Today's Fantasy Rx.

I'm tired of Jess's Articles having all the original titles, so instead of Yes, But What Does It Mean? Part II through Part XXII, I hope nobody minds if my titles head towards more interesting instead of exclusively informative.

Pluralitas non est ponenda sine neccesitate

Occam's Razor, translated as "plurality should not be posited without necessity", or more directly, the simplest theory is often the best theory, certainly applies to valuation calculations.

The quantitative categories can be computed with yesterday's fairly simple equations, and in standard 4x4 and 5x5 leagues, CD allows for the easy calculation of either 62.5% or 70% of the required categories. This principle applies more directly to the ratio categories as discussed below.

In order to maintain the ability to continue inflation adjustments for all categories, including BA, ERA, and WHIP, we need to convert these averages into CD equations. We need to compute each player's share of the available dollars in the qualitative categories. Therefore, we need to combine a player's BA with his AB into a ratio of (player's BA value / total BA value).

Every fantasy participant knows that finishing last in a category still earns you one point. Much of the literature on SGP and replacement value derives from this basic premise of "You win just by playing; everyone goes home with something." The worst team(s) in the history of roto still finished with 8 points.

The simplest way to compute a player's earned BA value is by determining how much that player helped you over the last place BA team in your league. If the last place team's BA is .270, all players with a BA over .270 earn positive BA$, players with a BA of .270 earn 0 BA$, and players headed down towards the Mendoza line earn negative BA$.

A player's BA contribution is also obviously weighted by his number of AB. So the calculation of BA$ develops into the following equation:

(Player's BA - BA of Last Place Team) * Player's AB = Player's Batting Average Value (BAV)

To complete the following example, we'll use .2659 for the BA of the last place team. Please be assured that we will return to this calculation later, but for now we need a number.

Phil Nevin compiled 167 base hits in 2001 while accumulating 546 at-bats for a .306 BA. Plugging these numbers into our equation, we find that:

((167/546)-.2659) * 546 = 21.8186 BAV.

Using .2659 as the last place team BA, the total BAV for the top 168 2001 National Leaguers is 1074. Nevin's BAV earns him the following BA$:

21.8186/1074 * $507 = $10.2998.

Now that we've determined these numbers, inflation calculations follow with ease.

We'll remove Albert Pujols@$2 from our list, a reasonable salary for those leagues drafting prior to the finalization of 25-man rosters last season. His .329 (194/590) BA earns him 37.119 BAV. Removing that from the total 1074 increases Nevin's share from about 22/1074 to 22/1043.

21.8186/1043 * $507 = $10.606, again raising Nevin's BA$ by a rounded dollar.

For pitchers, the same equations are adapted for ERA and WHIP as follows:

(Player's ERA - ERA of Last Place Team) * Player's IP = Player's ERAV (Earned Run Average Value)

(Player's WHIP - WHIP of Last Place Team) * Player's IP = Player's WHIPV (WHIP Value)

These numbers may not seem significant when dealing with one or two players, but in many leagues where each team must keep at least five to seven players, usually all below draft value, the remaining player values start rising somewhat dramatically.

Now that we've established that category inflation can be calculated for the qualitative categories, we return to the normal primary benefit of CD over SGP, the reduced degree of risk in calculations.

Unfortunately, due to the mostly arbitrary nature of the "last place team statistic in x category", CD possesses no additional internal validity over SGP in the qualitative categories. John Benson's method uses the median of the projected qualitative statistics as the best approximation for predicting the last place team's statistic in BA, ERA, and WHIP. He states that he arrived at the median after extensive research, and we've enjoyed success using this method in the past.

Instead of discussing a hundred different calculations to arrive at a suitable predicted number, we'll just refer to Occam's Razor. The simplest theory here, the median, already appears to work quite well, so there's no reason to haggle about finding a baseline within this method. Since the median seems reasonably effective, we should use that in calculating BA$, ERA$, and WHIP$.

Most spreadsheets include a median function, so simply replace "League average statistic" in the above BA, ERA, and WHIP formulas with the median of your projected player's BA, ERA, or WHIP. Include all players, not just the top 168 batters to avoid unfairly biasing your BA$ towards the top batsmen.

When using larger data sets, for example including projections for everyone on 40-man rosters, the median's effectiveness decreases as the difference between the number of players drafted in your league and the number of players who you've projected increases. Even a brief glance at statistics from previous seasons indicates that players with less AB often produce worse BA due to both the small sample size and reduced opportunity to their initial poor performance. Pitchers see even wider extremes as several pitchers each year will only start a single game in the majors. Including Joe Borowski's 32.40 ERA in 1.2 IP will unfairly skew the median.

You can't simply remove certain players to enable the use of the median; your projection set must either stay limited to those players on 25-man rosters, including about 225 hitters or 175 pitchers in standard roto leagues, or you'll need an alternative to the median.

The only acceptable alternative at this point appears to be an individual determination of a league's probable last place statistic in the qualitative categories, based upon your past observations and existing trends. Study the previous seasons of your league to determine the acceptable value. Using a league-specific number might cost us even more internal validity, but it also increases the relevancy for your projections for each of your leagues. Remember to ignore any team that appeared to intentionally tank a ratio category; use the second-to-last team's stat in those instances.

I hope I've done a more thorough job of explaining our valuation calculations. Tomorrow, I'll extend the inflation discussion and also develop these calculations into dollar values now that you hopefully understand the underlying equations.

Today's Fantasy Rx: Winter Olympic Opening Ceremonies @ 8/7 Central on NBC. If you can't watch it, tape it, and you'll fortunately miss co-hosts Katie Couric and Bob Costas attempting to out-perk each other in prime time.