Despite the controversy surrounding an illegal defense on the Chiefs' missed field goal at the end of regulation, the San Diego Chargers defied odds and clinched a postseason berth on Sunday. In overtime, Philip Rivers orchestrated a 17-play, nine-and-a-half minute field goal drive to start the extra quarter that ultimately sealed their win. The length of the drive, in this case, is just as important as the outcome as San Diego could advance with either a win or a tie.
Using our Markov model, let's take a look at the drive. Keep in mind, the model is best used for a standard drive when time and score differential would not greatly affect decision-making or play-calling. Since this was the opening drive of overtime, those standards will predominantly hold true, although not perfectly given the leverage of the situation.
The biggest play of the drive (and quite possibly the game) was the fake punt on play five on 4th-and-2 from the Chargers own 28-yard line. With a punt, the Chargers would initiate sudden death, giving the Chiefs a 59% chance of winning the game. 4th-and-2 converts roughly 57% of the time on fakes. If the Chargers fail, they initiate sudden death and the Chiefs would win 83% of the time. With a successful conversion, the Chargers would be looking at about a 56% chance of winning.
Based on league-average expectation, E[WP Fake] = 56% * 57% + 17% * 43% = 39% < E[WP Punt]. So, just looking at the raw numbers, punting is very slightly the better option. Let's look at some of the local factors that would affect these probabilities, though. Despite winning for the majority of the game, Kansas City had their backups in the entire game - and San Diego was heavily favored. In addition, the Chargers have the No. 3 and No. 29 opponent-adjusted offense and defense in the league respectively. Both of these factors would sway the probabilities toward going for it (as it would increase the Chargers chances of converting and winning on a conversion, and decrease their chances of stopping the Chiefs on a failure or punt). Last, as we mentioned before, the Chargers could play for the tie. That means we really cannot just use the complements to calculate expectation, since tie probability is significantly non-zero. A conversion would greatly increase the chances of a tie in this case.
Let's just play with some numbers as an example. In the last two years, there have been two ties in 38 overtime games (~5%). So, let's assume there is a 5% chance of a tie at the point of the Chargers' decision-making. With San Diego able to play for the tie, let's (arbitrarily) assume a conversion means the chance of a tie increases to 15% (we'll take half of this out of the Chargers' chances of winning and half out of the Chiefs'):
E[Make Playoffs | Fake] = 56% * (57% + 7.5%) + 17% * (43% + 2.5%) = 43.9% > 43.5% = E[Make Playoffs | Punt]
Again, this is using league-averages so we would assume that would tilt the scales further toward the Chargers. There is no doubt that Mike McCoy would have been killed in the media had the fake failed. Ultimately, while certainly a high risk decision, the data at the very worst supports the decision as a near coin flip.
Keith Goldner is the Chief Analyst at numberFire.com - The leading fantasy sports analytics platform - and creator of Drive-By Football. Follow him on twitter @drivebyfootball or check out numberFire on Facebook.