I'm not sure if this strategy has been discussed before (it's pretty simple compared to others I've read on this site, just based on intro stats concepts), but this is what I used last year (and won), so I'm curious if it has any major flaws as I prepare for this year.

First, I enter the projected statistics of the top n players in our league. So, in my league we have 12 teams, 13 hitters (only 1 C), and 9 pitchers. Thus, # of hitters = 156 and # of pitchers = 108.

Second, I compile z-scores for each statistic, which are equal to: (player x's score-league average score)/standard deviation. For any "zero-ideal" stats, where lower is better (e.g., era, ratio, errors), multiply this value by -1. For the counting statistics, the z-score is the final step. However, for the ratio statistics (e.g., oba, slug, era, ratio), there is an additional step. For these statistics, I create a simple ratio score of at-bats and innings pitched by dividing player x's score by the average score and multiply this by the z-scores for the appropriate ratio variables.

Third, add up the z-scores for each category to obtain a player's total z-score. This provides a rank ordering of the players in the league.

My league is auction format, so the next step is to convert these total z-scores into dollar values. This is where I've run into difficulty and could use some help. One thing to consider is position scarcity, which can be approximately measured by obtaining the average z-score at each position and ranking them. I know that the lowest ranked players would be given a $ value of 1 and I believe the average player would be given the average value of my league (i.e, 260/22). However, after that I kind of played it by ear and just gave descending values until they were equivalent to total league spending (i.e, 260*12), with some minor tweaking.

I created difference scores by subtracting my projected values from the values published by the roto times website for what players actually earned last year, and they were fairly accurate. The mean of the difference scores was close to zero and the distribution of the difference scores had positive kurtosis, meaning that more scores were close to the mean than would be expected if they were normally distributed.

I'm pretty sure there is a way to convert these projected z-score values into $ amounts, but I haven't figured it out. Any feedback would be greatly appreciated.

[joncarlos]

One thing you could try, which might be too simple, is to sum up all the Z-scores and divide that number by (n*c) where N=number of teams in your league and C=total salary available (like 12 teams * $260 is $3120).

Then you have a $ per Z score ratio and can find each player's projected earnings by multiplying by their Z-score.

Alternatively, you could break up the pitching and hitting 65/35 or whatever split you want, then divide up each category (so 5 hitting categories would each be worth 13%, or 1/5 of 65%). Assign the total $ value per category and then sum the Z-points in that category, and do the same as above to find each player's dollars per category.

[onejayhawk]

But you are correct. It is. I like the idea of using the Standard Deviation as the scaling factor.

J

[Diamond Dog]

I have used a method similiar to this for a couple of years now. A player that is exactly average in every category will have a z-score of 0. So, I convert a z-score of 0 to the average salary. For example, let's assume a set of z-scores of -3,-2,0,5, and an average salary of 10. What I would do is divide 1 minus the average salary by the absolute value of the lowest z-score. So, here, we'd have abs(9/-3) for a result of 3. Then, multiply that result by each z-score and add the average salary (to make the z-score of 0=avg salary, and the lowest z-score=1). So, we'd end up with values of 1, 4, 10, 25. The problem I've discovered is that this doesn't take into consideration the spread among each position. If every catcher is exactly the same, they'd all have z-scores of 0 and end up with 10 dollar (or whatever the average is) salaries. If they are all the same, their values should all be 1. This fact has caused me to scrap my whole system and start over this year.