Introducing Statistics: Passer Rating

Passer rating is probably the most common stat to toss around when evaluating quarterbacks.  When announcers are covering an NFL game, they regularly update viewers on what a QBs in-game rating is.  But the number itself has no intrinsic meaning.  Touchdowns tell you how many passes a quarterback has thrown that have resulted in a touchdown.  Interceptions tell you how many of a quarterbacks passes have been completed to the opposition.  But what about passer rating what does it do?  First, we need some background to explain why anyone should care.  Next let’s focus on the equation itself.  Finally, we will wrap by highlighting passer rating potential failures.

Quarterback touchdowns are a little like RBI’s in baseball. They highlight the most important part of a sequence while ignoring the rest. In the end, the most important base to advance in baseball is from third to home. Similarly the most important pass is the one that goes across the goal line. But it matters how you get there. If Adrian Peterson takes the ball at his own 3 and breaks a 90-yard run, he does not get credit for a touchdown. If on the next play, Brett Favre completes a 7-yard touchdown pass, he receives as much credit as Ryan Fitzpatrick received for his 98-yard touchdown pass last week. Passer rating is an attempt to correct for the assymetry of Favre receiving disproportionate credit in the example above. To correct for problems like this, Don Smith in 1971 created passer rating.

In college football the formula for passer rating is:

{(8.4 \times YDS) + (330 \times TD) + (100 \times COMP) - (200 \times INT) \over ATT}

In college this number is nearly infinite. A great game goes up and up, while a horrible game continues to drop. The NFL modifies the formula to give an upper bound of 158.3, lower than the number Colt Brennan had for the entire 2006 season at Hawaii of 186.0. This makes the substantially more complicated:

[25 + 10 * (Completion Percentage) + 40 * (Touchdown Percentage)
– 50 * (Interception Percentage) + 50 * (Yards/Attempt)] /12

The extra terms are attempts to cap a quarterback’s performance. Thus NFL quarterbacks can have perfect games, though no one has ever approached that over multiple games.

So what? First, passer rating tells you little when comparing across time. This is a problem in the NFL generally, when the sport regularly expands the schedule and makes the massive change from one-platoon football to unlimited substitutions. Nevertheless rules about defensive pass coverage have also changed dramatically, leading to massive changes in completion percentage that are at the heart of passer rating. Second, passer rating is dependent, to an extent, on factors outside a quarterback’s control. The formula hopes that drops by receivers (a QB’s bad luck) will even out with freakish runs after catches (QB’s good luck). That may or may not be true. Passer rating is a stat that has its uses. A high rating, over 100, tells you someone had a good season. A low rating, under 80, tells you someone had a poor season. But the exact number is meaningless, and you cannot put too much stock in single-game variations or slight gaps between one QB and another.

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