Fun with numbers, NFL-style

I am fascinated by different ways to analyze sports. Thus my interest in a book like “Moneyball” or in this article by Allen Barra that describes using a quarterback’s yards-per-pass as a predictor of winning. I’ve started using this performance metric and, it does indeed have a high R-squared adjusted. Here’s one recent example. In Week 3 the Buffalo Bills defeated the New England Patriots 34-31. Buffalo’s Ryan Fitzpatrick threw for 369 yards in 40 attempts for a yards-per-pass of 9.225. Tom Brady threw for 387 yards but required 45 passes for a YPP of 8.600. In case you’re wondering, Brady does lead the league in the YPP statistic thus far, with 1,327 yards on 133 attempts for 9.98.

Here’s what Barra wrote:

Want to delight and amaze your friends this football season? Try this trick: Next Monday morning ask someone at the office to check the NFL box scores. For each game, ask that person to give you just the number of gross yards each team passed for and the number of times each team threw the ball. With just that information, tell him who won—the odds are you’ll be right.

The team with the higher yards-per-pass average will have won more than 80% of the time.

How will you do it? By dividing the number of yards passing by the number of throws. The team with the higher yards-per-pass average will have won more than 80% of the time.

Why will it be that way this season? Because that’s the way it’s always been in the modern National Football League.

In 1995, George Ignatin and I—we did a column for The Wall Street Journal for several years called By the Numbers—did a study of the first 35 seasons of NFL history, starting with 1961, and found that in about 84% of NFL games the winner was the team that averaged the higher yards per throw. Ten years later I updated the study with California researcher T.J. Troup. The needle stayed at 84%. All research since then confirms our findings: Simple yards per throw—or, as some phrase it, yards per pass (YPP)—is the most underrated statistic in pro football and the single most important indicator of a team’s strength on offense.

YPP also remains, despite its obvious significance, the best-kept secret in the NFL. The next time you’re watching a game, just wait for an announcer to mention Yards Per Pass, but don’t hold your breath.

The pro-football establishment seems bound to the NFL’s official passer rating system, a method so complicated that Matt Damon’s math savant in “Good Will Hunting” would be hard-put to make sense of it.

If you want to try to decipher it, go to the NFL’s explanation at:

Defenders of the NFL’s passer rating are everywhere. For instance,, one of the leading disseminators of football misinformation, recently commented: “Don’t tell us that a stat that identifies winners all by itself 80% of the time isn’t one of the most important stats in sports.” No, all we’ll tell you is that you can get the 80% or better using a far simpler statistic.

The NFL’s demonically complicated method was introduced in 1971 by an analyst named Don Smith and was revised two years later. I’m greatly oversimplifying it, but basically it mixes four criteria: completion percentage, average yards gained per attempt, percentage of touchdown passes per attempt and percentage of interceptions per attempt.

The second and fourth factors are essential—yards per pass attempt and interception percentage correlate with winning the way that frat parties correlate with beer kegs. But the first and third factors are pretty much arbitrary—and complicate the issue without bringing any real value. For instance, why pass-completion percentage? Would you rather complete two of three passes for nine yards or one out of three for 10?

That leaves just the two important statistics: yards per pass attempt and interception percentage. Yards per pass attempt was first discovered by pro football’s pioneer statistician, Bud Goode, who defined the statistic as the number of net yards a team gains by passing, divided by the number of attempts, with a sack counted as an attempt. He called it “Killer Stat 1” and considered it the best basic team statistic. “When I die,” Mr. Goode said to me in 2004, “my tombstone can say, ‘Here lies Goode. He told the world about average yards per pass attempt.'”

Yards per pass attempt ties together the great NFL teams from all eras, no matter the rules or the style: Johnny Unitas and the Colts; Bart Starr and the Packers; Joe Montana and the 49ers; Tom Brady and the Patriots; Ben Roethlisberger and the Steelers; and, most recently, Aaron Rodgers and last season’s Super Bowl champion Packers. Some, like last year’s Packers, throw a lot (about 34 attempts per regular-season game), while others, like the 1966 Packers of Mr. Starr’s best season, averaged just less than 23.

The important point is not how often a team throws or how many yards it gains, but how well its passers throw the ball.

Yards per pass, which leaves out sacks, is an even better gauge of a quarterback’s performance without factoring in the effectiveness of pass blocking he can’t control.

In 1966, Mr. Starr threw for just 14 touchdowns, but his yards-per-throw average was a league-leading 9.0, one of the highest in the NFL over the past 50 years—higher even than Mr. Rodgers, last season’s Super Bowl MVP, who averaged 8.3 with 28 TD passes.

In any era, the great ones lead the league in passing efficiency, and that is spelled with three letters: YPP. There are things that yards per pass attempt can’t quantify: luck, so-called intangibles like leadership, the importance of a quarterback’s surrounding cast (including a strong defense). But YPP gives you better than 80% of it, which is better than any other stat in pro football, and you don’t need a math degree to figure it out. Find out for yourself next Monday morning.

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