This post was originally written by numberFire Chief Analyst Keith Goldner for his personal site, Drive-By Football. Check it out!
In response to news that Roger Goodell is considering removing the kickoff from football and replacing it with a 4th-and-15 attempt from the 30, we recently looked at an overview of the frequency and probability implications of Greg Schiano's suggestion. In this portion of the analysis, we will look at when teams should attempt the 4th-and-15.
First, let's look at expected points. This will tell us how often, in general, teams should attempt the 4th-down conversion. We will use the values from the last post and assume a fake punt and conversion attempt both convert at 20%.
EP(Normal Punt) = -1.02
EP(Conversion Success) = 2.23
EP(Conversion Failure) = -3.28
Next, we set up the equation to solve for the break-even conversion rate:
2.23 * x - 3.28 * (1 - x) = -1.02
x = 0.41
So, teams should go for it if they believe they can convert over 41% of the time. Since the estimated conversion rate is about half that, teams should very rarely go for it. That does not mean they should never go for it, as there are obvious elements of game theory involved -- success probability would increase as your opponent's belief in you attempting the 4th down decreases. And, most notably, at the end of the game, we must take win probability into account.
Let's first look at a surprise attempt -- fake punt -- taking place in a tie game nearing the end of the 3rd quarter. Most teams would not be expecting a fake here.
WP(Normal Punt) = 0.45
WP(Fake Success) = 0.59
WP(Fake Failure) = 0.38
Solving the same equation, we get x = 0.33, closer but still higher than our estimated conversion rate. This goes against previous analysis of surprise onside kicks.
Regular onside kicks typically happen when there is less than a 15% chance of winning the game. Take the following scenario: Your team just scored so you are down three with three minutes left.
WP(Normal Punt) = 0.12
WP(Conversion Success) = 0.38
WP(Conversion Failure) = 0.06
Here, x = 0.1875 < 0.20 so the team should attempt a conversion rather than just punting. Obviously, timeouts are a factor in this scenario, but generally, the analysis applies.
It will only make sense to attempt the conversion if your team has less than a 15-20% chance of winning the game. Above you can see a (very) rough estimate of the break-even points based on the estimated win probability if the team were to punt the ball normally rather than attempt to convert on 4th-and-15. The thick red line represents the estimated conversion rate on 4th-and-15; a team would only be recommended to attempt to convert when the break-even point was at or below the red line.