Same song, third (and fourth) verse

First, let's get the tight ends out of the way, because their story is relatively short, and it's predictable. In particular, it's the same as the story for WRs. To refresh your memory, WR weekly totals are hard to predict. You knew that already. What we learned last week is that, at least from a strictly mathematical standpoint, the only meaningful predictor (that I know of) of how a WR will do in a given week is his year-to-date yardage per game average. TDs don't tell you anything if you already know yardage. Further (and a little surprisingly), knowing how well the opposing defense has done against WRs in the past doesn't help you either. The data says: in general, there is no reason to believe that defenses that have stopped WRs well in the past will stop a particular WR in the future.

All of the above is true for TEs as well: a math geek with no football knowledge would tell you that your weekly TE cheatsheet should simply have the players ranked according to their year-to-date yards per game averages. He'd also tell you not to expect spectacular results from this prediction method. Well, we all know not to expect spectacular results from any TE cheatsheet. The question is whether this naive cheatsheet would do any better than a typical "expert" cheatsheet. At some point, hopefully in the near future, I'm going to automate a system for ranking cheatsheets, and we can find out for sure. For now, here's my guess:

1. A yardage-only cheatsheet might do better than the expert cheatsheets (at least some of them) because I suspect most expert cheatsheets overanalyze matchups. Less is more.
2. A yardage-only cheatsheet would do worse than the expert cheatsheets because the experts can tell which TEs are "actually" good, as opposed to simply having good numbers. For instance, a yardage-only sheet would rank Billy Miller ahead of Marcus Pollard right now. Most experts would rank them the other way around. I'd agree with the experts.

Which of those two effects would win? Probably the second, but I'd like to find out.

Now, the QBs...

This one is a little stickier. First, QB scoring systems vary widely. I'm going to have to apologize up front for not being able to analyze how these results might vary with the scoring system. At this point, my programs aren't flexible enough. Second, there are a lot more aspects to a QB's game than there are to a WR's or a TE's game. A QB can get points via rushing yards, passing yards, rushing TDs or passing TDs. In a lot of leagues, interceptions play a role as well. It turns out that, as you may have guessed if you read the past two weeks, yards (both rushing and passing) are meaningful predictors of future fantasy production, but TDs are not. Interceptions are meaningful, if your league counts off for them. And strength of defense is too.

Using a scoring system of 1/25 per passing yard, 1/10 per rushing yards, 6 per any TD, and -3 per INT, here's the formula my math geek friends would recommend:

Predicted fantasy points = 3 + .052 * PYD + .203 * RYD - 2.65 * INT + .325 * DEF PYD = the QB's season-to-date passing yards per game average RYD = the QB's season-to-date rushing yards per game average INT = the QB's season-to-date interceptions per game average DEF = the opponent's fantasy points per game allowed vs. QBs (compared to league average)

My friends would be sure to caution you that this formula was obtained by looking only at QBs who were averaging at least 8 fantasy points per game and had played at least four games. Thus, we shouldn't attempt to apply it to anyone who doesn't meet those conditions.

Here's what the formula produces for this week:

 Name                  OPP  PYD  RYD   INT    DEF    Proj
----------------------------------------------------------
 Michael Vick          nor  153   55  0.00    2.4    22.9
 Rich Gannon           kan  341   10  1.00    8.3    22.7
 Donovan McNabb        nyg  234   41  0.67   -3.6    20.5
 Drew Bledsoe          det  314    4  0.71    5.7    20.0
 Daunte Culpepper      chi  260   30  2.00    7.2    19.7
 Trent Green           oak  237   18  1.14    4.8    17.6
 Steve McNair          cin  245   20  1.50    3.2    16.8
 Brian Griese          nwe  270   10  1.14    0.7    16.3
 Peyton Manning        was  264    8  1.33   -0.4    14.7
 Jake Plummer          sfo  191   21  0.83   -2.0    14.3
 Tom Brady             den  292    6  1.50   -3.5    14.2
 Aaron Brooks          atl  235   17  1.00   -6.1    14.1
 Jeff Garcia           ari  191   23  0.67   -5.6    14.0
 Trent Dilfer          dal  227    5  1.00    2.4    14.0
 Jim Miller            min  243    2  1.20    3.3    13.9
 David Carr            jax  167   20  1.00    2.5    13.9
 Mark Brunell          hou  197   14  0.67   -2.8    13.3
 Quincy Carter         sea  209   13  1.14   -1.2    13.2
 Brad Johnson          car  221    2  0.71   -4.1    11.7
 Joey Harrington       buf  168    1  1.00    7.2    11.6
 Kerry Collins         phi  261   -1  1.33   -6.6    10.7
 Chad Pennington       cle  184    2  0.60   -3.0    10.5
 Tim Couch             nyj  197    8  1.20   -3.9    10.4
 Chris Redman          pit  172    1  0.50   -5.3     9.2
 Tommy Maddox          bal  198    0  1.25   -4.0     8.8
 Rodney Peete          tam  192    2  0.67  -10.8     8.0

