During a draft, and throughout a season, we’re presented with many trade-offs in fantasy baseball. It’s pretty easy to get a good sense of what your team’s strongest and weakest categories are, and one of the toughest question a GM faces is how to approach trades and free agent acquisitions. Should I bolster my strongest categories and try to construct a team that’s so good at a few categories that they’re “automatic wins?” Or should I focus on my weak areas, and trade talent from categories I’m doing well in for talent in my weaker categories?

For a lot of managers, that question is one that leads to decisions based on gut feel. However, with a little bit of math you can get quick insight into what the correct avenue to pursue is.

When examining the question of which category to improve, the first step is understanding that not all performance is equally valued. Vince Gennaro explored this idea a few years ago when he wrote about the monetary value of a player’s performance. In short, going from 90 to 92 wins is far more valuable than going from 70 to 72 wins, because the former carries with it a significantly higher chance of reaching the postseason.

Extending that thought, a team trying to sign a player worth two additional wins should be willing to pay more for that player if their win projections are in the 80s or 90s, versus the 60s or 70s. Note too, that at 105 or 110 wins, additional talent becomes superfluous (at least for the regular season). A team that wins 105 games is all but guaranteed a playoff spot, and getting 107 wins is just extra icing on the cake. Icing that isn’t worth paying for.

So let’s apply this to fantasy baseball. I took a look at one of my 12-team head-to-head leagues from this past season, and recorded the weekly runs and RBI that each team put up. Because I eliminated All-Star week and double-week postseason play, I have 272 run totals and 272 RBI totals. The overall mean was 30.6 Runs and 29.5 RBI. What does this tell us? If you’re a team that can expect to score 30 Runs or 30 RBI, you can then expect about a 50/50 chance of winning that category for the week (to keep things simple, I’ll continue this article as though the means were both 30). What we want to know is: How much does it help our chances of winning if we go from an expectation of 30 runs to 31 runs? Likewise, what about going from 25 to 26, or 35 to 36?

If each additional run and RBI carried with it the same value as any other, we’d have a linear chart. Looking back at my 272 samples, no team scored more than 50 runs in a week and no team scored less than 14, so you could graph the value of each run versus your chance of winning like this:

However, as Vince outlined, not all wins (or runs, or RBI) are worth the same amount. We can look at standard deviations to examine how performance impacts one’s chances of winning. Scoring the exact mean number of runs would by definition be 0.0 standard deviations from the mean, and that comes with an expected win percentage of 50%. Consulting a table of standard deviations, I can see that being 1.0 SD above the mean would lead to an 84% chance of winning, and likewise being 1.0 SD below the mean would lead to a 16% chance of winning. Here is a complete chart showing the interaction between standard deviation and winning percentage:

Going back to my 272 observations of run totals, the samples had a mean of 30.6 runs and a standard deviation of 6.9 runs. So the mean of 30.6 is the point at which a team has a 50% chance of winning, and one standard deviation above that is 37.5. A team scoring 37.5 runs would be expected to win about 84% of the time. Here is the same chart as above, but with run totals in place of the standard deviation numbers:

The steepest portion of the line indicates the most marginal gains per additional run. As you move away from the mean (in either direction), the line flattens out; changes in Run totals at each end have very little impact on a team’s chance of winning a matchup. So let’s answer the original question: If you’re looking to improve your team, what categories should you look to trade into? Find the categories in which you’re at the steepest part of the graph: the mean. Whether above the mean or below it, gains in expected runs (or RBI, or wins or batting average) near the league average will bring you the greatest returns in terms of winning.