DPAR is Dead

by Aaron Schatz

It's a big day around Football Outsiders. We've now officially put the KUBIAK fantasy football projections on sale [1]. You can purchase them either alone for $20 or in a package with Premium DVOA Database access for $50. (This year, there is no coupon code to get $10 off Premium later on -- you need to purchase them both together at the same time to get the discount.) We've also put the 2008 game charting data in the store; you can purchase that for $60.

We also found out that Pro Football Prospectus 2008 is now shipping from online booksellers. In fact, we even have a reader who found a copy in a Barnes and Noble last Thursday. As longtime FO readers get their hands on America's number one preseason football guide and smash-tastic weapon of mass mosquito destruction, they will page through to look at the comments on their favorite players, and immediately wonder one thing.

Where the hell is the DPAR?

The newfangled statistics we feature here at Football Outsiders are by no means a finished product, and we are always looking for ways to improve them. The best time to do that is usually the offseason, where we can introduce the changes when we publish the new version of PFP. That's what we did when we updated team DVOA to the current "version 5.0" in 2007. This year's project was to work on the individual stats, which needed to be improved in two ways: accuracy and accessibility.

The new version of individual DVOA is based on five years worth of data, 2003-2007, and has a number of changes that will bring them in line with the changes we made the year before in team DVOA.  Individual DVOA ratings now use more complicated (and accurate) opponent adjustments. Passing and receiving DVOA now includes defensive pass interference as a positive play, just like team DVOA does. We found that while there's no correlation from year to year in how often a player gets DPI, the year-to-year correlation of (catches + DPI) is slightly higher than the year-to-year correlation for just catches. In addition, the bonus for plays in the red zone for individual DVOA has been dropped to 10 percent, as opposed to 20 percent for team DVOA. This improved DVOA correlation for players from season to season.

Once we had improved the individual baselines and opponent adjustments, the next step was to improve the accuracy of "replacement level." Originally, we estimated replacement level by simply using a scale similar to the one our partners at Baseball Prospectus use for hitters and pitchers, putting replacement level about three-eighths of the way between average (0%) and the worst starters in the league. For example, since the worst quarterbacks are usually around -35% DVOA, the replacement level was -13.3% DVOA. It was time to come up with something we felt was more accurate than "this is sort of based on what BP does."

For quarterbacks, we analyzed situations where two or more quarterbacks had played meaningful snaps for a team in the same season, then compared the overall DVOA of the original starters to the overall DVOA of the replacements. We did not include situations where the backup was actually a top prospect waiting his turn on the bench, since a first-round pick is by no means a "replacement-level" player. By comparing the replacement-level quarterbacks to the quarterbacks they replaced, as well as the quarterbacks who played the entire season, we determined that the replacement level for quarterbacks is roughly -12.5% DVOA, fairly similar to what we had before.

The same is not true at other positions. There was no easy way to just separate running backs and receivers into "starters" and "replacements," since unlike at quarterback, being the starter doesn't make you the only guy who gets in the game. Instead, we decided to use a simpler method. First, we ranked players at each position in each season by attempts. The players who made up the final 10 percent of passes or runs were split out as "replacement players" and then compared to the players making up the other 90 percent of plays at that position. This took care of the fact that not every non-starter at running back or wide receiver is a freely available talent. (Think of Jerious Norwood or Anthony Gonzalez, for example.) Replacement level is now higher in most ways, but by different degrees, and replacement level actually went down for both running back receiving and wide receiver rushing

That takes care of the improvements to accuracy, but what about accessibility? This has admittedly been a problem at Football Outsiders since the very beginning. The challenge of any new stat is to present it on a scale that's meaningful to those attempting to use it. DPAR (Defense-adjusted Points Above Replacement) came about because the DVOA system measures success in "success points" that represent yardage and progress towards a first down all wrapped together. Saying that Carson Palmer was worth 106.3 success value points over replacement in 2007 has very little value without a context to tell us if 106.3 is good total or a bad one.

The solution to this problem was to translate "success points" into "actual points." I put together a complicated spreadsheet that estimated how many "success points" ended up in X number of points scored, combining both offense and defense, and we used that estimate to translate success values into DPAR. For example, Carson Palmer in 2007 was worth 51.8 passing DPAR.

Unfortunately, DPAR isn't exactly the easiest thing to understand either. The reason is obvious: Do you know anyone who refers to a player's value by how many points he scored? I mean, we know touchdowns are six points, and we talk about kickers in terms of points when we talk about fantasy football, but people don't think of football players in terms of points. They think in terms of yards.

