Tango on Baseball Archives

Redefining Replacement Level (June 26, 2003)

Nate Silver has his (excellent) take on Replacement Level.

At Fanhome last year, several of us were also discussing this concept of time-dependent replacement level*, and we talked and talked, but never got around (and talked and talked!) to getting something done.

Nate's approach I like. As he pointed out, you can put in refinements to account for selective sampling, positions, park, etc. But, the brilliance of it is that it's so darn simple-loooking.

(*) Check back later today, and I'll post something.
--posted by TangoTiger at 06:26 AM EDT

Posted 9:48 a.m., June 26, 2003 (#1) - Patriot
I think this is very interesting because we(mostly you and Rob, actually) discussed this from the perspective of a team, and how expansion teams went from replacement level to .500 in X years. He comes at it from a different approach that gives similar results. Looking back at the thread in question, I see that you had a rough formula based on the team approach, W/L=.12ln(X)+.65, with X being years. If you convert this to a run ration rather than a win ratio and compare to Nate's formula using his assumption of 800 runs and 650 PA, you have:
YEARS Repl-Nate Repl-Tango
1 .76 .81
2 .84 .86
3 .88 .88
4 .92 .90
5 .94 .92
6 .96 .93
The estimates get further apart as you go, but it is encouraging to see some similar results from two approaches based on the same general concept but approaching it in radically different ways.

Posted 10:31 a.m., June 26, 2003 (#2) - tangotiger
Patriot, good stuff! I had forgotten about that equation. (I think I was looking for something where it would cap at a ratio of 1, and never got around to it.)

The other thing that we should remember is that Nate groups them by classes, when really, we want the aggregate to that point. For example, if you have a 10-yr time frame, you don't want the guy with 5000 AB, but *all* the guys up to the guy with 5000 AB. I'm not sure if I'm saying it correctly.

From that standpoint, I would guess that you might get similar results (as this would slow down Nate's curve) using completely different approaches, which as you say, is a great thing.

As well, we have to remember about "chaining", which is a concept that Patriot I think introduced. This is easier to think about with hockey, where you have 6 defenseman, each getting ice time based on their (perceived) talent. When the #1 guy goes down, the other 5 get more ice time, and the 7th defenseman comes in to play with limited ice time. The #1 guy was replaced by a combination of the other 5, and this 7th guy. When the #6 guy goes down, the #7 slides right into place. The "replacement level" is higher for the #1 guy than the #6 guy, because of the chaining effect. In baseball, it's a little different because of the positions not being so interchangeable, and the talent depth not being so even at each position/team.

Posted 11:04 a.m., June 26, 2003 (#3) - Patriot
"The other thing that we should remember is that Nate groups them by classes, when really, we want the aggregate to that point. "

So you're saying that Barry's first 500 AB should be included in that group, right? Because when we start out(ignoring minor league data), we can't tell the difference between Rey and Barry. Makes sense.

Posted 4:23 p.m., June 26, 2003 (#4) - Vardibidian(e-mail) (homepage)
Just trying to understand here ... comparing career values, we'd want to adjust for Raffy, because if you replaced his 2400 games, you'd wind up doing it with a string of guys, some playing 5 games, some 50 games, some 500, etc., and the guys who play 5 would really stink. Is that it? And the more games you play, the more likely the string of guys would might otherwise have played would include stinkeroos?

I got thrown by the transition between the narrative part and the "Here, let's look at the data" part. I followed that the value of Posada has a lot to do with how much you'd lose by replacing him at little or no cost, and that that value is different at different times. I missed where Posada and his potential replacements were on the graph.

Thank you,
-Vardibidian.

Posted 4:28 p.m., June 26, 2003 (#5) - David Smyth
There is little question that this approach gives a "true" answer to some question or set of questions. Therefore it will be useful in certain lines of analysis. The problem I have with it (and also chaining) is that it does not answer the "main" question about player value, and is thus not a very good format for the general evaluations or comparisons of ballplayers.

Posted 4:40 p.m., June 26, 2003 (#6) - tangotiger
Using a running total of Nate's numbers, I'll add a 3rd column to Patriot's chart

YEARS...Repl-Nate...Repl-Tango... running-Nate/Tango
1 .76 .81 .80
2 .84 .86 .85
3 .88 .88 .88
4 .92 .90 .91
5 .94 .92 .94
6 .96 .93 .95

and it caps out at 1.00 at 11 years.

