Tuesday, August 10, 2010

YAC+ and Truncation

My friends at Football Outsiders have introduced a fascinating new statistic for receivers called YAC+. Bill Barnwell has used the unique charting data that FO puts together every year to try and control a receivers actual performance after the catch for where they catch the ball. The idea is that certain locations lend themselves to higher YAC and some players may have higher YAC totals because they catch more balls in high YAC locations. For example, the data shows that the average YAC on a ball that is caught in the center of the field, five yards form the line of scrimmage is 3.7 yards, while the average YAC on a ball that is caught on the left side of the field at the line of scrimmage is 6.2 yards. Clearyly if a player (mostly RBs) catch more balls on short passes on the left side vs mid range passes in the middle, the player will look better on YAC. Player's who are really good with the ball after the catch, should, in theory, be better that average on a consistent basis, which is exactly what YAC+ tries to measure.

YAC+ goes a long way towards improving our understanding of receivers abilities after the catch (or in the case of Reggie Bush the lack thereof). It does however have a basic mostly correctable problem related to the calculation of the average YAC by location. The estimate of average YAC for shorter passes is likely fairly accurate (though there may be some issues related to different routes run in the same location, but that is for a different post). Longer passes however, have a likely underestimated average YAC. The underestimation comes from the fact that the field is only 100 yards long. When a ball is caught 30 yards from the line of scrimmage, there is only so far a player can actually run after the catch, no matter how good they are. This is known as truncation and what happens is that when the line of scrimmage is the fifty, and a ball is thrown 30 yards down the field, the receiver can't run more than an additional 20 yards even if he could go another 100 if given the opportunity.

The at least partial fix for this, is estimating the average YAC by yardage with linear regression instead of just straight averages (with some smoothing). The graph below shows the average YAC for passes to the left side of the field, by distance from the line of scrimmage.

The graph shows that the calculated average YAC for passes 35 yards down the field is 7.5 yards, while, with basic regression (a weighted regression is likely more appropriate) estimates the average YAC for those passes to be closer to 9 yards.

The underestimate for the longer passes, likely pushes some receivers who catch a higher proportion of long balls up the rankings in YAC+, as they appear to be above average more consistently than players who catch more mid range balls.

All of that said, YAC+ is another significant advancement produced by Football Outsiders allowing us to think and analyze the game from a more and more accurate point of view.

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