PYD = average passing yards per game
RYD = average rushing yards per game
INT = average interceptions per game
DEF = strength of defense vs. QBs (positive = bad D, negative = good D)

Interesting features of this model:

1. It likes running QBs. Note that, from a predictive standpoint, a rushing yard is worth about four times as much as a passing yard (the coefficients are .203 and .052 respectively) despite the fact that, in this scoring system, a rushing yard is worth only two and a half times a passing yard. What this says (I think) is that rushing yards are a bit more stable than passing yards are.
2. Strength of defense plays a much greater role here than it does for RBs.

Finally, here is the RB list for this week:

 
 Name                  OPP  FPPG   Y/G  DEF  PROJ
-------------------------------------------------
 Priest Holmes         oak  27.9   159    0  21.8
 Fred Taylor           hou  18.0   140    0  19.2
 Charlie Garner        kan  19.3   133    2  18.5
 Travis Henry          det  18.2   114    7  16.9
 Jamal Lewis           pit  15.6   126   -3  16.8
 Deuce McAllister      atl  18.0   128   -5  16.8
 Edgerrin James        was  12.9   119   -1  16.1
 James Stewart         buf  13.9   103   -2  13.9
 Jamel White           nyj  10.0    83   14  13.9
 Stephen Davis         ind  13.4    94    5  13.9
 Corey Dillon          ten  13.1   101   -4  13.2
 Duce Staley           nyg  12.9    99   -3  13.1
 Emmitt Smith          sea   8.3    75   13  12.6
 Tiki Barber           phi  12.0   100   -8  12.5
 Anthony Thomas        min  11.6    86    3  12.5
 Shaun Alexander       dal  17.0   100   -8  12.4
 Clinton Portis        nwe  10.9    83    3  12.0
 Thomas Jones          sfo   9.7    85    1  12.0
 Garrison Hearst       ari  13.1    91   -4  11.9
 Lamar Smith           tam  14.3    91   -7  11.5
 Eddie George          cin  14.0    80    2  11.4
 Michael Bennett       chi  10.1    80   -1  11.1
 Michael Pittman       car   8.9    89   -7  11.1
 Curtis Martin         cle   8.9    69    4  10.3
 Antowain Smith        den   8.0    70   -2   9.4
 Moe Williams          chi  11.5    65   -1   9.0
 Marcel Shipp          sfo  10.7    62    1   8.8
 Kevan Barlow          ari   8.8    68   -4   8.8
 Olandis Gary          nwe   7.2    57    3   8.5
 Mike Anderson         nwe   8.6    56    3   8.4
 T.J. Duckett          nor   7.4    54    0   7.6
 Jerome Bettis         bal  10.6    56   -5   7.1
 Warrick Dunn          nor   8.9    49    0   6.9
 Mike Alstott          car   8.3    48   -7   5.6
 Stacey Mack           hou   7.3    25    0   3.7

Over on the message boards, a poster named "Skippy the one-eyed beagle" has been keeping track of how well my RB formula has been doing against the Bryant/Dodds created cheatsheets from the main page (see this thread. and this one). Preliminary results are that Bryant and Dodds are outperforming the formula by a good bit. I'll talk about this next week.

After that, I'll get off this mathematical model business and move onto something else. As always, let me know if you've got any ideas in mind.

Unless otherwise noted, all stats come from football-reference.com and the disclaimer applies