01.25.08

A Note on the NFL Single-Season Touchdown Receptions Record

Posted in Math, Sports at 8:24 am by leingang

One of my Math 1a students this past term is a member of the new Harvard Sports Analysis Collective. They enjoy sabermetrics and the analogues in other sports. And it’s not just a hobby; a couple of ivy leaguers (Paul DePodesta and Theo Epstein) have gone on to manage major league baseball teams using statistical analysis to change the way players are valued.

I had an interesting discussion on their mailing list about DVOA, a statistic to measure defense in football which I thought I invented but turned out to have been beaten to the punch by Aaron Schatz several years ago. On a less mathy note, Jason blogged a little bit ago about the single-season touchdown records set recently by Randy Moss and Tom Brady:

The previous holder, Jerry Rice, only played 12 games in the year he caught 22 touchdowns (A 24-day players’ strike reduced the 16-game season to 15. The games that were scheduled for the third week of the season were cancelled, and the games for weeks 4-6 were played with replacement players). Thus, Rice actually caught about 0.40 more TDs/game than Moss (about 1.83 vs 1.44). This certainly does not take away from Moss’ accomplishment, nor does it tell us that Rice was more valuable to the 49ers than Moss is to the Pats, or that Rice had the best receiving season ever and Moss had the second best—and this per/game analysis really doesn’t reveal anything new to us. However, it does remind us how great Jerry Rice was, and we can only wonder how many TDs he would have caught that year had he played 16 games. He won the Associated Press Offensive Player of the Year Award this season.

There’s a similar argument on the other end of the pass, and it seems to be a little more heated because it involves current players. Peyton Manning’s achieved his 2004-record 49 touchdown passes in the span of 15 games. His backup played most of the 16th game because it was irrelevant for playoff positioning.

After 15 games, Tom Brady had “only” 48 touchdown passes, one less than Manning at the same point of the season. Thus Peyton did average more touchdowns per game. So some, mostly Colts fans, will argue that Brady didn’t break Peyton’s record.

This is true as long as you change the record in question. Brady didn’t break Peyton’s record of “most touchdown passes in the first 15 games of a season” or “most touchdown passes per game”. But these aren’t records you’ll find in any books.

On the other hand, Peyton’s passer rating that year was 121.1 compared to Brady’s 117.2 this year. These are first and second all-time, and third-place is another four points down (Steve Young in 1994 had a 112.8).

See the NFL’s record book for passers and 2007 passing stats.

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Tags: statistics, football, hsac

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11.29.07

Game Theory, NFL style

Posted in News, Sports at 11:19 pm by leingang

Shankar Vendatam reported in the Washington Post a while back about the pyschology of football coaches “going for it” on 4th down.

With just over five minutes to play in yesterday’s game against the New York Jets, the Washington Redskins found themselves on their own 23-yard line facing a fourth and one. The team, which was ahead by just three points, elected to do what teams normally do in such situations: They played it safe and punted rather than try to keep the drive alive.

The Jets promptly came back to kick a field goal, tying the game and sending it into overtime. While this particular story had a happy ending for Washington, which won, 23-20, it illustrated the value of an analysis by David Romer, an economist at the University of California, who has concluded that football teams are far too conservative in play calling in fourth-down situations.

You don’t have to be particularly interested in sports to find Romer’s conclusion intriguing: His hunch about human behavior in general was that although people say they have a certain goal and are willing to do everything they can to achieve it, their actual behavior regularly departs from the optimal path to reach that goal.

[…]

New England Patriots coach Bill Belichick is among those who has said he agrees with Romer, and Belichick happens to be one of the more successful coaches in the league. Two Sundays ago, as the Patriots were piling up an astronomical score against Washington, Belichick took a chance on a fourth-down play and got his team seven points instead of the three he might have gotten had the team tried a field goal.

The article goes on to say that most coaches have ignored Romer’s findings. Last week John Madden made a stir when he gave a game plan for the Eagles for their (then) upcoming game against the Patriots:

“I’m not a big guy for going for it on fourth down — but I think you have to go for it on fourth down [in this game] because you have to get touchdowns instead of field goals. It has to be a very, very aggressive approach because offensively, they’re going to take a very, very aggressive approach to you.”

In the middle of the first quarter of the game, the Eagles did go for it on 4th-and-1 at the New England 15. It was basically their first drive, as the Patriots had intercepted a pass three plays into their actual first drive. Generations of coaches have played it safe in similar situations (early in the game, already down 7), kicked a field goal, and tried again on the next drive. But converting the 4th down led to a touchdown which set the tone for the rest of the game: matching scores until the Patriots scored last and forced another two interceptions.

(HT: Sendhil)

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Tags: gametheory, football

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