Sports Reference Blog

Everything You Ever Wanted to Know About Approximate Value

Posted by Neil on May 22, 2012

We get a lot of questions about our Approximate Value system, so I thought it might be a good idea to re-run this explanatory post from December 2010...

Created by PFR founder Doug Drinen, the Approximate Value (AV) method is an attempt to put a single number on the seasonal value of a player at any position from any year (since 1950). The following links will help explain the theory behind the AV system:

Introductory Blog Posts:

  • Part I - this is where Doug explained, in very broad general terms, what his goal was in creating this metric, and what his strategy would be for building it.
  • Part II - this is where Doug explained, in fairly gruesome detail, how the system works for offensive players.
  • Parts III and IV were posted while Doug was fine-tuning the system for defensive players. He invited readers to give opinions on the results.
  • Here are a couple of examples of uses for the method. Studies like these would be hard to do without an AV-like method.

Doug's Brief AV Explanation:

"AV is not meant to be a be-all end-all metric. Football stat lines just do not come close to capturing all the contributions of a player the way they do in baseball and basketball. If one player is a 16 and another is a 14, we can't be very confident that the 16AV player actually had a better season than the 14AV player. But I am pretty confident that the collection of all players with 16AV played better, as an entire group, than the collection of all players with 14AV."

"Essentially, AV is a substitute for --- and a significant improvement upon, in my opinion --- metrics like 'number of seasons as a starter' or 'number of times making the pro bowl' or the like. You should think of it as being essentially like those two metrics, but with interpolation in between. That is, 'number of seasons as a starter' is a reasonable starting point if you're trying to measure, say, how good a particular draft class is, or what kind of player you can expect to get with the #13 pick in the draft. But obviously some starters are better than others. Starters on good teams are, as a group, better than starters on bad teams. Starting WRs who had lots of receiving yards are, as a group, better than starting WRs who did not have many receiving yards. Starters who made the pro bowl are, as a group, better than starters who didn't, and so on. And non-starters aren't worthless, so they get some points too."

Weighted Career Approximate Value

At the top of every player's PFR page, you will see "Weighted Career AV" and a ranking since 1950. This is Doug's way of balancing peak production against raw career totals; for each player, he computes the following weighted sum of seasonal AV scores:

100% of the player's best season, plus 95% of his 2nd-best season, plus 90% of his 3rd-best season, plus 85% of his 4th-best season, ....

And so on. You can read a more detailed explanation of this metric here.

(Note: "Weighted Career AV" should not be confused with "career AV", which is just the unweighted sum of a player's AV scores.)

Similar Players by AV

On a player's page, you may see a table marked "Similar Players". This uses a method Doug invented to find other players who were similar in terms of the quality and shape of their AV career arcs. You can read more about this process here and here.

Where to Find AV on the Site:

4 Responses to “Everything You Ever Wanted to Know About Approximate Value”

  1. Johnny Says:

    Some the AV links are not working.

    Also, some of the active players do not have their career weighted updated after there were some AV corrections for 2011.

    For example, Ray Lewis has a 158 weighted AV but on the leaders list (active or all time) it still has him at 154.

  2. Neil Says:

    The links should be fixed. Weighted AV will be updated when we re-run the AV stuff (and fix the Jacob Lacey bug, etc.)

  3. Johnny Says:

    Thanks Neil.

    I assume that will include adding pro bowl bonuses to any of the replacements that aren't credited yet (James Harrison, Ryan Clark, London Fletcher for example)?

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