A few tweaks to VUM

As I was going over some player projections and thinking about VUM, I noticed one major problem with VUM as a statistic: it doesn't take into account floor effects. That is, generally a major league player can only perform so poorly before losing playing time.

This isn't a big deal for Home Runs or Steals. A player can be productive while not every hitting a dinger or swiping a bag (though probably not both). For some statistics, however, this doesn't hold. For example, a player just by dint of having a certain amount of playing time will score runs and accumulate RBI. No player is ever likely to get none of either. Furthermore, a player can only have so bad a batting average- something in the .220 to .240 range, depending on their power output- before they lose playing time. No player worthy of a roster spot is ever going to hit .000; it was a big deal when Carlos Pena only hit .198 last year. Similarly, if your league counts strikeouts, it's difficult not to strike out at least 40-50 times given an ample number of at-bats.

This is an even bigger deal for pitchers, who have two categories with a high floor: WHIP and ERA. It's extremely difficult for a pitcher with a significant number of appearances to have a WHIP under 1.00 or an ERA under 2.50, and even those would be major accomplishments. Likewise, a player who has a WHIP over 1.50 or an ERA approaching 6.00 is in danger of losing playing time, if not an outright release.

What this means is that some stats end up with a disproportionate weight. A batting average of .200 would roughly translate into a VUM of roughly .652; this is equivalent to 25 home runs (depending on the position). As you can imagine, a .200 batting average is not nearly as good as 25 home runs. You draft people because they hit 25 bombs, you avoid people who hit .200.

The solution, which is rather simple, is to account for the minimum production a regular player gets. This leaves you with an excess (or marginal) value under maximum. You do this by simply subtracting the minimum statistic a player gets given a prediction of playing time I'd recommend 400 at-bats and 40 innings pitched (or if there are specific SP/RP spots, 40 IP for relievers and 100 IP for starters). The formula then becomes:

VUM= [2*(x-min(l))]/[max(l)+max(p)-min(l)]

Where x is a player's production for a given category, max(l) is the maximum value for the league, max(p) is the maximum value for a position, and min(l) is the minimum production for the league.

So using the example above, a .200 batting average would have a VUM of 0 (since it's likely the worst value), while 25 home runs is still a VUM of 0.632. That's a much more accurate description of the relative value of the two performances.

Even with these adjustments, VUM still works exactly the same. It's still a percentage of best possible production (scaled slightly for position), and ranges from zero to one. It's still a ratio, it's still additive across categories, etc.

There is one change (that I probably should have made anyway). When looking at negative statistics (such as ERA/WHIP) where lower totals are better, you simply add (1-VUM) instead of subtracting VUM outright. This change means that the aggregate VUM now ranges from zero to the nubmer of categories (e.g. 0-5 in a 5x5 league) rather than from number of negative categories to number of positive categories (e.g. -2 to 3 for pitchers in a 5x5). It also makes pitchers and hitters more easily comparable. So for example (in a 5x5 league), to get a pitcher's aggregate VUM you do the following (all statistics are VUM values):

VUM= K + W + SV + (1-ERA) + (1-WHIP)

And for hitters you do this:

VUM= R + RBI + HR + SB + Avg

This change doesn't shake up positional rankings any, but it does change the overall rankings some. This matters less now that the season has started, but I'll be using this new definition of VUM for in-season roto and H2H category analysis.