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February 8, 2005 |

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Unlike Super Bowl XXXVIII, which included a highly controversial two-point-conversion attempt, the contest between
New England and Philadelphia
was virtually free of the kinds of decisions analyzed at *footballcommentary.com*. This article will therefore be brief. We will examine Philadelphia coach Andy Reid's decision to attempt an onside kick despite having two timeouts, after the Eagles scored with 1:48 remaining in the 4th quarter to close the deficit to 24-21.

Notice that if New England gets possession and makes a first down, the game is over. Therefore, if the Eagles kick deep, they have to use both their timeouts and force a three-and-out. Conditional on a three-and-out, a central case would be for the Patriots to return the kickoff to their own 27-yard line, gain 5 yards on their first three downs, and punt the ball a net 38 yards. The Eagles would then get the ball at their own 30-yard line with about 0:45 remaining and no timeouts.

If the Eagles attempt an onside kick and are successful, they get the ball at about their own 42-yard line, and have nearly 1:48 left in the quarter and two timeouts. Even if the Patriots recover the onside kick, Philadelphia has a chance if they can force a three-and-out. Unless the Patriots get very close to a first down, they will not be in position for a field-goal attempt. (In fact, it's not clear that even a 50-yard attempt, with roughly a 60% chance of success, would be worth the risk.) So conditional on the Patriots failing to make a first down, the overwhelmingly likely outcome is a pooch kick, following which Philadelphia's expected starting field position is their own 10-yard line. From Philadelphia's standpoint, then, the difference between a regular kickoff and a failed onside kick is about 20 yards of expected field position.

Of course, for Philadelphia, recovering an onside kick is much better than kicking off deep and forcing a three-and-out: With an extra minute, two timeouts, and (expectationally) better field position, the Eagles not only have a better chance for a field goal that sends the game to overtime, but also a real chance for a touchdown that wins outright.

Obviously one of the key inputs to the analysis is the probability of recovering a fully-anticipated onside kick. During the Monday Night Football broadcast on September 13, the commentators said that during the previous five seasons, the kicking team recovered 24% of anticipated onside kicks. This feels like an overestimate of the actual probability. We will assume that Philadelphia's probability of recovering the onside kick is 0.2.

Another key input is New England's probability of making a first down. This season, the Patriots failed to make a first down on 30% of their possessions. Against teams with good defenses, the figure was 37%. Philadelphia's likelihood of forcing a three-and-out is presumably even higher, because they know New England is going to run the ball. We think 0.5 is a reasonable probability that the Patriots fail to make a first down in that situation.

Let *q* denote Philadelphia's probability of winning the game if they recover the onside kick. Let *p* denote Philadelphia's probability of winning if they kick deep and force a three-and-out. Finally, let *p* is Philadelphia's probability of winning if they unsuccessfully attempt an onside kick but then force a three-and-out. (The factor θ represents the effect of the extra 20 yards of field position.)

Philadelphia's probability of winning the game is higher with the onside kick than with a regular kickoff if

0.2 *q* + (1 − 0.2) 0.5 θ *p* > 0.5 *p*,

which reduces to

*q* / *p* > 2.5 − 2 θ.

We suspect that *q* is at least 2.5 times as big as *p*. (In fact, our estimates would be *q* = 0.18 *p* = 0.07. * no * chance to win following an unsuccessful onside kick — the onside kick is still the correct choice. A more reasonable value for θ is 0.5. With that value, the onside kick is correct provided *q* is more than 1.5 times as large as *p*. That surely is the case, so we feel confident that Reid made the right decision.

Copyright © 2005 by William S. Krasker