Posted 5:31 p.m., June 26, 2003 (#7) - Walt Davis
Well, this is better than the other two Silver articles that he brags about at the beginning of the piece (and he misstates his own conclusion from the Coors piece which was that high-K, low-BB hitters benefit). (I bring that up only because I almost stopped reading the piece at that point)

Nevertheless, the problems with defining replacement level are just another reason to measure relative to average. Sure, there are advantages to replacement level, but they quickly disappear if either you don't know where replacement level really is or calculating proper replacement level becomes cumbersome.

By the way, average C EQA for 2003 is listed as 254, and Flaherty's is listed as 244 (not 220 as Silver wrote), which puts him just below average. That's better than Miguel Olivo, Geronimo Gil, and even Bobby Estalella and Charles Johnson. In fact, by my count, he's got a higher EQA than 11 starters and 16 backup Cs. Last year the average C EQA was 246 and his EQA was 239, again just below average, so it's not a complete fluke. Sad as it may be, he would seem to be well above replacement level (at least on offense).

Which gets us back, in its way, to Nate's (and others) point about problems with replacement level. According to BP's site, 72 C's have played in the majors this year and 30 (40%) of them are below replacement level. Unless there are at least 18 above-replacement level C's in the minors, we would seem to clearly have replacement level set too high. Otherwise it is in fact nearly impossible to get a replacement-level replacement C.

Posted 6:02 p.m., June 26, 2003 (#8) - Patriot
I'm not sure you can make judgements like that based on 1/2 season at one position. Catchers are quite possibly picked for their defensive contributions more than their offensive contributions, and it seems as if backup catchers especially tend to be catch and throw type guys, and most of the guys who are listed by BP as below replacement have few PA. The great majority of the starting catchers rate as above replacement level as we would expect.

Posted 6:04 p.m., June 26, 2003 (#9) - David Smyth
"Nevertheless, the problems with defining replacement level are just another reason to measure relative to average."

No. Why is it better to use an "exact" calculation which has limited real-world utility, than a more "inexact" calculation which has proper real-world relevance? That might satisfy the human urge for math exactitude, but the "primary" goal should be to try to measure, as best possible, what logic tells us is a better concept of value.

It is better to simply recognize that many/most below-avg players have value, and to try to come up with a reasonable model for that, then to get bogged down in an obsession with getting a stat which is mathematically exact.

So, give me 80% of avg, or 75% of avg, instead of 100% of avg.

Posted 8:06 p.m., June 26, 2003 (#10) - RossCW
No. Why is it better to use an "exact" calculation which has limited real-world utility, than a more "inexact" calculation which has proper real-world relevance? ... what logic tells us is a better concept of value.

It seems to me that measuring from a barely discernable starting point means you have to account for that in the result. You may have a tape measure accurate within inches - but the actual accuracy of your measurement is closer to yards or even miles if your starting point is that far off.

The problem I have will Silver argument is that it seems to move from a theoretical replacement level to a practical one. From a practical standpoint, replacement players available to a team for little or nothing are the ones already on their major league roster. Any other player at minimum requires opening a roster spot and exposing some other player to waivers. Moreover teams use both the major league and minor league rosters to store spare parts. So if a team doesn't have a player on those rosters who meets the replacment level then it is likely because one wasn't available to them. That means the real replacement player level is the worst AAA replacement catcher (distinguishing replacement catchers from starting catchers who are prospects but may currently be even worse than their backup).

Posted 8:35 p.m., June 26, 2003 (#11) - FJM
I'm surprised that no one has mentioned there is a serious problem with the regression in the paper. It can most easily be seen if you put his first table into a spreadsheet. Then multiply n, the number of players in each group, by Mean PA. This gives you the number of PA's for all players by group. For example, in the 1-5 PA group we have 53 players averaging 3.8 PA's each, or a total of 201 PA's. At the other extreme we have 24 players averaging 7,271 PA's, or a total of 174,504 PA's. (Actually, the next-to-last group has even more: 49x4,835=236,915.)

