# NFL OT: Where randomness prevails…or not?

A lot of ink has been wasted discussing the OT rules in the NFL.  The argument goes that a lot of power is given to a random coin flip.  In particular, a few years back it used to be the case that the team that would receive the kick-off (which was decided based on a coin flip) would have the chance to end the game with a “sudden death” score (either touchdown or field goal).  A lot of discussion was generated around the impact of the random outcome of the coin flip on the result of the game. Academics have also studied the problem with one of my favorite readings being the work based on the so-called Pythagorean formula. The NFL decided to change the OT rules in 2010 for the playoff games only, and an opening possession that resulted in a field goal did not end the game.  These rules came into effect for regular season games in 2012.

Given that there is so much discussion around this topic I thought why not add some more noise in the discussion with my own thoughts…! There are a few things that I examined using the regular season data for the NFL games for the last 7 seasons (2009-2015).  During this period there were in total 115 games that went into overtime, from which 112 ended with a winner.  Using the rest of the games that did not go to overtime (and excluding the games during the first weeks of each season) I explored the importance of home field advantage and strength differential on the outcome of the game.  The strength differential is captured through the win/loss percentage of the teams during their matchup.  In particular, we model the probability of winning through a logistic regression model:

The feature vector x includes the strength differential of the teams and whether the team is playing home or on the road. This model can be trained (i.e., obtain the coefficient vector a) using the game data.  However, given the very large sample there is the problem that unimportant significant relationships might be picked-up.  Hence, in order to avoid this “Too big to fail”-problem, we trained the model using randomly selected smaller samples and the model obtained is the following:

As we can see the standing differential is significant at the 5% level, while the home field advantage is significant at the 10%.  These results align with our intuition that a team playing in its field has an advantage and that a stronger team is more probable to win.

So this creates our baseline model that we will try to “recreate” using data from the games that went to overtime! We will further differentiate games prior to 2012 – when the old overtime rules were in place – and games after 2012.

Seasons 2009-2011

During this time the old rules were in place.  We have in total 43 games in our set (we exclude games during the fist weeks of every season).  Using these data we train the above logistic regression model, adding this time an additional feature on whether the team received the ball for the first drive of the OT (i.e., won the coin flip).

There are three important observations here:

• Home field advantage and strength differential is not anymore significant
• The outcome of the coin flip is significant at the 10% level!
• The impact of the coin flip is the opposite on what expected/claimed! Teams that receive first tend to lose!

While the reason for the last point is not clear – e.g., it might be the case that defending teams are more alert because of the perception for the first possession and hence, tend to “over-deliver” – what is clear is that the outcome of the coin flip is more important as compared to the home field advantage and the strength difference!

Seasons 2012-2015

During this period the OT rules changed in an effort to eliminate the randomness of the coin flip.  Was this change succesful? Training exactly the same model as above with the relevant data we get:

As we can see the impact of the coin flip (i.e., which team receives the first possession) is not significant anymore! This goes towards the right direction.  Furthermore the home field advantage is significant at the 10% level (similar as in the case of games that did not go to OT).  The strength differential is not an important factor but this might not necessarily be bad (?).

One of the reasons for the insignificance of the strength differential can be the fact that games that end up going to OT might be matchups between teams with similar strengths anyway.  In order to example this we estimated the distribution of the strength differential between the matchups that went to OT and the games that did not.  The following figure presents the empirical cumulative distribution function for the standing differential for the different matchups.

As we can see the differential in the standings of the matchup is very similar for both the games that go to OT as well as those that are decided by the end of regulation.  In fact, the p-value of the Kolmogorov-Smirnov test is 0.56, which means that we cannot reject the hypothesis that the two empirical CDFs  are the same.  Therefore, the non-significance of the standing differential cannot be attributed to different distribution of this differential for the matchups that go to OT.

Another interesting point is related to the number of touchdowns in OT. Prior to 2012, in the 45 games that went to OT, there were only 5 that ended with a touchdown, i.e., approximately 9% of the games.  On the contrary, after 2012, with the new OT rules, 22.3% of the OT games ended with a TD!

Should there be more changes? Clearly I do not have a good answer to this, but I think the sudden death is not a good approach (even soccer has eliminated it).  Even though since 2012 it seems that the lack of the draw is not a factor to deciding overtime games anymore, the strength of the teams also seem to not be important. So one idea would be to let all 15 minutes of OT play out as a regular extra quarter.  If no winner emerges then we can have a situation similar to penalty kicks in soccer; have 3 attempts for a 50+ yards FG that will decide the winner.  We can even skip the 15 minutes and go directly to the FG kicks to keep things short! This is totally based on the team skills at the kicking position (maybe the kickers can again become relevant to the game 🙂 ).  However, one of my favorite ideas is to keep the OT rules as they are now (or even prior to 2012) and use elements of truthful bidding (e.g., VCG auctions) in order to decide which team will receive the ball first.  At the beginning of the extra time the captains of the teams instead of choosing between heads or tails they will provide a sealed envelope to the referee with the yard line they want to start their opening drive from.  The team that bids closer to their own goal line will receive the ball and start the drive.  This will create the potential for interesting game theoretic optimizations that have to account for which line of the team is stronger (offense vs defense), which line of the opponent is stronger (hence, trying to predict the bid of the opponent), historic bids of the teams will be analyzed to inform decisions and so on.  I doubt that the league will go for such a solution but it might be the most elegant and fair while at the same time keeping the OT as short as possible.