Years ago when I first started taking part in auction leagues, I wanted to figure out how to calculate the dollar valuations of players but could not find much on web about the topic. More recently there have been discussions (here, which also links to here), and even a website (lastplayerpicked.com) that explained the process in detail, although as of this writing the website is no longer up. Listed below are detailed steps on how you can calculate your own values, where I distinctly include a second method - a league-specific approach - which I use as well.
Step 1: Define your player universe and their projected stats. With Houston switching leagues this year, a typical 12 owner AL-/NL-only league will use fourteen hitters (2 catchers, the 4 infield positions, 1 corner infielder, 1 middle infielder, 5 outfielders, and 1 utility) and ten pitchers, which gives you a universe of 168 hitters and 120 pitchers. Try to make sure that the universe includes the minimum required number of catchers (2 x 12 = 24) and middle infielders (3 x 12 = 36) as those positions contain the weakest hitters.
In terms of the pitcher universe the only factor you should account for is how many starters versus relievers could go in your auction. This is where your type of league will matter; since rate stats (ERA & WHIP) account for half of the 4x4 pitching categories, 4x4 leagues will value relievers higher - whose ERAs and WHIPs are typically lower than the average starter - whereas 5x5 leagues value starters higher because of the strikeout category. What I do in my leagues is account for how many starters have been auctioned off in past years and use that as a guide as to how many will go in the upcoming season. If you are joining a new league or one where you cannot get its past history, you can figure out an "optimal" starter/reliever ratio which is the last step, covered in my next column.
For stat projections there are a number of sources, some of which are free and some at a nominal cost. The first set of projections that I use is the Bill James projections, since they are the earliest available in early November for $9.95. I usually only get them just so I can set up my spreadsheets early. By the time the second Bill James update is available in March, a number of free projections can be used including ZiPS, Marcel, CBS Sports, CAIRO and Rotochamp, to name a few. By Draft Day I will use the average of about four or five free projections, since any more than four or five will not change your overall projections much. I will also adjust or override the projections (at-bats, innings, and saves) based on new information (playing time, injuries, etc.) as Spring Training is in full swing.
Step 2: Calculate the averages of every category. For each of the counting categories (home runs, RBI, saves, etc.), take the sum of the projections of all players and divide by the number of players. For the rate categories (batting average, ERA and WHIP) sum all the projected at-bats, hits, innings pitched, earned runs, hits plus walks to get the averages for those categories.
Step 3: Calculate each category's points of every player. This calculation determines how good or bad a player performs in comparison to an average player in your league. A positive point total means the player is better than average, a negative total means he is worse. The average player will have a point total of 0.0. I will use Mike Trout as an example, who for now I have him projected to hit .314 and hit 29 home runs. For my AL-only league, I am projecting the average hitter to hit .271 and 15 home runs. Listed below are the two approaches I use in order to calculate player point totals.
Step 3a: Counting stats. Normal Method: Trout's HR points would be (29 - 15) / 8.84 = 1.58, where 8.84 is the standard deviation of the projected home runs among all AL hitters in your universe. League-Specific: In the denominator I will look to the past HR standings of previous seasons to see how the value of a home run is influenced in the league. For example, if last year in a 12-team league the HR leader had 250 home runs and the worst team had 180, then the value would be (250 - 180) / (12 - 1)* = 6.36, which is the incremental value of a point in the HR category that year. This would make Trout's HR points to be (29 - 15) / 6.36 = 2.20. The closer the league is bunched together in a category, the lower the denominator in the formula and the higher the player's point total for that category. That makes inherent sense: if the league as a whole values home runs more, then they should be closer together in the standings in that category and players with higher home run totals will have higher "league-specific" value.
Step 3b: Rate stats. Normal Method: First change the rate stat to a counting stat. I have Mike Trout projected to have 189 hits in 601 at-bats. The average hitter in 601 at-bats - hitting .271 - would normally get 163 hits, so the counting stat used would be 189 - 163 = 26 "extra hits". Trout's batting average points would be 26 / 10.1 = 2.57, where 10.1 is the standard deviation of all hitters' projected "extra hits". Those hitters with a batting average below .271 will have negative extra hits and hence negative batting average points, and the more at-bats those hitters have the worse their batting average point total. For the pitching categories, the only difference is that you will reverse the sign in the numerator, since getting a lower ERA and WHIP versus the league averages are a positive for the pitcher. League-Specific: Since batting average is a rate stat, we must also convert the league-specific standings to a rate stat. If the owner with the highest batting average had .280 and the lowest was .260, then the incremental value of a point in the batting average category would be (.280 - .260) / (12 - 1) = .00182. We must then multiply this number by the average projected total at-bats per team. In my 12-team league I am projecting about 74,000 at-bats, or 6,167 at-bats per team. So Trout's batting average points would be (26 / (.00182 x 6167)) = 2.32 points.
Similar to counting stats, both approaches rank rate stats similarly. The best hitter/pitcher with the highest batting average, ERA, and WHIP - while accounting for the number at-bats and innings - will gain the most points in those categories, regardless of which approach you use. As a check in this step, the sum of all player points in each category must equal zero.
Next up: How to calculate auction dollar values, Part 2
*Note: If owners in your league punt certain categories i.e. saves, you'll probably want to exclude them from this calculation by ignoring their spot in the standings, so be sure to remove them both in the numerator and the denominator of the calculation. Also, in the denominator I use (n - 1) teams since in a 12 team league you can only move up 11 spots from the bottom. You could use 12 instead of 11 in the denominator; I just happen to use (n - 1) instead of n. Either way should be fine; it should not have that much impact on your calculations.