On Monday I discussed the importance of understanding your league parameters. There is perhaps no more important parameter than "replacement value".

While most parameters are set explicitly in the rules, replacement value is set implicitly as a result of them. It's essentially the depth of the league as determined by the roster requirements, number of owners and universe of eligible players. In an 12-team AL-only league with two catchers, a first, second and third baseman, a corner and middle infielder, five outfielders, a utility player and nine pitchers, replacement value is extremely low. The hitters on the waiver wire are mostly fifth outfielders with limited upside, backup catchers and utility infielders without much speed or power. In that case, losing even an average player like Derrek Lee or Carlos Quentin is significant. In a 12-team mixed league, those losses would be negligible.

To determine replacement value, we look at the number of players drafted at a particular position, and see what's left once you remove them from the pool. In a 12-team mixed league with five OF, that means 60 OF are taken, and replacement is roughly the average between OFs 61-70. (We take an average of 10 to make sure our replacement value numbers aren't overly skewed by a couple of speed-only players, or power hitters with low averages). That average represents the rough contributions of the freely available outfielder in your league. If you lose a star OF like Ryan Braun and are forced to pick up a free-agent replacement, you don't lose all of Braun's stats; instead, you lose the difference between Braun and that replacement outfielder. As such, it can be said that Braun's value is not his actual numbers, but the difference between his numbers and the replacement ones, i.e., his value over replacement.

This has big and somewhat counterintuitive implications for Braun's value in a given format. In a deeper one, say a 12-team NL only league, replacement value is low, and so Braun's value over replacement is high. But in that league even Braun's teammate Casey McGehee's value over replacement is high. In fact, nearly every player guaranteed regular at-bats has value in such a format. Whereas in the 12-team mixed league, value over replacement is much higher, the difference between it and Braun's value far less, but Braun is worth |STAR|much|STAR| more. How is this so?

Because in the shallower mixed format, McGehee's value over replacement is almost zero, i.e., subtract out the significant replacement value at third base from McGehee's projected stats, and there's very little left. The shallower the format, the higher the replacement value. The higher the replacement value, the higher the bar to being significantly above it. Therefore in shallow mixed leagues, only the superstars are difference makers. In deeper leagues, every decent player is significant, and there is therefore less of a difference between a superstar and a decent player. Put differently, in a deep league, if McGehee is x above replacement, Braun might be 2x above it. In a shallow league, if McGahee is x above replacement, Braun could be 20x above it.

Consequently, if you're in a 12-team mixed auction, you don't want to use AL-only and NL-only values to guide your bidding. Instead, you'll want to determine player value with your league's replacement level players in mind. You'll find that the stars are worth significantly more in a mixed format and the mid-level players far less.

Once you've established everyone's value over replacement for your league, you still have the problem of determining what to pay for each player. If Braun has 15 more homers 40 more RBI 40 more runs, 12 more SB and 30 points of average in 1.1 times the number of at-bats over a replacement outfielder, and Carl Crawford has 0 more homers, 12 more RBI, 60 more runs, 35 more SB and 20 more points of batting average in 1.3 times the number of at-bats, who is worth more and by how much?

This is the problem of comparing value across categories that I brought up at the end of yesterday's post. To simplify, let's just answer the question I posed - what's more valuable 45 homers or a .340 average in 600 at-bats?

Another way of asking that question is: what number is more of an outlier in its respective category, or what number deviates more from replacement-level production? To find an answer, we need to figure out the "standard deviation" in each category for the pool of rostered hitters and see which number, the 45 homers or the .340 average (adjusted for at-bats), is more standard deviations over replacement and therefore has a bigger impact on a team's standing in that category.

As it turns out, the standard deviation for home runs among the top 168 players (14 offensive players |STAR| 12 teams) in a mixed league was 9.3, and the standard deviation for batting average was 26.5 points. The replacement value for home runs (among all positions) was 9|STAR|, and the replacement value for average was .266. That means 45 homers was 36 above replacement value, or 3.9 standard deviations. The .340 average was 74 points above replacement value or 2.8 standard deviations. But remember that average was accumulated over 600 at-bats. That's 100 - or roughly 1.2 times - more than the average amount (500) for a replacement-level player. When you multiply 2.8 |STAR| 1.2, you get 3.4. Still, the 45 homers were more valuable than the .340 average over 600 at-bats based on last year's stats. But it's pretty close.

|STAR|In reality, that number is low because many of the players in the 169-192 range (the next 24 batters) had their rankings depressed due to injuries. Because an owner would shuttle healthy replacement-level batters in and out of his lineup as needed, replacement level for homers is probably closer to 14 or 15. However, the same can be said for the 500 at-bats on which the 1.2 multiplier for average is based - an owner would likely get closer to 550 at-bats out of a replacement slot. For the sake of simplicity, I omitted these considerations.