Therefore, along with the new set of replacement baselines comes a new way to think about Football Outsiders' advanced stats for individual players: DYAR, or Defense-adjusted Yards Above Replacement. Carson Palmer's season is now worth 1,215 DYAR, which ranked sixth in the NFL last year. By comparison, Jeff Garcia's season was worth 694 DYAR, Rex Grossman's season was worth -168 DYAR (yes, below replacement level), and Tom Brady's season was worth an all-time record 2,788 DYAR. Turning "success points" into yards was actually easier than turning "success" into points, since we happen to have tangible yardage totals for all the players we are measuring.

Here's a comparison of the top players in 2007 according to the old method (DPAR) and the new method (DYAR).

There are a number of reasons why players shift around a little with the new DYAR values. Drew Brees is hurt by the slight rise in replacement level, because he had so many pass attempts. The more complex, more accurate opponent adjustments make the difference between DVOA and VOA smaller for some players (Tony Romo) and larger for others (Ben Roethlisberger, who now ranks 11th). Changes in the baseline for various down-and-distance situations will have a small impact on every player, in ways that are hard to see without breaking it all down. Of course, small changes in our stats should not be treated as gospel truth. We believe the new individual baselines and formulas are more accurate, but it is possible that the next time we improve things, David Garrard's 2007 season will move back ahead of Tony Romo's 2007 season. So don't flip out when, for example, the 1995 quarterback stats finally go up and you see that Brett Favre's MVP season, which was number one when I first ran the numbers [2], now has a passing value 30 DYAR behind Scott Mitchell and 22 DYAR behind Erik Kramer.

The changes are larger when we look at old individual DVOA and new individual DVOA, primarily because improving opponent adjustments tends to move extremely high and low DVOA ratings towards the mean. Minimum 100 passes here, as usual.

Translating player performance into yardage rather than points allows us to introduce one more statistic, which we hope will make Quick Reads much more accessible to the general population of football fans. The new stat is called Equivalent Yards (EqYds). It is very simple: Equivalent Yards (EqYds) are DYAR with replacement-level performance added back into the total. This provides an easy comparison: in general, players with more Equivalent Yards (EqYds) than standard yards played better than standard stats would otherwise indicate, while players with fewer Equivalent Yards (EqYds) than standard yards played worse than standard stats would otherwise indicate.

(Note July 8: Unfortunately, as some readers have noticed, Equivalent Yards (EqYds) does not seem to be showing what we thought it was supposed to show. We're looking into how we can fix it.)

Here's the same list of top ten quarterbacks from 2007 in DYAR, along with the top ten quarterbacks in Equivalent Yards (EqYds) and in standard passing yards.

Obviously, Equivalent Yards (EqYds) are not the best way to measure value because they are heavily dependent on usage. That's why Jon Kitna and his 616 pass attempts (including DPI and sacks) rank eighth in Equivalent Yards (EqYds). The fact that Kitna has more actual yards than Equivalent Yards (EqYds), however, gives a clear indication that Kitna's performance was generally below average (-1.2% DVOA, to be exact).

For those curious, the replacement level is 4.93 yards per pass attempt. However, it is 5.63 yards per equivalent pass attempt, "equivalent pass attempts" being the translation of the "league-average" baseline on all that quarterback's passes into a pass attempt number. The reason for the difference is that there end up being more "success points worth of pass attempts" than there are actual total pass attempts. Yes, this is complicated, but the good news is that nobody needs to see the gears behind the curtain on a week-to-week basis.

The colors in that table reflect that numbers on the player stats pages will now be color-coded. DYAR and DVOA, the main opponent-adjusted stats, will be blue. Equivalent Yards (EqYds) will be red. Everything else will be the usual black.

How will this affect Quick Reads? The plan is to still list players by DYAR, but to give an example, here are the top quarterbacks from Week 14 of 2007 in standard passing yards.

That was the week Peyton Manning eviscerated Baltimore on Monday Night Football, with 249 yards on just 17 passes, while Tom Brady threw for nearly 400 yards against Pittsburgh. You can see how things change when we look at the same quarterbacks through the lens of Equivalent Yards (EqYds) and DYAR.

It might sound like things will get confusing with all these stats, but it won't, because not every one of these stats will exist from here on out. As of August, Football Outsiders will never be using DPAR again. Pro Football Prospectus 2008 lists all players in DYAR, and we'll list all players with DYAR and Equivalent Yards (EqYds), not DPAR. Right now, the 2007 stats pages have been changed to represent DYAR instead of DPAR. You can take a look at quarterbacks [3], running backs [4], tight ends [5], or wide receivers [6]. Over the next couple weeks, I'll be writing a series of articles looking at the best and worst seasons and games of the DVOA Era (1995-2007) according to the new stats. As we do each position, we'll put up all the DYAR and Equivalent Yards (EqYds) stats going back to 1995. Yes, finally.