Before we get into the auction conversion, there are a couple notes that need to be addressed.
Weighing Rate Stats – We can all agree that a batter that hits .300 in 600 at-bats is more valuable than one who does it in 400 at-bats, right? We have to take this into account and adjust for AB’s and IP in rate stats. Simply multiple a players normal z-score in the batting average category by their AB total. We’ll call this wBA. Once that is done for every player at that position, you take the z-score of those wBA numbers and you have your final batting average value. You do the same with ERA and WHIP as well, using IP instead of AB. It can actually end up helping some players with poor ERA numbers, because having a 5.00 ERA isn’t as bad if it’s only 150 innings. On the flip side, power hitters who play everyday and have a bad batting average will be penalized even more for it.
Pitcher Adjustment – Because pitchers can only contribute to four stat categories (SP don’t get saves, and it’s always best to disregard RP wins), we need to curb their value. I do this simply by multiplying their FVAAz number by 0.8 to reflect the ⅘ ratio.
Inputs - Please note, and this is a biggie, that this system is only as good as its inputs. If your projections are way off, the rankings might be, too.
Now that we’ve gotten that out of the way, we can take a look at how to convert FVARz into auction values.
The auction conversion formula takes into account the number of players on each team, as well as the simple idea that every player taken in an auction has to cost at least a dollar. The conversion formula is below.
[(Team Budget – (1*no. of players per team)) / number of players per team] * (z-score above replacement / average z-score for above-replacement players) +1 = Dollar Value
Note: “Draftable” player are considered to be players who are projected to produce at a level above replacement level.
In our case, a 12-team standard league, it would look something like this:
[(260-(1*23))/23]*(FVARz / average FVARz for above-replacement players) + 1
If you want to make things easier, you can substitute 3.0 for “average FVARz for above-replacement players.” The number varies a bit year-to-year, but it is usually around 3.0. So our final formula is
This formula works because it makes two things clear: The average player should be payed the average amount of money a team can spend on a player, and a replacement level player is worth $1.
A Small Sample Using Marcel
In case you’re having a hard time visualizing this whole process, I have done a small sample of FVARz using the Marcel projections found right here on FanGraphs. The sample is done using a 400 AB minimum, and the positions are done simply based on what Marcel says.
If you want to view the sample, click here and your wish will be granted.
While I was the only one doing any direct work on this project, many others helped me out by letting me bounce ideas off them, and other such things. So, let me thank Michael Jong and Joel Goodbody, as well as FanGraphs’ own David Appelman and Eno Sarris.
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