One question: have there been studies done to try to look at the position-specific assumptions for a replacement-level player?

It would seem to me that the skill set required to play a replacement level corner OF or 1B is one that is more plentiful than say, SS or CF….mostly from a defensive perspective.

Now obviously the league average offensive numbers are higher at the former two positions (so the replacement level “unskilled” player would have to hit more than the skilled player), but again just subjectively, it seem like there are guys bouncing around the minors or on benches who have isolated power and/or isolated walk ability and maybe some platoon struggles or whatever but who would not murder your team defensively in LF, but not exactly tons of guys with average defense at those more skilled defensive positions like SS or CF.

Moreover, if you could find a roughly average stick in the minors to play one of these “unskilled” spots, it doesn’t seem (to me again) likely that their defensive deficiencies (given the demands of the positions like LF or 1B) would be as large as the offensive deficiencies of a league-average defensive CF or SS replacement. Just on the basis of skill scarcity, after all there are less SS and CFers on the planet than 1B/LF/DHs.

Again maybe these are erroneous preconceived notions, but in general it seems reasonable IMO to expect an injury at a more scarce, skill position to have more of a negative effect on a team than an injury at a LF/1B position. This would then obviously have an impact on the replacement level value calculation WRT positions

I am assuming you all have given this some thought; any studies/articles that really crystallize the decision to use a universal replacement value across positions?

Not a good assumption.

I use roughly:
2.25 wins per 700 PA (non-pitchers) above replacement for the average nonpitcher, of which there are 8.65 per team
+.11 wins per 9 starter innings, for the average starter (65% of innings)
+.05 wins per 9 relief innings, for the average reliever (35% of innings)

Add it up: 2.25 * 8.65 + .11*162*.65 + .05*162*.35 = 34 WAR

Since the average team has 81 wins, then the replacement level would be 34 below that, or 47 wins, for a win% of .290.

(Because wins are not totally linear, an actual such replacement team will win closer to .300.)

Willie Bloomquist is my main man as the perfect explanation of a replacement level player. The only reason he’s been allowed to accumulate as many PA as he’s had is because of his “local flavor”. This is good for us as sabermetricians, because he gives us the sample size we need to prove our point. Most true replacement players will be over and done in under 500 PA.

On the math, two points:

1. I think you are dropping defensive runs allowed from the calculation above. That is, 5.40 FIP * 1450=870 runs allowed. But you still have to add those defensive runs back in as well. FIP was designed to tie in with ERA, not RA. The average AL RA last season was 4.72. So 870/(4.35/4.72)=944 RA.

2. I think you need to be careful about applying AL specific measures to NL players like Chase Utley and Chipper Jones. Your calculation above using NL numbers:

The average NL team scored 734 runs last year. 734 – 208 = 526. That’s your offensive replacement level for a team.

Average FIP for an NL team was 4.28, and the average NL team threw 1446 innings. Based on that, an average NL pitching staff was responsible for 688 runs.

A 5.40 FIP team would have allowed 868 runs. Since FIP/RA for the NL was .9187, I would use 868/.9187=945 runs allowed.

[526 RS^2/(526 RS^2+945 RA^2)]*162 games = 38.3 wins.

That said, a 1.8 exponent is probably better, and that will get you to about 42 wins. I don’t think the real disagreement here is much over the math (but I do appreciate you taking the time to explain how the numbers were derived).

The idea is not to get 25 guys who are below average. The idea is to fill in the 10 spots or so that you have no pre-FA above replacement level players with free agents. Econ 101: spend if marginal revenue is at least equal to marginal cost. Here, marginal revenue comes from the marginal revenue of an additional win (in expectation) times the number of wins extra that you will receive by signing a guy. Marginal cost is dollars that could have been allocated elsewhere.

Don’t think of signings as “taking up a roster spot”. Think of them as replacing a player who is replacement level with a player who is not replacement level.

So you are trying to add those 13 wins with a limited number of FA roster moves. And, even then, you aren’t really trying to be “average”, you are trying to win it all. So really you are still trying to find a way to add more like 20 wins when you start allocating those dollars (and they don’t all go to FA, some go to getting players like Utley and Rollins under contract).

For me, the availability of a significant pool of non FA talent that will perform more cheaply makes it even more important that you generally allocate those FA dollars and remaing roster spots towards players who are at least average or better. I would find it hard to justify spending much more than MLB minimum on a player who was expected to be 1 win below average. A roster of 25 of those guys would only win 56 games. That’s something you can probably accomplish for near minimum.

-20 runs per 600 PA * 6250 PA = -208 runs. The average AL team scored 775 runs last year. 775 – 208 = 567. That’s your offensive replacement level for a team.

Average FIP for an AL team was 4.35, and the average AL team threw 1450 innings. Based on that, an average AL pitching staff was responsible for 700 runs. A replacement level FIP set at 5.40 (combined starters and relievers, obviously they are different baselines for different roles) * 1450 innings = 870 runs allowed.

567 RS^2/(567 RS^2+870 RA^2) = .298.

.298 * 162 = 48 wins for a replacement level team.

Replacement level is about .300 for a team. That does not mean that replacement lever pitchers are .300 and that replacement level hitters are .300. There are different replacement levels for position players and pitchers, but the a team full of replacement players would be around .300.

I suspect that for players with less than six years service time, the average teams gets about 20 wins above replacement level more than their salaries would dictate. Add that to the 48 wins that a replacement level team would get and figure that about $52MM of that payroll is spent on free agents, and you conclude that about 13 wins are bought via free agency. Adding those together, 48+20+13=81, and on average you have 81 wins.

The standard deviation in team performance is about 11 wins. Of this, there is a mixture of randomness due to a binomial distribution over 162 games– if all teams were the same the standard deviation would be about 7 wins by chance. Therefore, a little statistics tells us that the standard deviation in team ability is approximately 8-9 wins. I would guess that most of this 8-9 win discrepancies is probably due to variance in the savings on players with less than six years of service time more than it is due to variance in amount spent on free agents.

This is where being “strong up the middle” can be extremely valuable because the upside of outperforming the average offensive value is so large. Take the 2008 Phillies for example. Jimmy Rollins played SS and provided $24.1MM of value for $8MM, Chase Utley played 2B and provided $36.8MM of value for $7.8MM, Shane Victorino played CF and provided $17.9MM of value for $0.5MM, and Carlos Ruiz played C and provided $2.8MM of value for $0.4MM. That’s $81.6MM of value for $16.7MM. I imagine most playoff teams have huge discrepancies like that. Only Rollins has six years of service time among those four.