Saturday, August 25, 2012

Back in a Zipf

Man, I love me a good Zipf pun.  They’re just terzipfic.  OK, done now.

            In case you’re just joining us, my last post detailed a method for valuing and drafting players coming into the 2012 fantasy football season, although without giving much actual information about how I’m doing it or what I found out.  Ever a man of the people, I’ll see what I can scrounge up in terms of lessons learned.

            First, a recap:

  • It’s much better to evaluate players at different positions when you consider their fantasy production against a replacement-level player at their position, thus allowing us to think quantitatively about how valuable a top quarterback is compared to a top running back, for example.  This value is quantified using points above replacement (PAR)
  • While it’s all a crapshoot anyway, aggregating projections for the upcoming season from a bunch of sources is a more robust way to guess at a player’s output for 2012, because the projections take into account changes in personnel or injury since the end of last season.  That’s the data I’m using to figure out each player’s PAR, and for the sake of this discussion I’ll make the assumption that these projections are relatively accurate, and a good guide for drafting purposes.
  • I claim that if fantasy owners were perfect drafters, they would take the available player with the highest expected PAR for the season (ignoring the issues of what position they play for the moment).  If that were the case, draft order would exactly mirror PAR rankings.
  • The Zipf distribution (for fantasy football purposes) is a graph of each player’s PAR against his rank in that statistic, and looks kind of like a less dramatic exponential decay function regardless of what kind of data you use.  This graph would represent the perfect draft referred to above.

Once I compiled all of this data for each position in its own table as well as combined them into an overall spreadsheet, there were two kinds of information I was looking for:

  1. “Substantial” deviations between average draft position (ADP) and PAR rankings, resulting in points on a graph being far above or below the line formed by the Zipf distribution.  Since it’s a bit too subjective to just look at a graph and make these distinctions, I took the percent difference between these two rankings, and marked those players who showed at least a 1-standard-deviation difference.
  2. “Substantial” dropoffs between two consecutive players’ PAR when ranked by PAR, indicating a gap between two tiers.  This is more valuable within a position, generally.  Again, I figured out players that qualified for this by either looking at a graph or finding greater-than-1-standard-deviation gaps between players.

So what did I learn?  Let’s look at the tape.


1. Despite the hype around the Falcons’ passing game, Matt Ryan is still being drafted too low.  Projections have him outperformed only by Rodgers, Brady, Brees, Newton, Stafford, and Vick, but he’s being drafted below Romo, both Mannings, and Rivers as well.

2. There is a substantial difference between the top 5 (Rodgers, Brady, Brees, Newton, Stafford) and the rest of the position.  To illustrate, the gap between projected 5th QB Matthew Stafford and projected 6th QB Michael Vick is the same as the difference between Vick and the 11th QB, Philip Rivers.

3. Eli Manning is being drafted, on average, with the 43rd pick, around the likes of Mike Wallace, Dez Bryant, and Marques Colston.  When you throw PAR into the mix, it looks like he should be drafted in the late 50’s, around Jeremy Maclin, BenJarvus Green-Ellis, and Willis McGahee.


1. It looks like the projections aren’t as worried about Ryan Mathews’ clavicle injury as the people of fantasy world.  Even giving him only 235 carries, he’s still ranked as the 16th player overall by PAR, just above Marshawn Lynch and DeMarco Murray.

2. There appear to be a few undervalued backs in the top 20, including Shonn Greene, Steven Jackson, Ahmad Bradshaw, and Fred Jackson (in order of how much they’re being underdrafted).

3. After the top three, there’s a tier of 14 backs between Chris Johnson and Michael Turner that is chock full of injury, workload, and holdout concerns (OK, that last one was just for MJD, obviously).


1. Obviously, Calvin Johnson needs to be drafted in the top 10 overall, and it appears that drafters have it right that Larry Fitzgerald is clearly the second receiver that should be taken (drafted on average 6 picks before any other receiver).  After that, there are two big tiers -- 9 receivers between Greg Jennings and Wes Welker, and 13 receivers between Steve and Torrey Smith -- that aren’t really that differentiated from one another.

2. That being said, Fitzgerald should really come back to the pack a bit in terms of draft position, and within that top group, veterans Andre Johnson and Wes Welker are being drafted about a round too early.

3. It’s hard to make a profit chasing last year’s breakouts, but Victor Cruz, AJ Green, and Percy Harvin are still being drafted a bit over their heads (Harvin most of all).


1. This system loooooooves tight ends.  Since they don’t score that many points anyway, there’s not as much room to fall below replacement level, so all the “meh” guys get shifted up.  Of the 35 players whose percent undervalued-ness (?) between PAR rank and ADP is at least one standard deviation above average, 13 are tight ends.

2. The more teams in the league, the less overvalued the top tight ends become (read: Gronkowski, Graham, Gates – whoa, three G’s).  This is because the gap between the 7th and 18th tight end isn’t very big, so adding more players will cause other positions’ value above replacement to increase relative to tight ends.

3. PAR analysis does justify Gronkowski and Graham being drafted in the first two rounds, but it also justifies the strategy of waiting until the end of the draft to take Dustin Keller and Brent Celek instead of taking Brandon Pettigrew, Jacob Tamme, or Fred Davis several rounds earlier.

Hopefully that was at least marginally informative for some people, but let’s be real here, I’m not about to open myself up to exploitation by my family, with whom I have yet to draft.  After that goes down, I’ll give my list of the guys I’m putting my faith in this year, as well as writing up a nice, thorough draft analysis.

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