Bets: http://blogs.wsj.com/dailyfix/2010/02/08/the-count-paytons-gutsy-calls-were-the-safer-bets/
Advanced NFL Stats – Onside Kicks: http://www.advancednflstats.com/2009/09/onside-kicks.html
Superbowl XLIV. The Indianapolis Colts and the New Orleans Saints, winners of the AFC and NFC championships respectively, were playing a final game to determine the outright champion of the 2009-2010 NFL season. After one half of play, the Saints found themselves trailing the Colts with the halftime score at 10 to 6. While the game was well within reach for the Saints only trailing by four points, Saints’ head coach Sean Payton decided to open the second half with arguably one of the gutsiest calls in Superbowl history: an onside kick. Catching the Colts completely off guard, the Saints were able to execute the onside kick to perfection, recovering the ball at the 42-yard line. The Saints’ offense capitalized on the possession change, driving 58 yards to score a touchdown to take the lead and shift the momentum into their favor. The Saints would go on to win Superbowl XLIV and many can argue that the onside kick call to start the third quarter ultimately decided the game.
Video Clip of the Onside Kick: http://www.youtube.com/watch?v=wUM0m2q2gN4
What would compel head coach Sean Payton to go for an onside kick to open the half? NFL teams typically only resort to calling onside kick plays within the final minutes of the game when the losing team desperately needs to retake possession of the ball in order to have any chance to score and win the game. Teams are rarely willing to call an onside kick outside of those circumstances since a failed onside kick would give the opposing team excellent field position making it much easier for them to score. This had been the first time in Superbowl history that an onside kick had been attempted before the fourth quarter. To gain a better understanding of the dynamics of an onside kick as it relates to game theory, consider the table below:
|
|
|
Colts |
|
|
|
|
Defend Onside |
Defend Kickoff |
|
Saints |
Onside Kick |
5, 25 |
25, 5 |
|
|
Kickoff |
25, 5 |
5, 25 |
After looking at this table one notices that this scenario is representative of the Attack-Defense Game where the defender gets a higher payoff if it defends the correct play and the offense gets the higher payoff if the defense defends the wrong play. Notice how in this game there is no pure strategy Nash Equilibrium. After further calculations, one determines that there is only a mixed strategy where the equilibrium would have the Saints calling an onside kick with a probability of .5 and the Colts defending against the onside kick with a probability of .5. However, if this is supposed to be the mixed strategy equilibrium, then why aren’t there more onside kicks during games?
The answer lies in the fact that the game time environment influences the probability of the kickoff team to perform an onside kick. In games where the team is leading the game or trailing by a few points or even if when there is a large amount of time remaining in the game, the probability of the kickoff team going for an onside kick decreases greatly. Thus, as the probability of the kickoff team kicking off approaches one, the best response of the opposing team would be to defend the kickoff.
At the opening of the second half of the Superbowl, the probability of the Saints performing an onside kick was below the .5 mixed strategy equilibrium. This resulted from the fact that they were only down four points with an entire half left to retake the lead. Since the probability of the Saints going for an onside kick was close to zero, the Colts’ best response was to defend the kickoff rather than the onside kick. However, the Saints went against this likely probability and as a result caught the Colts off-guard.
Football researcher and analyst Brian Burke analyzed the success rates of onside kicks by NFL teams citing that overall onside kicks are successful approximately 26% of the time. Burke, however, notes that most teams use the play when they have less than a 10% chance of winning. This would signal that the defending team that their best response would be to defend the onside kick since the probability of the kickoff team kicking an onside kick is approaching one (since they are desperate to regain possession of the ball). Because the defense is now prepared for the onside kick the success rate of the onside kick is much lower (about 20% according to Burke). However, when the defense is not expecting the onside kick (when the probability of the onside kick is closer to zero) the success rate is much higher (about 60% according to Burke). These statistics are reinforced by principles of Game Theory since the defense’s best response is based off whether the probability of the offense to kick an onside kick is closer to zero or one. When the offense goes against that probability they are able to catch the defense off-guard and that played a significant factor in influencing the Saints’ decision to call the onside kick. Their decision to go against their probability paid off and ultimately led to them winning the Superbowl.