The Wall Street Journal's 'Numbers Guy' Carl Bialik asked me the other night about the Bengals' 4th and 11 conversion attempt late in overtime against the Browns. With a just over a minute left in OT, the Bengals faced a 4th and 11 from the Cleveland 41. Quarterback Carson Palmer was able to scramble for 15 yards and a first down, and Cincinnati went on to kick a field goal to pull out the win. At the risk of sounding like a broken record on the topic of 4th down decisions, here's a summary of what I told Carl.
This is a tough question because it was so deep into overtime, and a tie was a very real possibility. Here is a breakdown of the decision according to the Win Probability model. The table below lists the probability of winning, losing, and tying based on the 3 possible outcomes from that 4th and 11 situations. They could go for it and succeed, go for it and fail, or punt. If you consider a tie as half a win, the total value reflects the sum of the win probability plus half of the tie probability.
4th and 11s are converted about 30% of the time in that region of the field as a league-wide average (using 3rd and 11s as statistical support). Therefore the total expected value of the conversion attempt would be:
0.30 * 0.945 + (1-0.3) * 0.40 = 0.56
Punts are punts, so the value is a static 0.46. So it's 0.56 vs. 0.46 in favor of going for it. But that's only if you value a tie as half a win, which isn't necessarily the case. Also, these estimates are rough because we are literally in uncharted territory. Rarely do overtime games go that deep, so there isn't a lot of data to work with. Some of my numbers were estimated based on drive scoring rates in close games in the 4th quarter.
I can't imagine Marvin Lewis could have made an estimate like this. He must have been very confident in Carson Palmer and made a gutsy call. Plus, the memory of last year's tie against Philadelphia must have weighed heavily on Lewis' mind. Imagine the outcry in Cincinnati if they didn't make it, and the Browns were able to get into FG range. Bold call.