More on Adjusted PAR

I've been thinking about how I've been using adjusted PAR (and to a lesser extent, projected points) in draft prep. To date, I've been using a top-to-bottom qualitative ranking for both measures as the basis for a draft order, rather than treating each quantitatively. That begs the question: what does happen if you use xPts and adj PAR as quantitative values, rather than using qualitative rankings?

The short answer is, it depends. Namely, it depends how you take both into account. A straight average of the two is .5*(xpts+adj PAR), or:

This in turn simplifies into:

The quantities (xPts-rPts) cancel out, and by turning ".5" into "1/2" we get:

This is as good a way as any to do it, though you can weight the average if you wish. Weighting it is only going to modify the base ratio (xPts^2)/rPts.

This retains the same basic advantages of adj PAR, in that it squares xPts (putting more value on extra points accrued at the top while bunching players in the middle and bottom), scales for replacement value at a position, and preserves positional rankings.

Using a straight average, though, what we see is a greater weight put on total points. Players at deep positions (large rPts value) move up in the draft. For example, Miguel Cabrera, Adrian Gonzales, Joey Votto, Mark Teixeira, Prince Fielder, and Billy Butler all move up four to ten spots; in some cases it's not more only because they cannot go higher (e.g. Gonzales moving up to #2; he can't leapfrog Pujols since they play the same position but Pujols will score more). This becomes even more pronounced beyond "replacement range," which we'll call anything outside the top-15 at a position.

The reason for this is that within that range xPts rank greatly outpaces adj PAR rank; the latter is negative and so it cannot rank above the total quantity of starting players (for Bernie's Bombers, that would be no higher than #171). The further outside "replacement range" you get, the more pronounced this effect becomes. As an example, take Adam LaRoche. He projects to 469 points, which is #20 among first basemen. This is going to give him a very negative adj PAR (-81.06, to be exact), which is 353rd among ranked players. However, his 469 points is 136th-most overall. Players with discrepancies this large between adj PAR and xPts rankings are going to benefit the most from this new calculation.

The opposite is going to happen at shallow positions, such as catcher. Every single one of the top-20 catchers moves down in the draft order, because (generally) they will have relatively poor xPts rankings but high adj PAR rankings. The same holds true for pitchers, both starters and relievers.

Essentially, at positions where xPts rankings are higher than adj PAR, the players will (on the whole) move up. Where xPts rankings are lower than adj PAR, the players will (on the whole) move down.

This doesn't affect the top of the draft so much, since those players have high xPts values anyway. In fact, the top-10 in my rankings changes in order but not in composition, and while the order changes a lot only three new players move into the top-50 (first five rounds) and four new players move into the top-100 (though the order is shuffled more the more the list expands).

This greater weight on total points is, perhaps counter-intuitively, more valuable in deep leagues (more spots to fill, more teams). In shallow leagues such as mine, you have plenty of opportunities to roster high-point players, so you need to maximize your edge at shallow positions. At first base, the difference between the #4 first baseman and the #8 first baseman is only 50 points, less than a 10% difference. As such, who I get in that range doesn't matter so much. At catcher, the difference between #4 and #8 is 90 points, which is a 21% difference. In that case, it matters a great deal if I miss out on a top catcher. Since everyone can get a good first baseman, it's relatively more important to get a good catcher.

In deeper leagues with more teams and/or more positions (such as corner or middle infield), not everyone can get a good player at a deep position, much less a shallow one. There's also more flexibility if the added positions are more open. In a 10-team league with corner infield, middle infield, and two utility spots (these do exist) one person can play up to four players from any infield position (or six outfielders, or three catchers). The increased flexibility means a set position is a smaller part of your overall roster composition, so the scarcity at that position matters less. It's better for me to draft an extra first baseman (whom I can still start) who will score more points than whatever catcher I have to reach for.

In larger leagues, the percentage of teams in an equivalent position to you if you miss a shallow position is greater. If you miss a top-4 catcher in a 10-team league, then 60% of the teams are scrambling among flawed starters. If you miss a top-4 catcher in a 16-team league, then 75% of the teams are in the same position. How much you're "marginally screwed" by a missed position decreases, so there's little or no point in making sure you get the best of the dregs. It's better to concentrate on where you can actually get points instead, which is usually at a deeper position.

The moral of the story is that there's no right way to use a metric or create pre-draft rankings, but the manner in which use a metric or create rankings has to be carefully thought out. You need to account for roster size, roster flexibility, number of teams, etc. You can create a mathematical/statistical reason for a certain ranking system, but just as often it's as easy or easier to try out a couple of systems and eyeball it. No draft is going to proceed perfectly efficiently, so the general rankings (e.g. how to weight scarcity, the rough area a player occupies) matter more than specific ranking positions.