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Why a touchdown is worth ten yards

Posted by Doug on October 22, 2007

Last week Chase posted a through-six-weeks list of quarterbacks ranked by what he called "rearview adjusted yards per attempt." The rearview part means that the numbers had been tweaked to modify the differing schedules that each QB had played against during the first six weeks. The adjusted part means that, following some decades-old research by Pete Palmer, John Thorn, and Bob Carroll, he wasn't just using yards, but was rather giving a 10-yard bonus for each touchdown pass and a 45-yard penalty for each interception thrown.

Over at the message board, Chase decided to use that post as a starting point for his case for David Garrard as the league's through-six-weeks MVP. The resulting thread went about like you'd expect it to go, but a little bit of interesting discussion emerged. One of the main points of contention is that someone who has thrown six TDs in five games can't possibly be as valuable as someone who has thrown 21 in six games. That is, many people thought the 10-yard bonus for a touchdown pass is too low. A bit of discussion about the appropriateness of the 10-yard bonus broke out in the comments to Chase's original post as well. So I figured I'd spend a post talking about why I think it's about right.

First, let's get some disclaimers out of the way. It's clear that there is no static TD-to-yard translation that is going to be right for all situations. Some touchdowns are worth more than others, and some yards are worth more than others. We're trying to hit the average here.

Now, the key to understanding this is to realize that we're not saying that a TD is equivalent to ten yards. We're saying that the marginal value of a TD, compared to a non-TD pass of the same yardage in the same situation, is about the same as the marginal value of ten generic yards. Here is a hypothetical situation, which has been sterilized to remove some of the issues in the disclaimer mentioned above.

It's the first game of the season, the first drive of the game. Your team is on offense. You and your opponent are evenly matched. You have first-and-ten at your own 30 yard line. Which would you rather see on the next play?

  • A 69-yard pass that puts you at 1st-and-goal at the one,
  • A 70-yard TD pass, followed by a 15-yard excessive celebration penalty (so you'll kick off from the 15 instead of the 30)?

If you have to think about it --- if it's not immediately clear --- then you must think that the marginal value of the TD, compared to a same-yardage pass that is not a TD, is worth approximately 15 yards. Try this experiment next weekend: take every TD pass you see and ask yourself, "if I were coaching the offensive team, and I could trade that TD for the ball at the one and 10 yards of field position on my opponent's next possession, would I do it?" Better yet, write down how many yards of field position you would trade to erase that TD and put the ball at the one instead. Average those numbers.

I don't know if ten is exactly the right answer, but it feels about right.