One of the cool things to do with a Win Probability model is to look at the total Win Probability Added (WPA) of a player. Each play in a game changes a team's chances of winning either positively or negatively, and the WPA for the plays in which a player takes part can be tallied. WPA discounts 'trash-time' performance, and emphasizes 'clutch' performance. The result roughly measures the past value of a player in terms of what matters most--winning games.
WPA is a narrative statistic. It tells the story of how a player performed, but it does not predict how he'll likely play in the future. It includes all the flukes, miracles, and everything else that makes football unpredictable and fun to watch. In essence, WPA is what the MVP award is all about.
I've tallied the WPA for the notable MVP candidates through Week 12 of the 2009 season. The table below lists various players and their WPA expressed a few different ways. There is total WPA, which is simply a raw sum. There is also WPA per game and WPA per play, which tell a slightly different story.
Right now, according to total WPA Brett Favre is the league MVP, but Drew Brees is in a close second place. Frankly, I'm very surprised. I thought it was the Vikings' defense and Adrian Peterson who were carrying the load for Minnesota, but it's really Favre who's mattered most. A healthy chunk of Favre's 2.4 is from his last second heroic touchdown throw against the 49ers to win the game.
Peterson's negative value is shocking. I double checked it to be sure, and also looked up a few other RBs for comparison. For example, Ray Rice in Baltimore had a total WPA of -1.7, Marion Barber had a WPA of 0.2, and Joseph Addai had a WPA of -0.3. Peterson's fumbles are certainly hurting him, but it's running in general that appears to be the problem. Most runs in the NFL may actually be setbacks, and except for their handful of breakaway runs almost all NFL running backs are indistinguishable--Peterson included. The exception this year is the Titans' Chris Johnson, who is the very definition of breakaway in 2009. He is third on my list with +1.2 WPA.
I'm also surprised by the bad numbers for the Texans' Matt Schaub and Andre Johnson. I guess they've been too inconsistent, particularly in high-leverage situations. I would guess much of their more traditional positive stats have come after a game has effectively been decided.
In terms of WPA per play (or more precisely "per mention"), it's Reggie Wayne who tops the list. Receivers and other positions besides RB and QB don't have their number called as frequently, so it's very hard for them to accumulate a high total WPA. I should note that anytime the intended receiver was apparent on an incomplete pass, his name is mentioned in the play description, and the loss of WPA is charged to both the passer and intended receiver regardless of whose fault it was. But WPA is a narrative metric, so fair or unfair, this is how players are seen and valued.
The WPA system is most unfair to defenders. For example, if the other 10 Steeler defenders miss a tackle and Troy Polamalu is the last guy able to run down a ball carrier for a gain of 20 yards, that's a great play on Polamalu's part. But WPA only see's Polamalu's name mentioned in conjunction with giving up a 20-yard play. If Polamalu missed the tackle and gave up an 80-yard touchdown, his name doesn't even get mentioned, and he's not charged with the loss of WPA. So when valuing defenders, it is probably best to compare them within their position if at all. That is, compare Polamalu to other safeties or Jared Allen to other defensive ends.
Then again, maybe the WPA is most unfair to blockers. You never read a play-by-play description say "10-yard gain by 28-C.Johnson. Great block by 68-K.Mawae."
Unfortunately, at this point I can't just click the mouse to generate a list of the top players. I need to do a search for each specific player, then tally his WPA. So if there are any other players of note that you'd like me to look up, please mention it in the comments.