So, what's the problem? Regression proceeds by minimizing the sum of the squared errors, ASSUMING that the data at each point along the regression curve is equally significant. But that is obviously violated here. When you have around 200,000 PA's, you can be very confident that the measured value is very close to the real value. When you have only 200 PA's (from 53 different players, no less!) you really can't conclude anything at all. Yet the regression treats the first point as if it is every bit as significant as the last.

To do the regression properly, you would need to "weight" each point by the total number of PA's it represents. That is, if the first point appears once in the regression, then the last two points would appear about 1,000 times each. (Actually, the next-to-last point would appear 236915/201=1,179 times, the last 174504/201=868 times.)

Of course most regression routines can't handle anywhere near that many points. But that's OK, because what this tells us is that there is very little useful information in the small PA groups anyway. In that case, you can throw them out of the regression altogether without affecting the result.

In this case, I'd probably throw out all groups with less than 5,000 PA's, which in this case turns out to be up through the 71-110 PA group. Then the smallest group becomes 111-150, with a total of 6,630 PA's. If that data point enters the regression once, then the next-to-last group should go in 236915/6630=36 times, which is certainly feasible.

I don't have time to do it now, but I'll post the result tomorrow.

Posted 12:50 p.m., June 27, 2003 (#12) - MAH
Great stuff. Will want to revisit the article and threads. My immediate take-away is that Nate has developed an elegant model for estimating the likely, practical impact on a team of losing a particular player. The per-game impact is higher for the first few games, and declines with time, as more and better replacement alternatives become available.

I wonder how this model should inform our thinking about all-time player ratings. Should we give a player with a twenty-year career "credit" for his value *each year* above "emergency" replacement level? Something tells me that we should use the two- or three-year replacement level; i.e., 85% - 90% of average.

Posted 1:45 p.m., June 27, 2003 (#13) - tangotiger
A nice quick simple function would be

repl rate = 1 - 1 / (2n + 4)
where n = years

You get the following

years, repl rate
0.001 0.75
0.25 0.78
0.5 0.80
1 0.83
2 0.88
3 0.90
4 0.92
5 0.93
6 0.94
7 0.94
8 0.95
9 0.95
10 0.96
11 0.96
12 0.96
13 0.97
14 0.97
15 0.97
16 0.97
17 0.97
18 0.98
19 0.98
20 0.98

Posted 2:00 p.m., June 27, 2003 (#14) - FJM
Here is the regression equation using the "weighting" scheme outlined above: BR/PA = 0.01656 * ln(PA) - 0.129.

I must admit I expected the effect of the change to be more dramatic. To refresh your memory, Nate's version was BR/PA = 0.0154 * ln(PA) - 0.117. Although the two equations look similar (and, in fact, produce similar results over most of the range) they differ significantly at the upper end. For the group with the most data (4201-5000), which has an actual BR/PA of 0.0102, Nate's model gives 0.0134 while mine says 0.0118. His model fits the data better than mine in the 4 lowest ranges: 111-150, 151-200, 201-300 and 301-400. That's to be expected, since they get very little "weight" in my regression (1, 1, 2 and 2 respectively). On the other hand, mine fits better than his in all but one of the other ranges.

Ironically, the lone exception is the very last group (5,501-10,184). Both models seriously underestimate the actual BR/PA here, but his does come quite a bit closer (Actual: 0.0231, His: 0.0199, Mine: 0.0186). I suspect the reason we both do so poorly here is that this group, which has only 24 members, includes some truly exceptional players. Note that their productivity as a group was more than double that of the next lower group. It would be helpful if someone could produce the individual numbers for each member of this group.

This led me to another flaw in the analysis. Nate says: "I've compiled the performance of all non-pitchers whose careers were completed between the years 1973 and 1992..." I assumed he meant that he compiled the career numbers for all players who retired during that period. But he goes on to say that the player with the most PA's was Dave Parker with 10,584. Well, both Pete Rose and Hank Aaron ended their careers during that period, and they had roughly 15,000 PA's each. Apparently he only included PA's that occurred during that 20-year period, which means players like Aaron and Rose are misclassified and their numbers are incomplete. An even greater distortion occurs in the case of Willie Mays. He retired in 1973, the first year of the study, with about 250 PA's and a .211 BA. Please rerun the study, either by including the entire careers of all these players or, if that is not possible, by excluding them entirely.

