Wins Above Replacement - Is it taken too seriously?

For some sportswriters, the statistic known as Wins Above Replacement, or WAR for short, is viewed as the end-all, be-all of evaluating baseball players.  The basic idea is this: using the information from a large number of different hitting statistics (or including fielding statistics in the full version), determine the "number of wins" that a player contributes to a team, compared to an average player, over the course of a 162-game season. For a fuller explanation, see, for example, this description at FanGraphs.

The high-level formula is this:

WAR = (Batting Runs + Base Running Runs +Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win)

This statistic is very favorable to players like Mike Trout.  Now Trout is an excellent player - let there be no doubt about that.  He's one of the best hitters in the league, is an excellent fielder, and a strong baserunner who can steal bases.  I just wonder if everything is calibrated properly.

Here's a snapshot from ESPN.com, showing the top 10 hitters in the American League, sorted by batting average.  (Aside: batting average has largely been replaced by on-base percentage in the thinking of modern sabremetricians, but it still is used as a default stat for sorting.)

What interests me here is the disparity in WAR between Trout, Betts, and Altuve versus other hitters who seem to also be having good seasons, like Pedroia and Ortiz.  I should make it clear that the WAR listed above is the total over hitting, baserunning, and fielding.   But curiously, very little of Trout's WAR is from fielding.  His OWAR ius 9.36, compared to Betts' 5.96 and Ortiz's 4.89.  Betts gets a lot of WAR from his fielding - 3.1-3.2, depending on what the round-off error is.  Trout has .6-.5, while Ortiz might get as little as .06 defensive WAR - an unsurprising fact since he only plays defense on the rare occasion that the Red Sox are playing on the road in a National League park  (and even then he takes some games off.) 

I simply don't believe that, as an offensive player, Mike Trout is worth twice as much in terms of WAR as David Ortiz.  Trout has a slightly higher OBP, but a lower slugging percentage.  He has 39 more runs scored, but 27 fewer RBIs, and is much lower in most power categories - fewer doubles and home runs.  Many more walks, but also many more strikeouts.  Trout has the advantage with stolen bases, but still, that's only 26 SBs - one per roughly every six games.  I view stolen bases as analogous to walks - just extra bases to be added to the total base sum.  

So - where does the huge number come from?  I don't know.  There are many explantions like the one above that indicate what WAR is supposed to mean, but I cannot find a closed formula for it that letss me plug in numbers.  I  have found a "Simple WAR calculator" at wahoosonfirst.com, but it doesn't produce the numbers I see above.  

Bill James on the BCS

More precisely, Bill James on the abomination known as the Bowl Championship Series.

James echoes the argument made by Hal S. Stern in the Journal of Quantitative Analysis of Sports against statisticians' participation in the sham known as the BCS.

Stern says:

1. That there is a profound lack of conceptual clarity about the goals of the method;
   
2. That there is no genuine interest here in using statistical analysis to figure out how the teams compare with one another. The real purpose is to create some gobbledygook math to endorse the coaches' and sportswriters' vote;
   
3. That the ground rules of the calculations are irrational and prevent the statisticians from making any meaningful contribution; and
   
4. That the existence of this system has the purpose of justifying a few rich conferences in hijacking the search for a national title, avoiding a postseason tournament that would be preferred by the overwhelming majority of fans.
   

James feels most strongly about 3), pointing out correctly that it makes no sense to involve statisticians when the purpose of their involvement is never defined. Are the rankings supposed to find the team that is most likely to win any head-to-head contest? Or the team that has been the most dominant over the course of the season?

Worse, as James points out, after 2001 any "computer rankings" used by the BCS have been prohibited from using data about the scoring margin when calculating rankings. The professed nobility of this decision was to keep teams (like Nebraska at the time) from running up the scores against weaker opponents.

From a learning theory standpoint (my field), this is breathtakingly stupid. Statisticians are instructed to ignore possibly the most interesting data from each and every contest. Information discarded can only make the resulting system weaker. Thus is, to choose a random example, Rutgers beats Va. Tech by 1 point while Maryland beats them by 55 points, the rating system is instructed to view each game only as "a win".

The decision to exclude margin of victory in any rankings reminds me of the decision of the IOC to ban site visits when deciding to choose the locations of future Olympics. Yes, there has been a lot of abuse of site visits, but the solution surely would have been to have more oversight and regulation of site visits, rather than jettisoning the practice entirely! How can a voter from Oceania decide between a site in Brazil and one in South Africa without being allowed to visit the locations? It's madness! Yes, it can be done, but it's silly to go down that path at all!

I would say that I'm participating in the "boycott" of the BCS, but it would be more honest to say simply that the way the system has been constructed has left me feeling that it's more of a PR exercise than a serious attempt to find out who the best team is. Regardless of who wins the Oklahoma-Florida game, you're going to be hard-pressed to convince me that the team in question is better than USC or Texas.

And that doesn't even bring up Utah, which has gone undefeated including an impressive bowl win over Alabama!

College football needed a playoff including all of the following teams: Utah, Oklahoma, Texas, USC, Penn State, Florida, and Alabama. If the ACC and Big East need to feel relevant, invite Cincinnati and Va. Tech. But really you shouldn't. You'd have been more justified inviting Boise State. Texas Tech is out for being blown out by Oklahoma.

If you are seriously interested in finding the "best" team, then at least the first seven teams should be invited. And yes, I know winning a tournament isn't the same as being the "best team" (see last year's NFL season, for example), but winning a tournament is surely better than winning a single game when participation in the game is based entirely on the arbitrary judgments of voters.