Extra point for putting kickoff through the uprights? Do Tucker and Harbaugh have a point?

Justin Tucker and John Harbaugh made the case this week for making the kickoff a little more interesting by giving the chance for an extra point if the ball goes through the uprights.  I have to admit that in the beginning it sounded strange, but then I thought of various reasons why this is not that bad of an idea after all.

First of all, one of the reasons that the NFL changed the touchback rule this year was to increase  the number of touchbacks and hence, minimize the collisions between the kick returners and the special-teams defense. However, this might lead to other kickoff strategies such as pinning the ball inside the 10 yard line so as to force the return and hence, the goal of the new rule is not achieved (I still need to crunch the data for this but this will be part of a different post).  By giving the possibility for an extra point after the kick, this can potentially further increase the number of touchbacks and thus, achieving the original goal of the league.

Secondly, depending on how this extra point rule is designed it can make for some very interesting decision making from the coaches with regards to the PAT.  If both kick PAT and 2 point conversion attempt PAT are followed by the chance of an extra point kickoff, then nothing is going to change in the decision of the coaches to go for two or not.  This is because the difference in the expected outcome between the two PAT alternatives will remain the same (and even though the 2PT conversion has been shown to have higher expected points, the difference is small and coaches appear to prefer to maximize the risk adjusted return- that is, expected gain over the variance).  I have identified two variations though that can potentially move teams away from the kick PAT as the default and automatic decision.

I. Extra kickoff point only after a 2PT conversion attempt

In this first alternative the extra kickoff point will be allowed only if the team attempted a 2PT conversion for  the PAT.  Hence, the expected outcome from a 2PT conversion attempt would be:

s_{2PT}\cdot 2 + s_{kickoff}\cdot 1

where s_{2PT} is the success rate for the 2 point conversion and s_{kickoff} is the success rate for the kickoff attempt going through the uprights. This means that compared to the current situation going for 2 will provide an added benefit of $latex s_{kickoff}\cdot 1$ points, thus further increasing the benefit from the 2 point conversion as compared to the extra point PAT.  Of course this added benefit depends on s_{kickoff}.  Tucker said that he thinks he can have a 20% success rate, but given that most of the kickers do not have as strong of a kick, I would think that a success rate of around 8-10% is more possible.

II. Extra kickoff points depends on the PAT decision

The second alternative provides the same benefit in terms of points but has a different framing that can potentially have an impact on whether coaches will alter their decision making or not.  In particular, in this alternative the team that decided to go for the PAT kick, will have the chance to get one point at the kickoff, while the team that attempted the 2 point conversion will have the chance to get 2 points at the kickoff. Of course, the additional expected benefit from choosing to go for 2 is still $latex s_{kickoff}\cdot 1$, i.e., exactly the same as the above alternative.  However, given the different framing there might be different decisions made.

My hypothesis is that at the first scenario more coaches will decide to go for 2, while in the second case more coaches will decide to go for the kick PAT.  Maybe though they use good analytics and will avoid the impact of the framing effect…However, the idea put forward by Justin Tucker and John Harbaugh should not be dismissed without thought!

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