Thursday 20th June 2019

A Touchdown is Worth Three Times as Much as a Field Goal (But Only Twice as Much as a Safety)

A Touchdown is Worth Three Times as Much as a Field Goal (But Only Twice as Much as a Safety)

If you read that headline, you might think I’m bad at math. The answer, though, depends on the formula you are using. If you look only at a touchdown as 7 points, a field goal as 3, and a safety as 2, then it seems silly. But think of a NFL game as a series of smaller contests. Each starts with a kickoff, and ends when one team scores, by touchdown, field goal, or safety (or time runs out). Then, another kickoff occurs and another mini-contest begins.

So rather than 7 vs. 3 vs. 2, football presents an algebra problem where it’s 7 + P vs. 3 + P vs. 2 – P (Where P is average expected points for that next mini-contest). If P is approximately 1, then my title statement is true. When you score, you then give your opponent the next possession advantage if P is negative (that is, your opponent is more likely to score next). In that way, it’s like tennis, where the server has an advantage. The difference, of course, is that the advantage doesn’t automatically alternate, and the size of the “win” matters.

Now, before I go any further, I want to acknowledge that I’m not inventing the wheel here, but I still think it’s important to re-iterate and refresh some points known by a minority of us who study the game, for those that may not have been exposed. This same rationale has been part of football analysis for awhile. “The Hidden Game of Football” was published 30 years ago, and looked at expected points based on field position. Professor David Romer published his famous research “Do Firms Maximize: Evidence from Professional Football” almost 15 years ago. (Doug Drinen of Pro Football Reference did a breakdown of Romer’s work). Brian Burke did work on expected points added (EPA) on a per-play-basis using similar rationale.

Romer had looked at the first quarters of games from 1998, 1999, and 2000, and concluded that the value of a kickoff was -0.62 (The P in my case). That represents the expected points following a kickoff, for as many possessions as it take for the next team to score. It includes immediate kickoff return touchdowns surrendered, turnovers, punt exchanges, and doesn’t just represent the points surrendered on the next drive following the kickoff.

By Romer’s measure, then, a touchdown (followed by a kickoff) is worth roughly 6.4 points, while a field goal would be worth 2.4.

Again, though, that data was from twenty years ago, and we’ve seen offenses continue to explode in the NFL, and we’ve seen changes to the kickoff rules in terms of both the starting point and the touchback starting spot.

Which brings me back to my statement that a touchdown is worth three times as much as a field goal.

I went through the first nine weeks of the 2017 season. Unlike Romer, I looked at the first three quarters (and this is because I don’t see that teams adjust their strategy until much later than the first quarter when it comes to bleeding clock or sacrificing points for win probability). I excluded all kickoffs that happened inside the last minute of the first half, and only included kickoffs in the third quarter that reached a resolution to the “mini-contest” by the end of the quarter. So, for example, let’s say one team scored near the end of the first quarter. I would then record who scored next–and how much–even if it happened with 20 seconds left. If there was no remaining score before , I would count that as a net zero for that contest. I went through all the eligible kickoffs and recorded who scored next, and how much.

There were 757 eligible kickoffs from Weeks 1-8 of the 2017 season, and the average expected points (for the kicking team) for the next mini-contest was -1.09. Possession may be nine-tenths of the law, but it seems to now be worth more than nine-tenths of a point. At slightly more than one point after a kickoff, a field goal would really be worth about 2 net points, and a touchdown worth about 6 net points.

It should not be a surprise that the value is higher than what Romer found based on data from 20 years ago (there’s also the possibility that the value of a kickoff would have moved toward -1 if the second and third quarters are included, as scoring tends to be lower in the first quarter).

What does this mean? Well, we’ve known coaches are too conservative anyway. But as the relative value of a touchdown versus a field goal increases, the break-even point for going for it changes, and teams should be more aggressive.

That will only increase as the value of possession increases as turnovers go down and pass efficiency continues to escalate.

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