Value Under Maximum: Position by Statistic Targets

Value Under Maximum is a nice compound measure. At it's core, it is the percentage of best possible production a player gets across all categories slightly scaled for position. In a 5x5 league, a player with a VUM of 5 is leading the league in all five standard categories (and is therefore the best possible contributor in all 5 categories), while a VUM of 0 means the player contributes literally nothing.

But VUM is aggregated by adding the VUM at each statistic/category; and these individual VUMs give you a good idea of who to target given a position and statistic of need. You can do this just as easily by looking at statistic totals, to be honest. But you can set a specific aggregate VUM cutoff first and eliminate players with serious liabilities.

If I may put on my statistics wonk hat for a moment, you can assess "significantly worse than average" by using a 1-tailed student's t-test. For the top 250 batters, that means any player who is worse than the mean by roughly 1.66 standard deviations is, in a statistical sense, worse than average with a probability of 95 percent. What that means is that the projected performance is worse than average by an amount more than what could be accounted for by normal year-to-year differences in player performance.

In a standard 5x5 league, the mean aggregate VUM is 2.52 and the standard deviation is 0.654, meaning a significantly below-average player has an aggregate VUM of roughly 1.44. Using that as a cutoff, we'd actually only be left with the bottom 20 fantasy players. So let's be more lax. Let's put the probability at just better than 50-50, which leaves us with a cutoff value of 2.08. Any player with a VUM of less than 2.08 is therefore probably more trouble than they're worth to roster. But anyone with a VUM between 2.08 and 2.52 is worse than average, but not by so much that they hurt more than they help.

By position, here are the best players to target for a specific statistic who are flawed but won't have a significant downside (parentheses are overall VUM, stat-specific VUM):

First Base:

Runs- Justin Smoak (2.49, 0.61). Home Runs- Justin Smoak (2.49, 0.47). RBI- Freddie Freeman (2.40, 0.62). Steals- Daric Barton (2.21, 0.174). Average- Xavier Nady (2.17, 0.89)

First Base is incredibly deep, and the criteria established eliminate the top-20 1B. In a 10-team league, you don't need to dig this deep.

Second Base:

Runs- Brian Roberts (2.47, 0.80). Home Runs- Bill Hall (2.23, 0.53). RBI- Juan Uribe (2.39, 0.64). Steals- Chone Figgins (2.17, 0.85). Average- Howie Kendrick (2.39, 0.93)

Third Base:

Runs- Placido Polanco (2.45, 0.73). Home Runs- Kevin Kouzmanoff (2.40, 0.43). RBI- Kevin Kouzmanoff (2.40, 0.62). Steals- Placido Polanco (2.45, 0.16). Average- Placido Polanco (2.45, 0.92).

Shortstop:

Runs- Yunel Escobar (2.38, 0.68). Home Runs- Alex Gonzales (2.26, 0.39). RBI- Yuniesky Betancourt (2.31, 0.61). Steals- Alexei Casilla (2.50, 0.51). Average- Starlin Castro (2.39, 0.89).

Catcher:

Runs- John Jaso (1.82, 0.62). Home Runs- Chris Ianetta (1.86, 0.6). RBI- Matt Wieters (1.99, 0.65). Steals- Russel Martin (1.72, 0.28). Average- Yadier Molina (1.77, 0.86)

For catchers, only Mauer has a VUM above the mean and the only catchers that meet the original qualifications are the rest of the consensus top-5 (McCann, V-Mart, Posey, Santana) plus Kurt Suzuki. As such, I simply picked the best catcher that wasn't one of the top-5 for each category.

Outfield:

Runs- Logan Morrison (2.50, 0.72). Home Runs- Tyler Colvin (2.50, 0.52). RBI- Marlon Byrd (2.49, 0.57). Steals- Julio Borbon (2.41, 0.48) or Michael Brantley (2.35, 0.41) if you hate Borbon as much as I do. Average- Logan Morrison (2.50, 0.87).

Consider all these guys mid- to late-round stat boosters. They are the best at the statistic listed at their position who meet the "below-average-but-not-horrendous" qualifications.