If you haven't already read about DVOA, then I would suggest starting with that as it is referenced throughout this explanation.
Theory: DVOA isn’t perfect by any means. One of the main issues is that, as it is a “rate statistic”, it doesn’t take in to account the cumulative value of a player performing successfully over a number of plays. Even if a player is performing at the NFL average level, if they can maintain this over the course of a whole season (or an above-average level), then it’s providing more value (than a more inconsistent player). In addition, a player involved in a high number of plays can draw additional attention from the defense. Finally, DVOA wouldn’t give you any idea how much more value someone like Saquon Barkley gives you over his back up (or someone of the level).
DYAR: The guys at FootballOutsiders.com (FO) created DYAR or Defense-Adjusted Yards Above Replacement, to try and counter some of the flaws with DVOA outlined above. They borrowed the “Replacement” aspect from the advanced statistics that have been prevalent in Baseball for years now. The idea is to project what would happen should say, Saquon Barkley’s 261 rushing attempts last year went to someone of “replacement level”. The term replacement level is used because for each different team there is a different back-up running back. There is a much steeper drop off from Barkley to Wayne Gallman than that from Phillip Lindsay to Royce Freeman.
To solve that issue there is a general “replacement level” generated for each position for the given year. In the case of QBs, FO analyzed situations where two or more QBs had played meaningful snaps for a team in the same season, then compared overall DOVA of the original starters to that of the replacements. They do not include situations where the backup is a top prospect waiting in line.
At the other positions on the field, it is slightly harder to differentiate between “starter” and “replacement”. So when created the “replacement level” for positions such as RB or WR, they instead ranked all the players at each position in each season by attempts. The players who make up the final 10% of passes or rushes were used as the “replacement level”.
Once you have the “replacement level” in place for each position for a given year, you can compare players to how a replacement-level player would have done in their place. Thus, give you Yards Above Replacement. The one thing to note would be that if say Wentz has a QB DYAR of 500 yards, it doesn’t literally mean that a replacement-level QB would have gained exactly 500 fewer yards than him. First downs, TDs, and turnovers are all given an estimated yardage value in this system. So, what it really says is that a replacement-level player would have fewer yards and touchdowns (and more turnovers) that would total up to the equivalent value of 500 yards.
Again for a more thorough explanation on DYAR and many other advanced statistics please check out footballoutsiders.com
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