thinking about wWAR

I really like adarowski's wWAR concept.  It's a great way to quickly distinguish those players who were good for a long time from those who were great for a shorter amount of time.  For instance, being a Boston fan, I love Pedro Martinez, and wWAR does a little better than career WAR in accounting for the absurdity of his peak years when considering his overall career in a broad context.  While being aware of the caveat that WAR "means something" while wWAR does not, I will submit that every calculation means SOMETHING, you just have to decide what that something is.  In wWAR's case, it is a zeroth-order approximation of the additional value a team gets from a player who is better than average for a particular season.

There is a common notion that exemplary player seasons are even more valuable to a team's success than their WAR, and I think the intuition is correct.  If you had Josh Hamilton (8 WAR) and Ryan Theriot (0 WAR) on your team last season, they would have the same (theoretical) impact as Vernon Wells (4 WAR) and Brandon Phillips (4 WAR).  But if I told you to choose between the Wells+Phillips duo and Hamilton without specifying the second player, you would take Hamilton every time because the average 2B player will be better than Theriot and will give you ~2 WAR.  That is, major league rosters are limited, and there is an opportunity cost associated with spreading the WAR over more players.  wWAR at least goes in the right direction with this.

Nonetheless, objections have been raised to the wWAR methodology.  In particular, azruavatar notices that the wWAR components are (somewhat) arbitrary (because, e.g., the WAE cutoff is 3 rather than oh-I-don't-know 3.2) and it seems weird that someone should all of a sudden start getting double (or triple) credit for his home runs at some point in the season.  Both adarowski and azruavatar talk a bit about wWAR as a tool to think about Hall of Fame candidates (and I'm particularly looking forward to adarowski's latest project), but I would like to stay away from this since we would all want tools to compare the careers of players even if the Hall of Fame didn't exist.

Anyway, if you think wWAR needs to be improved upon, just replace the components (WAR+WAE+WAM) with another (possibly more complex) function that maps single-season WAR to a number that more accurately reflects the opportunity savings, fear inducement, and overall star power that a great player season affords a team.  The function f(WAR)=Real( (WAR-0.3)^1.3 ) weights value similarly to wWAR, but it is a smooth mapping that removes the arbitrary cutoffs of the wWAR components and starts giving extra credit to anyone above average.

Or perhaps a function like f(WAR)=2*WAR-2 would be a reasonable first-order approximation.  The rationale is that the average player on a team will give you ~2 WAR.  If four of those players could play a single position and occupy a single roster spot, then you'd have Josh Hamilton.  Josh Hamilton takes the contributions from four players, condenses them into a single roster spot, and clears the way for, on average, 6 more WAR from the players who will occupy those 3 other spots.  WAR-2 is the average opportunity gained from having a certain amount of WAR condensed from average players into a single player.  It turns out that the function f(WAR)=2*WAR-2 is pretty similar to wWAR, but it is smooth and it penalizes player seasons that are below average.

In any event, using a smooth mapping like these eliminates the arbitrary cutoffs that some people might find displeasing.  Of course, unless you justify the weighting, the weighting itself will be arbitrary.  But at least in my mind, a function that gives extra credit for excellence is a reasonable tool for considering the careers of players.