How to fix the 'perfect game'

Trent McCotter has written about numbers and sports for Baseball Digest, the Baseball Research Journal and has contributed statistical notes to nearly every Major League baseball team. His work has been cited in the New York Times and ESPN.com. A graduate of UNC and a second-year law student at UNC, he will write a weekly Sunday column on the connection between sports and statistics.

The NFL's perfect game

Athletic perfection is supposed to be easy to recognize: you bowl a 300, score a 10.0 in gymnastics, or retire 27 straight batters in baseball. But perfection in the NFL is 158.3. That's the highest Passer Rating score that a quarterback can receive in a game. A quarterback who scores 158.3 is considered to have thrown the NFL's version of a perfect game.

The Passer Rating stat has become the preeminent measure of quarterback skill.

At first glance, perfect games seem rare. The Arizona Cardinals' Kurt Warner had last season's only 158.3 game, and just two former ACC quarterbacks have had one -- Duke's Sonny Jurgensen with the Washington Redskins during the 1965 season, and Maryland's Dick Shiner, with the Atlanta Falcons during the 1973 season.

East Carolina's Jeff Blake had a perfect rating in a game during the 1995 season with the Cincinnati Bengals. No Carolina Panthers quarterback has ever thrown a "perfect" game. The best rating for a game by a Panthers QB is 143.4, by Jake Delhomme in 2004 (19 of 24, 214 yards, four TDs, no interceptions.)

But if anything, these perfect games are not rare enough and have been occurring more frequently than ever in recent seasons, leading some to call for a change in how the statistic is calculated.

Common perfection

The problem with the Passer Rating is that quarterbacks are becoming more efficient. From the 1970s to the 2000s, completion percentage has increased by almost 20 percent, and 45 percent fewer interceptions are being thrown.

Since Passer Rating rewards completion percentage and punishes interceptions, modern quarterbacks are repeatedly hitting the statistical glass ceiling and are throwing more perfect games than ever before. In the 1980s, there were only seven; in the 2000s, there have already been 15.

Passer Rating explained, sort of

Given that a perfect score is 158.3, it's no wonder that determining Passer Rating usually requires a calculator. In fact, the formula involves too many components to fully include in this article. Suffice it to say, the rating awards considerable points for a high completion percentage -- successful passes divided by attempted passes -- and levies a substantial penalty for interceptions.

For example, a perfect game must include a passing percentage of at least 77.5 percent, a yards per attempt of at least 12.5, and no interceptions. Touchdowns per attempt also factor in.

So far, so good. However, in the days before personal computers could solve complicated calculations, Passer Rating was calculated using printed tables of numbers. To keep from having an endless list of tables, all of the components of Passer Rating were given limits. For example, once a quarterback hit a 77.5 percent completion percentage, he could not get any more points for that stat. Even if his completion percentage was 100 percent, he still would only get credit for 77.5.

Out of tradition, the NFL still keeps these statistical limits, even though they no longer use the old tables. As a result, a quarterback's Passer Rating cannot exceed 158.3.

Improved perfection

Football analyst Pete Palmer, author of "The Hidden Game of Football," has recommended an improvement to the Passer Rating calculation. Palmer's suggestion is to remove the arbitrary maximums that keep quarterbacks from receiving additional points when they complete more than 77.5 percent of their passes, or when they throw for more than 12.5 yards per attempt. That is, break the log jam at 158.3 simply by awarding more points to a quarterback with a 90 percent completion rate than to one with a 78 percent rate.

For example, if we don't cap Tom Brady's stats for his Week 7 game versus Miami in 2007, then his Passer Rating goes from a "perfect" 158.3 to a "better-than-perfect" 211.1. In fact, Brady's Passer Rating for that game would be the second-highest ever, trailing only a 216.7 game by Johnny Unitas in 1967 -- six years before the Passer Rating was adopted in 1973.

If we use the version that doesn't impose the arbitrary maximums, Delhomme's best rating goes to 160.8 (the 94th highest-ranked game ever).

While there would no longer be a magical number that represents the ceiling of quarterback performance, removing the arbitrary limits for each component would once again allow quarterback contribution to be meaningfully ranked.

It remains to be seen whether the increasing frequency of perfect games will force the NFL to reevaluate one of its most influential -- and complicated -- statistics. Ultimately, the most telling sign that a 'perfect Passer Rating' has failed to live up to its name is that four of the 52 quarterbacks who have recorded a single-game rating of 158.3 lost the game.

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