Your opponent kicked a FG on the first possession of overtime, and now your team needs a TD to win or a FG to continue the game. Your offense has driven down to the opponent's 10-yard line, but the drive has stalled. It's 4th down and 3. Should you go for the risky conversion and ultimately a TD for the win, or should you attempt a FG knowing you'd be at a disadvantage giving the ball to the opponent in sudden death?
The new NFL OT rules are unique in a lot of ways, and by unique I mean convoluted and contrived. There are basically three possible game states:
1. The first drive in which no score leads to Sudden Death, a TD wins, or a FG spawns the second state...
2. A possible second possession in which the offense is down by 3 points. It must score a TD to win or a FG to continue into SD.
3. Lastly, traditional SD itself.
The three game states successively easier to model. The first possession must consider all the possibilities of the following two states. The second state must only consider itself and the possibility of SD. The second possession is also slightly easier to model because there is no punt option. An offense trailing by 3 points simply must score or lose.
It's that second possession that makes the OT so unique. We've seen plenty of end-game situations where a team can initiate SD with a FG, win with a TD, and lose by failing to score. But never before have we seen essentially un-timed scenarios with those potential outcomes.
Here is how I approached the problem as I described in my post on the first drive in OT:
We can look at the end-game of 4th quarters in which a team is down by 3. We can throw out all games that ended in expiration, and only look at combinations of field position and time remaining that realistically maximize the offenses chances of winning. For example, when we look at first down situations at a team’s own 20, at various times remaining, we chose the time in which a team roughly has the best chance of winning. That will be the point where time presses on them the least and the opponent does not have enough time to counter the drive. If we do this for all the various field positions, we can get a realistic estimate of how often teams in that kind of situation get a FG or score a TD.Here is a look at the resulting scoring probability estimates for the 'Down by 3' second possession in OT for 1st downs by field position. The blue curve is the probability of scoring a FG on the current drive and the red curve is the probability of scoring a TD on the current drive. The green curve is the total win probability given the scoring curves, which is a straight-forward calculation. A TD has a WP of 1.0, a FG has a WP of somewhat less than .50, and every other outcome has a WP of zero.
It's the green line we're most interested in, because that's the WP value for a successful 4th down conversion at the resulting field position. The WP for a successful FG attempt is the WP of kicking off into a SD situation. Applying the standard 4th down conversion rates and FG success rates produces the next chart. The colored curves represent the baseline WPs for the conversion attempt for various distances to go. The black curve represents the baseline WP for a FG attempt. All WPs are based on the line of scrimmage of the 4th down play (and not kick distance).
Wherever the conversion curve is higher on the chart than the FG curve, a conversion attempt is typically recommended. And wherever the FG curve is higher, a FG attempt is typically recommended.
You may have noticed that the conversion attempt curves are not continuously smooth. That's due to the increasing difficulty of converting as offenses approach the goal line. I used conversion probabilities based three ranges: from the goal line to the 10, from the 11 to the 20, and outside the 20. It would have been better to have uniquely blended/interpolated conversion values, but that's excessively difficult and would not affect the results much. Only the curves 2- and 3-yards to go would be affected. It was also easily correctable when producing the final chart below.
This is the final result. The blue line is demarcates the regions for going for the conversion and attempting the FG. A situation above the line suggests attempting the FG, and a situation below the line suggests going for the conversion. I have deliberately chosen assumptions unfavorable to the go-for-it option, such as saying that a successful conversion will not go any further than the line to gain. Therefore, on the line indicates that the conversion attempt is typically recommended.
Normally analyses like these result in seemingly wild recommendations, like going for it on 4th and 10 from the 20. But in these '2nd possession' situations, the conservative approach appears to be the way to go. In the scenario that opened the post, we faced 4th and 3 from the 10. In this case, a FG attempt would usually be the better bet.