Okay, so, in the first three parts, we’ve covered Batting, Fielding, and Position Adjustments, and hopefully you’ve been able to see how we’re arriving at the values used for each component. By combining those three parts, you get runs above or below average. However, as I mentioned at the end of the last post, we don’t really know how much average costs, but we do know how much replacement level costs, so we prefer to value players above replacement, as that gives us a fixed baseline of $400,000 in salary – the league minimum.

For a great read on replacement level, check out this article by Sean Smith. In it, he uses his CHONE projections to figure out the offensive production that a team could expect from players not projected to be good enough to make a major league roster next year. These guys have fallen into that Four-A category, where they show more ability than your average Triple-A veteran but not enough to hold down a major league job. They’re usually available every winter as minor league free agents, via the Rule 5 draft, or as cheap trade acquisitions where a team can acquire one of these players without giving up any real talent in return.

As Sean showed in his article, and has been shown elsewhere, the expected value of a replacement level player is about negative 20 runs per 600 PA. Or, to phrase it a bit differently, if you lost a league average player and replaced him with a freely available guy, you’d lose about two wins. That’s why the replacement level calculation in our Win Value formula is 20/600*PA. If you get exactly 600 PA during a season, your replacement level adjustment will be +20 runs. If you get 700 PA, your replacement level adjustment will be +23.3 runs. The more you play, the higher the replacement level adjustment, because you’re filling a larger quantity of playing time and that chunk won’t need to be filled by anyone else.

The replacement level calculation serves to do two things in our calculations – adjust the scale so that the baseline value is $400,000 at zero wins, and rewards players who stay on the field. For instance, Chipper Jones was outstanding in ’08, posting a .446 wOBA and a +4.9 UZR. However, he only racked up 534 PA, so the Braves had to give approximately 66 PA to people who weren’t Chipper Jones. Therefore, Chipper’s replacement level adjustment is just 17.8 runs – we presume that the folks who filled in for him were about 2.2 runs below average in those 66 PA, and that comes out of Chipper’s replacement level adjustment. Players who stay healthy and can take the field everyday have value above and beyond their rate statistics, and scaling the replacement level adjustment to plate appearances rewards them for that extra value.

If you’re having a tough time visualizing what a replacement level player looks like, there’s probably not a better example in baseball than Willie Bloomquist. Over the last three years, he’s racked up 644 PA – just barely more than one season’s worth – and accumulated the following totals:

-16 batting, -3.8 fielding, +0.9 position adjustment = -18.9 runs below average. He’s not a very good hitter, but he can play a bunch of positions, run the bases okay, and doesn’t cost much. He is, essentially, the poster boy for replacement players. By adding in the replacement level adjustment, we’re simply adjusting from saying that Chase Utley is +58 runs above average to +78 runs above Willie Bloomquist. And, since we know that players of Bloomquist’s quality are available for $400,000, we can then value Utley’s performance based off that baseline.

So, that’s wRAA+UZR+Position+Replacement. It comes out as Value Runs, and tells you how many runs above a replacement level player each position player was. Tomorrow, we’ll talk about the runs to wins conversion and the wins to dollars conversion.