Further analysis of pVORP

Earlier I detailed some of the difficulties in calculating value in a roto league. It is certainly more difficult than calculating value in a points league, to be sure. Each category has its own value, and so categories are not interchangeable. Furthermore, though the position of a player doesn't matter insofar as a direct contribution is concerned (as in, you should generally get power from 1B and speed from a middle infielder, but vice-versa yields no net difference), but getting less-than-expected contributions from a position does matter (it's harder to get power if you're not getting it from first base).

This led me to the idea of partial value over replacement player, or pVORP. You take a player's specific contribution to a category (x), and subtract from it replacement production for that statistic at that position (r), and divide by the total production in that statistic from an entire roster of replacement players (R). This yields (x-r)/R, which is essentially excess production given a position and a category/statistic. If you're in a 5x5 league, then every batter has five separate pVORP values, one each for runs, RBI, HR, SB, and batting average. You can then add them together to get an aggregate value for the player.

It's important to note, though, that a team of replacement players would yield one point in every roto category. Moreover, a team of replacement players would be in last place in every category by a significant margin. Positive pVORP values aren't "bonus" production, it's wholly necessary.

Here's a perfect example. Let's say you draft an OF who should steal about 30 bases. A team of replacement players might steal 130 bases, and a replacement outfielder will steal about eight. That makes this players pVORP for steals (30-8)/130 = 0.169. That's a good value, but even if it's the best value in the league all it means is that this particular OF will contribute about 16.9% more steals than expected relative to replacement level. If the remainder of your roster has little or no stolen base value, you'll still end up in last place in the category.

Moreover, imagine you have a 1B who steals 20 bases. Since you expect fewer steals at 1B, replacement level may be around 3. This particular player's pVORP for steals is then (20-3)/130= 0.131. This value is only slightly less than the pVORP for the above OF, but the OF is contributing 50% more steals. It's just that you expect more steals from an OF. The two do not make a comparable absolute contribution, even if they make similar relative contributions.

What this means is that pVORP is best used in comparing players within a position. It gives you a way to quantify the overall value of two different types of players, like Dan Uggla and Chone Figgins. When comparing pVORP between positions, then, some qualifications are necessary. If a 1B has a higher pVORP than a 2B, what it means is that the 1B is more valuable as a first baseman than the 2B is as a second baseman. It does not necessarily tell you which is more valuable overall.

The other thing to note is that pVORP is going to skew a little in favor of players who steal bases. Steals has a top-heavy distribution; replacement level at a position is often in the single-digits and always less than 20, and so the total replacement level for stolen bases is small. However, the best base-stealers can swipe upwards of 40 bags a season. For example, there are multiple outfielders who can steal 40+ bases, but because so many OF are rostered (and steals drops off so quickly), replacement level is only ten bases, give or take a few for roster composition. This skew means that a base-stealing OF will have a high pVORP in steals. This will give them a relatively high aggregate pVORP, whatever their other contributions may be.

There are possible statistics to use instead that would get rid of that, such as a value-under-maximum statistic. You would, essentially, take an average maximum for each statistic at each position over a given period of time instead of predicted replacement level and do essentially the same calculations. For example, if at 1B the average maximum number of HR is 40, then first baseman x has a production under maximum of x-40. You then calculate this maximum value for every position. You then add up these values (say, to 429 home runs). That gives you the number of HR you would get if that were the only stat you focused on. That 1B then has a value under maximum of (x-40)/429. Every player would have a negative value, with less negative values being better. This has flaws of its own, though.

pVORP is a fine stat to use, but like all measures it has its limits. In this case, that limit is that it is best used to compare within, as opposed to between, positions.