In the last article, I made the point that underdogs have a better chance of winning a game when each opponent has fewer possessions. Specifically I wrote, "The more possessions each team has, the more likely it is the better team is going to eventually come out on top. With fewer total possessions, the underdog has a better chance to win because randomness plays a bigger role relative to team ability in a game’s outcome." This article will estimate just how much an underdog can benefit by reducing the total number of possessions in a game.
I built a crude simulation of a football game in the PHP programming language. By specifying the number of possessions for both teams and the scoring rate of each team, a simulated score and winner can be determined. By running the simulation many times, we can get a good estimate of the win probability for various numbers of total possessions.
But first, we need to pick a couple of teams as guinea pigs. One needs to be a big underdog against the other. Hmmm, let's see. How about the Giants and Patriots?
The Patriots scored touchdowns in 42% of their possessions in 2007. And 13% of their possessions resulted in field goals. They gave up TDs in 17% of their opponents' possessions and allowed FGs in 7% . In contrast, the Giants scored TDs in 21% of their possessions and kicked a FG in 12%. They allowed TDs in 19% of their opponent possessions and gave up FGs in 11%. The table below summarizes each team's respective drive stats.
|Scoring Rate || NE (%)|| NYG (%)|
If we assume that the each team will score according to the mid-point between each offense's and defense's scoring rate, we can construct a fairly solid model. For example, given the Patriots' 42% offensive TD rate, and the Giants' 19% opponent TD rate, we could estimate the Patriots would score (42 + 19) / 2 = 30.5% of the time. (I realize this is pretty rough, but it suits the simulation's purpose.)
Unfortunately for New York Giants fans, the Patriots won the first simulation 38-7. That was for 12 possessions for each team, the most common number of team possessions in the NFL. But one simple simulation is pretty pointless. After 10,000 of them however, New England won 75.6% of the games and the Giants won 20.5%, with 3.8% of the games going into overtime.
But what if each team only had 10 possessions? How do the underdogs fare? The Patriots' win 72.7% of the games and the Giants win 22.4%. Reducing the number of possessions does boost the chances of the underdog, but only slightly.
The table below lists typical numbers of possessions for each team in NFL games along with the simulated probabilities of winning for each team.
|Possessions|| NE Wins||NYG Wins||Overtime|
First thing to note is that the Giants have an improbable challenge, no matter how few possessions to which they can limit their opponents. This method appears to confirm my standard logistic regression efficiency model that gives the Giants about a 1 in 4 shot at the title. But that's nothing to sneeze at. How much sleep would you get if you knew you had a 25% chance of your life savings being wiped out by morning? It's not a guaranteed victory for New England by any stretch.
The fewer the number of possessions, the greater the chance of upset. Letting the clock run is in the Giants' interest. Did you hear that Plaxico? Take the hit and stay in bounds, (as long as the score is close). You'll be helping your team more than you could ever understand.