The is the third part of a four-part article on 4th down decisions. In the first part, I reviewed the concept of Expected Points and the concept of expected utility. The second part detailed the kicking game and its expected values. This, the third part explores the value of 4th down conversion attempts. The final part of the article will put all the concepts together. Ultimately, I'll conclude with a chart of recommended decisions for 4th downs at every combination of field position and distance to go.
Going For It
The value of a successful conversion attempt would be at least the EP value at the 1st down marker. Often, conversion attempts would obviously go further than the marker, but for now let's consider the minimum value of the conversion. The minimum value of an unsuccessful conversion attempt would be the EP value of a 1st down for the opponent at the spot of the attempt.
The probability of a successful conversion is primarily dependent on the distance to go. Field position also affects the chances of success due to the compression of the field in the red zone. With less area to defend, the defense's task is easier. The graph below plots the probability of a successful conversion by distance to go, broken out by areas of the field.
For example, a 4th down and 3 at the 50 yd line could be converted 56% of the time. A successful conversion would (at worst) give the offense a 1st down at the opponent's 47, worth 1.9 EP. And an unsuccessful conversion would give the opponent a first down at the 50, worth 1.8 EP to them and -1.8 EP to the current offense. The value of going for it is therefore:
A Sample Situation
Let's start with a punt. From the 37, we would expect a net punt distance of 23 yards, coming to the 14 yd line on average. The 14 yd line corresponds to -0.2 EP for the opponent, which is +0.2 EP for your team.
A FG attempt would be successful 45% of the time. A made FG would yield 2.3 EP factoring in the kickoff. A missed FG would give the ball to the opponent at his own 44. This is worth 1.1 EP to him and therefore -1.1 EP to us. The total expected point value of a field goal attempt would be:
Continue reading the 4th and final part of this article.