The End-Game

Late in the game, when the score is close, it's pretty obvious what the trailing team needs to do. They need to score. But what about the team ahead? Should they try to score and pad their lead? Should they pass the ball instead of running it, risking interceptions and stopping the clock? Or should they rely almost exclusively on the run, limiting risk and letting the clock run?

Combining two concepts of utility in football--expected points (EP) and win probability (WP), I'll analyze team strategy in the 4th quarter. Ultimately, we'll find out if NFL coaches are making the right strategy decisions in the end-game. If my analysis is correct, it would have meaningful implications for NFL strategy in close games.

Recap

Before I get to the meat of my theory, I should review the concepts on which it's based. EP is the average number of points scored next at each field position. For example, at an opponent's 10 yd-line, a team can usually expect about 5 points on average. But on their own 10, a team would expect -0.5 points because the opponent is actually more likely to score next. For the NFL as a whole, here is what the EP curve looks like for a 1st down at each position on the field.


WP is the probability a team will win a game given the current score, time remaining, and any other relevant variables including field position, down and distance to go, and time outs remaining. Here is a graph of WP for selected score differentials. So far I have not made adjustments for field position or other variables, but we can already notice some very interesting things. To read the graph, each curve represents the WP of the team with the ball for a given point differential. For example, a team with the ball and a 7-point lead at halftime (30 min remaining) has a 75% chance of winning.



Observations

In the graph above, notice how the lines are somewhat steady until some point late in the 3rd quarter/early in the 4th quarter when they suddenly diverge. As time dwindles, teams with small leads become far more likely to win, and teams that are behind see their chances diminish rapidly.

Something big happens right around the 4th quarter mark that changes the nature of the game. This seems to be the point where teams stop playing a conventional contest of point maximization, and they start maneuvering for the end game. Teams that are ahead would take fewer risks while teams that are behind would take greater risks. Both teams would start managing the clock, either jockeying for that extra possession or running down the clock.

Also notice the purple line--the WP for teams with the ball and trailing by -1 point. Throughout much of the 2nd half, a team with the ball, down by 1 point, will probably win the game. I was a little surprised by that at first, but I shouldn't have been. The EP curve above shows that possession of the ball at anywhere past a team's own 30 yd-line is, on average, worth more than a point.

Effectively, this means that throughout much of the 4th quarter, teams on defense with a one point lead are already losing. They just don't know it yet.

Further, and more surprising, is the overlap in WP for teams with a +1 point lead and a -1 point deficit. In the first several minutes of the 4th quarter, a team with the ball that's down by 1 is actually more likely to win than a team with the ball and is up by 1!

What? How Can That Be?

Why would a team be better off being down by a point than ahead by a point? I think it has to do with mindset and risk tolerance. Teams that are down increase their risk tolerance and teams that are up decrease their risk tolerance. My theory is that, in general, almost all offenses usually play below the optimum risk level. They should typically be playing more aggressively. But teams may actually start to optimize when behind in the 4th quarter. Teams with small leads would restrict their risk tolerance even more, tilting further from the optimum risk-reward balance.

Consequently, teams with a very small lead need to count on the high likelihood that the opponent will score, and strategize accordingly. They should play as if they're behind, before they actually do fall behind. When the trailing team scores (and they probably will), it may be too late to become more aggressive and try to reclaim the lead.

If I'm right, we should see the EP curves for teams with small leads look different from teams with small deficits. The chart below illustrates the 4th quarter EP for teams with a +1 point lead (green), tied (red), and a -1 point deficit (blue). The data set has been narrowed considerably compared to the overall NFL expected point curve, so the curves are a little noisier, but the trends are clear enough to draw conclusions.

The chart excludes the last 5 minutes of the 4th quarter. The final minutes are excluded because teams with leads of any size could simply run out the clock and leave little or no time for an opponent to score. I wanted to be sure to exclude this final possession from the analysis which would bias the results. (I'm not cherry-picking the data, as including those final minutes actually makes the differences more stark.)

4th Qtr Expected Points by Field Position for Selected Point Differentials

The EP curve for trailing teams is much higher than the curve for teams with a lead. In other words, teams behind by 1 tend to score more points than teams ahead by 1, given a first down at any field position. Trailing teams appear to be playing much closer to the optimum risk-reward balance, and teams ahead seem to be playing far too conservatively.

There is one point at which teams with a +1 point lead become more efficient. That's inside the 20 yard line. Teams behind by a point, knowing they're within field goal range, tighten up. They effectively have a 2-point lead at this point and reduce their risk levels accordingly. Teams ahead by a point appear to keep grinding toward the end zone when inside the 20. Keeping the drive going keeps the ball out of the hands of the opponent and burns time off the clock. So the added risk of the continuing the push for the end zone may be balanced by the advantage of keeping the ball out of the opponent's hands. By this point in the game, you don't want to score too quickly.

Teams that are tied even seem to be playing very timidly. Their EP profile is very similar to teams with a +1 point lead. If tied teams or teams with a lead simply played normally, or even slightly less conservatively, they'd win more often.

My advice to NFL coaches would therefore be to become more aggressive with a small lead in the 4th quarter. In fact, whatever it is teams do when down by 1 in the 4th quarter, do that all game long, even with a small lead. Go for it on 4th down more often, go no-huddle, and air it out. You'll score more and prevent your opponent from scoring more often. Ultimately, you'll win more often.