from Amazon
Friday, February 09, 2007
The worth of SB, HR, and all other categories, in Fantasy Baseball
This is how I would value my players for a Fantasy team. I’ll lay out the basic framework, then you can adjust it for your particular rules.
This is a 5x5 league, with 2 players selected at each of the 8 positions, plus 10 pitchers. This is a 21-team league, drafting players from all 30 teams (i.e., the league is made up of 70% of the major league teams… if you draft an AL-only league, that’d be 10 fantasy teams). The total number of players is 336 hitters and 210 pitchers.
The categories are: AVG, R, RBI, HR, SB, and W, SV, K, WHIP, ERA.
The basic formula for hitters is:
HR/7.4 + SB/7.8 + xH/7.8 + R/17.2 + RBI/19
where:
xH = H - AB*.277
And for pitchers, it’s:
W/3.8 + SV/7.2 + SO/41 + xER/5.2 + xWHIP/9.5
where:
xER = (4.10-ERA) / 9*IP
xWHIP = IP*1.32 - H - BB
Now, how did I come up with all that? Let’s look at “HR/7.4”. What the “7.4” represents is the standard deviation of HR among the pool of 336 hitters expected to be selected in the draft. You could technically make it:
(HR - 14.5) / 7.4
And that would represent the player’s z-score (number of standard deviations from the mean). Ortiz and Ryan Howard for example are forecast for 40 HR, making their HR z-score = 3.5.
Now this equation:
(HR - 14.5) / 7.4
is really this:
HR/7.4 - 14.5/7.4
So, you can see that the second term is a constant for all players. We don’t need to carry it, but if it’ll make some people feel better, go ahead and carry it.
That’s all we’re doing, is calculating each player’s component z-score, for their 5 components. You simply add up their 5 z-scores, to get their overall score.
There is a little thing with the batting average. In this case, we’re looking to see how many hits above the pool mean is. The players are expected to hit .277. Pujols for example is forecast to hit .331. But that .331 is better than some part-time player’s .331. So, you can just take .331 minus .277 and divide by the standard deviation. Instead, you figure out how many hits above .277*AB he’ll be. Same applies to ERA and WHIP.
For pitchers, you figure out the total score of each pitcher, and report back the score for the 211th pitcher. That’s your baseline, and that pitcher is set to 0. Everyone else is readjusted to that level. For example, Dennys Reyes is +1.41 units. Santana is +19.07 units. So, relative to the 211th pitcher, Santana is +17.66 units above replacement level.
You repeat for the hitters, except in the case of the hitters, you look at the 43rd player at each position. The 43rd 1B has +20 units, and the 43rd SS has +12 units. Unadjusted, Pujols was +39 units, which gets reduced to +19 units. Jose Reyes, unadjusted, was also 39 units, but he’s now adjusted to +27 units.
Up until here, I’m perfectly happy with everything I’ve said. I haven’t played in 15 years, so I’ve never really had to think about the rest of what I’m about to say. Feel free to chime in.
Now, the issue is to convert the units-above-replacement-level into dollars.
I have a total of 3117 hitting units, and 601 pitching units.
With a minimum of $1 per player (26 players in all), that’s 234 marginal dollars per team; I’ll simply split on a 16-10 basis between hitting and pitching (I don’t think this part is right, which I’ll discuss in the future).
So, 234x21x16/26=3024 dollars for hitting and 1890 dollars for pitching.
Therefore, multiply a hitter’s units by 0.97 and a pitcher’s units by 3.14, and we have our conversion.
Jose Reyes is worth 28$ and Santana is worth 57$. I’ve got 9 pitchers ranked ahead of Reyes.
I’m positive my units-above-replacement methodology is correct, and I’m pretty sure I’m wrong about the units-to-dollar translation.
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Note: I know the roster rules I’ve set forth are pretty basic. I’ve also only counted a single position for each player, his primary position. You’ll have to adjust the framework to fit under your rules.