The Roto Grotto: z-scores applied

Z-scores based on the target stats for various roto tiers can be applied to specific team circumstances. Previously, the zTotal columns which were driving my overall value order were context-neutral. They could tell which players to select with your first pick in a fantasy draft based only on their final 2012 stats and league scoring, but overall value may not be what you need depending on your team composition, your accumulated statistics, and your distance from specific roto point tiers.

First, you need to have all of the means and standard deviations I use to calculate the Z-scores for each tier, so you can apply them given your situation in this and future seasons. These numbers are per game:

With that, let’s run through a couple of examples.

From my first one of these articles, I mentioned a hypothetical league where Team B needed steals and Team C needed batting average (both were chasing Team A in their respective categories). Let me flesh out the details. Theirs is a 10-team league—which has been my assumption for all of the Z-scores I’ve used. I’ll assume that Team B currently has five roto points in steals and could jump to six if he passed Team A. I’ll also assume that Team C currently has seven roto points in average and could jump to eight if he passed Team A.

For Team B, here is a table of player values based on the six roto points benchmark for stolen bases:

For Team C, here is a table of player values based on the eight roto points benchmark for batting average (which I left unscaled for at-bats because of the proximity to the end of the season in the hypothetical example. I’m just assuming that all listed players are receiving playing time):

The first thing that stands out is just how much more dispersed stolen bases are than batting average. It makes sense. A player that can’t hit won’t last in the majors for long, but a player than can’t steal can still be a great player.

So, what trade should Team B propose? Well, any positive Z-score player is one that will help him improve in a needed category. In other words, trading Joey Votto for Sam Fuld is a win for him in the sense that Fuld has a higher zSB than Votto does, and that is the only category that can make an impact for him.

Most fantasy players will probably never find themselves in a situation so idealized. However, that is why Z-scores can really become useful. Since these Z-scores are built around a target mean based on expected points needed to reach a certain roto tier, a trade where each side’s total Z-score based on his context—his ability to gain and lose roto points in various categories—is equal is a fair-value trade.

In the example, Joey Votto has a zAvg of 1.61. For Team B to break even in terms of contextual value, he needs to trade Votto for a player with a zSB of 1.61 or greater. Since stolen base is such a dispersed category, that should not be hard to do. Players like Angel Pagan and Dewayne Wise are close advantageous players he could target on Team C, if Team C has either player.

Again, a situation where an owner should want to trade Joey Votto for Angel Pagan is probably unrealistic. One that is more plausible is between owners—who I will call Team X and Team Y—at the start of the season and where Team X has decided to punt batting average.

Since the season is just starting, I’ll assume Team Y is targeting eight roto points in all categories. His top-25 looks the same as the generic one for his point benchmark (this time I am scaling average for at-bats):

The numbers are a little different than in previous articles because of a small code fix.

Meanwhile, Team X knows he will get one point in batting average, so he has to try to win every other category. His top-25 looks a bit different:

The top-10s look pretty similar because those players are major contributors in all categories. I expanded the lists to 25 players so you could see the biggest moves, B.J. Upton and Curtis Granderson. Removing the one category that hurts them makes each player a top-15 values and a likely trade target for Team X.