Someone posted a question about this in the forums, and I figured it would be useful to address it here, too:
The first thing we do when we evaluate a player is figure out what his numbers will look like. We create a projection for him. Everyone does this to an extent - you look at Adam Dunn and think - he'll probably hit 40, but his average could be around .250. (After I wrote that, I checked out Erickson's projection for him, and it turns out those are his projections exactly!).
But once we have everyone's projected (estimated) numbers, we still have the problem of translating those numbers into a ranking (or dollar value). You can just eyeball it and say you'd rather have Adam Dunn than Andruw Jones, but it gets tricky when we compare different kinds of players. Let's take Ryan Howard's stats from last year - 47 HR, 136 RBI, 94 R, 1 SB, .268 in 529 AB, and Ichiro's: 6 HR, 68 RBI, 111 R, 37 SB, .351 in 678 AB.
Which numbers are worth more? What basis do we even have for answering that? I guess you could eyeball it and decide which one was more of an outlier, but that's imprecise, and maybe you'd pick the wrong one.
To do this more precisely you need to take into account two factors: (1) Value Above Replacement and (2) Standard Deviation
The first one is easy enough to understand. If a player in a 12-team mixed league hits 12 homers, how much is that really helping you? Let's say there are 14 offensive players per team. That's 168 total offensive players. So players 169-190 or so are what we call "replacement value".
Those are the guys on your bench or on the waiver wire. Let's say the average HR total for those players is 10. So your 12 HR guy is really only getting you 2 HRs in that category. If you had a 3 HR guy, he'd be giving you -7 HRs. Remember every roster spot on your team has an opportunity cost. (Even before taking position scarcity into account).
OK, so we can do this value above replacement calculation for each category, pitching and hitting. But we still have a problem. Because let's say Ryan Howard is 37 HRs about replacement, but 12 points below replacement in batting average. Let's say he's plus 60 in RBI, plus 35 in runs, -6 in steals. And let's say Ichiro is plus-76 points in batting average (adjusted for his 678 at-bats which is about 120 percent of the average starter's). And Ichiro is plus 45 runs, minus 2 HR and minus 10 RBI. Which player is better, Howard or Ichiro?
There's no way to know without being able to compare ACROSS categories. How do we know if 47 HRs is worth more than a .351 average in 678 at-bats? The answer: Standard deviation.
Let's take last year's stats as an example: If we take into account the stats of every player in your league, we can come up with the standard deviation (the average amount by which a player differs from the mean) in each category). In other words, if there are 168 hitters drafted (14 hitters, 12 teams), then among those hitters, there's a mean (or average for each category). It might be 20 HR, 80 RBI, 85 R, .280, or something like that. Now if the average amount of home runs is 20, the standard deviation in home runs is the average amount a player differs from 20 home runs. In Howard's case, that number was 27. He hit 27 more home runs than the average. In Ichiro's case, it was 14. he hit 14 homers less than the average. But other players hit 21, just one off the average. Some hit 16, four off the average. If you average out all those differences (27, 14, 1, 4, etc.) for all 168 players, then you find the standard deviation for home runs. Let's say is was 8.
Now remember a player's stats don't start to count positively until they've done better than what's freely available on the waiver wire, i.e., until they are better than replacement value. And in a 12-team mixed league, we argued that the average replacement player was good for roughly 10 home runs. So Howard, who hit 47, was 37 home runs better than replacement. And how good is 37 better than replacement?
We can figure that out by asking the question: "How many standard deviations above replacement is it?" The answer: 37/8 or a little more than 4.5. So Howard's home runs are worth 4.5 on our scale. Ichiro batted .351 in 678 at-bats. How much better was that than replacement? First, we'd look at what the replacement batting average was - .275. So .351 -.275 = 76 points. Then we'd figure out what the average of 168 drafted players was. We came up with .280. We'd need to find the standard deviation - how much is the average difference from .280? Ichiro differs by 71, Howard differs by 12, other players differ by a few, let's say the average is 15 points. (I'm making these numbers up, but just roll with me here). It's 15 points, and Ichiro is 76 above replacement, so he gets 76/15 - roughly five points for average. But, he also has more at-bats than the average drafted player who has 500 or so. So that five points needs to be multiplied by 678/500. So Ichiro gets closer to seven points for batting average.
These numbers aren't precise (I'm making up the SD as we go for the purposes of this question) - though I do think Ichiro's contribution to batting average was probably bigger than Howard's to HRs in last year's context, but you get the idea. You need to compare players category by category in the context of the league to know which is more valuable. It's not simple, but understanding how it works can help you from underestimating average or overestimating other categories - they're all worth the same amount, and the question is really - how much of an outlier is each contribution relative to the rest of the league.
Once you get the number of standard deviations above replacement for each player for each category you can add them up. In Ichiro's case, it might be (and I'm making this up, too): +7 for average, -1 for HRs, -.5 for RBI +3 for runs, +4 for SB. You get 12.5. You can generate a total for every hitter.
To convert that into dollar values, you figure out the total amount of money spent on hitting in your $260 league - let's say $160 * 12 = 1920. That means the total dollar values of the top 168 players need to equal 1920. You add up all the totals (Ichiro's was 12.5) and get a number. Let's say it's 600. You divide 1920 by 600 which is 3.2. So you multiply each player's raw total by 3.2 to get his dollar. 12.5 * 3.2 = $40 in a 12-team mixed league. (Of course, I'm making these numbers up).
Now there are a lot of other components I'm leaving out like position scarcity and projection reliability (Derek Jeter's projections are far more reliable than Justin Upton's, for example), but this at least gives us the ability to compare and evaluate different kinds of players on one cheat sheet.