With the Winter Meetings now starting, the free agent class could potentially become a lot less top heavy very quickly. It is known around the baseball-verse that the Brewers are looking for a starting pitcher. The real question of the matter relates to selecting the appropriate player for the team. But which one?

Of all the players on the market, Ryan Dempster has been linked to the Brewers on a consistent basis. In an attempt to find a way to gauge his value, I searched for a correlation between a particular statistic and both ERA, an overall barometer for a pitcher's performance, and WAR, a way to measure a player's overall value. Eventually, I settled upon examining RA9, or runs allowed per nine innings. This includes unearned runs allowed by pitchers. For a normalization of the statistic, I subtracted RA9 from RA9opp, or the average number of runs scored by a pitcher's opponents per nine innings. To this value, I added a RA9def term for team defense corrections and subtracted RA9role, a factor between starting pitchers and relievers. This was necessary as relievers typically have lower ERAs than starters and this accounts for the variation. Finally, the value was multiplied by innings pitched to give weight to a year by year basis. In the end, the equation for the statistic (RAD) looked like this:

RAD = (RA9opp - RA9 + RA9def - RA9role)*IP

Ideally, this would give the number of runs a pitcher allows above or below what opposition typically scores. Lets examine the relevant numbers for Dempster.

Spanning his career, Dempster has allowed almost 600 more runs than the opposition scores on average. At a first glance, this doesn't sound overwhelmingly positive, but let's look at plots of RAD vs. ERA and WAR

The correlation between the data is not overwhelmingly strong, even after the first year of 7.08 ball is removed, but is still existent. If we can believe this numbers follow a normal distribution, we can cautiously project numbers.

Using these values, Dempster is likely to pitch somewhere between a 3.58 and 5.13 ERA, with a 50% chance he'll perform better than a 4.36 ERA and 1.84 WAR. However, these distributions/correlations could be off due to a small sample size. To account for this problem, more samples were added to the net pool from Dempster's top three comparables on Baseball Reference: Chan Ho Park, Hideo Nomo, and Darryl Kile.

These plots follow the same overall shape and correlation as Dempster's alone, adjusting the range slightly to 3.71 - 5.42, with a 50% chance of 4.57 or better. As pitchers typically do not age well, this is slightly unnerving, given Dempster's age and desire for long term contract.

Something interesting was found on Hideo Nomo's WAR graph:

Unlike the concave shape found in the Dempster, Park, Kile, and Overall WAR graphs, Nomo's displays a convex shape with a stronger correlation. This shape plots a higher WAR value for a given RAD value than the concave shape. Even when the polynomial power was raised to allow the line to fit better, the curve maintained a convex shape. Of the handful of possible free agent targets (Edwin Jackson, Brandon McCarthy, Shaun Marcum, Dan Haren, Anibal Sanchez, and Zack Greinke), only three maintained a convex shape: Marcum, Haren, and Sanchez.

Note: After removing Greinke's high and low seasons, the line flattened out but lost all correlation.

Shaun Marcum

Marcum's first season was removed due to its size and to achieve a better correlation. An odd quirk about Marcum's line is that he has maintained a positive RAD every season. Unfortunately, the correlation is not great and the sample size may be too small or eerily consistent, as there is a 68% chance Marcum pitches between 3.80 and 4.09 ERA to the tune of a 1.6-1.7 WAR. That's too specific to pass the logic test, plus coupled with injury concerns makes the situation not entirely appealing.

Dan Haren

Now those correlations look a little more friendly. Haren has only had a negative RAD twice in his career, once at the beginning and one last year. The ERA projections should be fairly accurate as the correlations are strong and the polynomial matches up with the linear relationship. Haren looks to have a 50% chance of pitching better than a 3.82 ERA and a WAR of 3.03. Though that may be slightly optimistic with injury concerns, Haren appears to be the most consistent, and, albeit, likely the most expensive of the profiled pitchers, strongest candidate.

Anibal Sanchez

Anibal the Animal. Somehow he has made a career allowing more runs than the opposition scores on average while still maintaining a respectable ERA and WAR totals. Though the correlations are not high, Sanchez looks to have a 50% chance of pitching better than a 4.25 ERA and a 1.74 WAR. Maybe he'll keep it up, or maybe luck will catch up with him and he'll settle into a #3 or #4 role.

Disclaimer: All statistical number crunching is fairly elementary and assumptions were broad, there could be no physical basis in these numbers.