After a tough loss, it is common practice to examine coaching decisions in search of culpability. Nowhere is this tendency more prevalent than amongst fans of the Fighting Illini. Perhaps this is with good reason. Ron Zook is, fairly or not, well known throughout the college football world as a coach who tends to make some odd decisions. Decisions like this, for example. While rewatching the OSU game this evening, I was struck by how vociferously the announcers criticized Zook for not taking the “sure” three points. There were donnybrooks on messageboards (Illinois Loyalty comes to mind) and support for Zook on Twitter from Mike Hall of the BTN. While the ultimately failed play was a victim of poor execution, we can use some statistical analysis to examine the possible outcomes of this decision.

There were two possible ways to get to a tying score of 17 at that point in the game. The Fighting Illini could have 1) kicked the field goal and hoped to recover the onside kick and drive for the tying score (scenario A) or 2) attempted to get the first down, scored a touchdown if successful and then recover the onside kick and drive for the tying field goal. (scenario B)

Let’s examine each of these probabilities piece by piece. First, the game situation: 1:20 remaining, 4th and 2, ball on the Buckeye 17.

I estimate that the probability of success on 4th and 2 to be 40%. The source for this number is the average success rate for 2-point conversion across all of NCAA FBS football for the last year. Why use this number? The game situation at this point (one chance to get 2 yards) closely resembles that of a two-point conversion. This assumption is a bit dirty, but a reasonable one.

The next step is to calculate the drive probability. To do this I counted the total number of drives the Illini had commenced this year: 72. I then counted the number of drives over 14(47), 28(38), and 56(23) yards and found the percentage chance the Illini had a drive of at least each length-65.2,52.7, and 31.9 percent, respectively. [Note: Drives which were shorter than any of these distances which resulted in touchdowns were counted as drives of that distance. So, a 27 yard TD drive would count as a 28 and a 56 yard drive as well. This is a generous assumption for scenario A.]

This leaves the score 17-14 with the Illini needing an onside kick recovery and a field goal. If the onside kick wound up going 14 yards (the average length of a defensive recovery of an onside kick over a 200-instance semi-random sample) and lasting roughly 12 seconds (same sample), the Illini would have the ball on their own 44 yard line and consume about 8 seconds in the process. According to the same semi-random sample, the rate of success for recovery of such a kick is around 27%. Dimke is a great kicker with tremendous range and the wind at his back. His career percentage from 40-49 yards is 81%. So let’s say the Illini want to set up a field goal in that range. They would need to advance the ball 28 yards in that remaining minute. At 8 seconds per play (lots of clock-stopping opportunities) they could use 6 plays at the aforementioned average of 4 yards per play. The tying field goal would be kicked right before time expires. Dimke has converted 93% of his kicks from 30-39 yards, so that is the probability for the shorter field goal if the Illini hadn’t gone for it on fourth down.

Let’s construct the probability of Scenario A:

.95 (short field goal)*.27*.31=7.9%

Scenario B:

.4(fourth down play)*.65(touchdown first)*.27*.53*.81=3.7%

So, simply looking at the straight probabilities (with, admittedly, some big assumptions) we find that Zook’s decision was about half as likely to have a successful result as simply kicking the field goal. However, there are confounding factors. Illinois would have had only 70 seconds and two timeouts to drive those 56 yards versus possibly about 50 seconds and 2 timeouts to go 28 yards. If the 4th and 2 play succeeds, my calculations suggest that the Illini would have had about a 7.4 percent chance to tie the game, for all intents and purposes the same as taking the “easy 3″. This is ignoring clock effects, which would probably tip the balance in favor of trying for the touchdown first.

The real pitfall here is throwing in the extra factor of the single play. If we were to add up the probabilities of all the individual plays needed on each set of drives(an odious and practically impossible task), we might find that Zook’s decision was the correct one. The simplest way to look at it, in my opinion, is that the Illini would have been giving up valuable yardage by settling for a field goal. With a shortage of time on the clock, it is my gut reaction that Illinois did the right thing.