One more thing I discovered

Posted 2:05 p.m., June 27, 2003 (#15) - FJM
Ignore the "One more thing I discovered" line at the end of the previous post.

Posted 5:45 p.m., June 27, 2003 (#16) - David Smyth
The problem with the long-term replacement concept of Silver/Tango is IMO that it is based on faulty assumptions about the 'granularity" of value. If you use the Silver/Tango procedure (substituting a continuous replacement for a player's entire career), you are implying that the "unit" of value for a ballplayer is not the PA, or the inning, or the game, or the season. Instead, it is the career.

But the Win Probability method that Tango has been promoting implies otherwise--that value is created on a discrete, play-by-play basis (and therefore that career value is essentially the sum of these independent PBP occurances).

If you accept this notion (that value for ballplayers is created on a PBP basis), then you must, in stating a player's value, be true to this notion. And that implies treating each PA as an isolated event, where if there is a substitution, there is no "time" to make a roster move, or to acquire a .500 player, or even to institute "chaining". And this implies that the expected replacement on this level would always be our old friend--the typical .375 player at the end of the bench.

As I stated above, there are certain lines of analysis in which the long-term framework will be appropriate, but I maintain that it is a limited "specialized" concept, and not what we are looking for in a general system of player evaluation.

Posted 6:25 p.m., June 27, 2003 (#17) - tangotiger
I'm not sure why we need a "general" evaluation system.

A player does add PA-by-PA value. From that standpoint then, he comparison level is always the average player, since that is the environment he faces himself in. Average teammates, average opponents, average pitchers, average park, average everything. His value is derived therefore against the average player. The average player is worth "0" relative to average. The "0" win value corresponds to the average salary of say 4 million$ for a regular.

The problem is that you also have a time component. The more you play, the more you can keep somebody else out of a job (the bad guy hopefully). This is worth positive dollars. And the longer you play, the longer you keep somone out of a job. But if you are a .400 player playing for 15 years, then, you kept a GOOD player out of a job. That creates negative absolute value.

Anyone above the sliding time-dependent replacement level scale creates absolute positive value, even if he has negative relative value. If you drop BELOW the replacement level, the you've create negative ABSOLUTE value.

If we insist one scale as a general evaluation system, I'd say to use the .450 scale or the 90% scale, as this corresponds to roughly say a player's 3 or 4 year career. But I really like the time-depedendent scale.

Posted 6:55 p.m., June 27, 2003 (#18) - David Smyth
I don't understand why, on a PA basis, the comparison should be to the avg player. We are looking at replacement, right? If, at some point in tomorrow's game, Sosa or Grudz or Patterson or Alou (to use a Cub example) needs to be substituted for, why should we assume an avg player instead of a .375 player?

Posted 7:53 p.m., June 27, 2003 (#19) - Patriot
On the PBP level, the player's value is not against who would be there if he wasn't, it is against the real .500 opponent that he is playing against. It's how the player changes the WE while he's on the field. That is his real value in the game. His value to the team is dependent on other factors, like how he compares to his potential replacement.

Posted 9:07 p.m., June 27, 2003 (#20) - David Smyth
No, Patriot, I don't agree that there is anything about the PBP level which inherently calls for the comparison to one's .500 opponenent instead of the replacement substitution...

Posted 10:00 p.m., June 27, 2003 (#21) - Patriot
I didn't expect you to agree :) But the very nature of Win Expectancy causes it to be in relation to a .500 probability of winning the game when it begins. This is natural and inherent in using a WE or RE system. You can argue that it should be fudged from that point, but it all starts with comparing to .500,

Posted 11:05 p.m., June 27, 2003 (#22) - tangotiger
I agree with Patriot that the starting point must be .500. You can argue that the final point should be something else like .450 or .400 or whatever.

But, the run values of all events, the win values of all events always presumes the actual context being played in. And the average actual context is average.

The reason that the HR has a 1.4 run value is because, given average teammates to get on base, average pitchers to hit against, average fielders, average park, average everything, we expect the HR to add, on average, 1.4 runs to the game.

So, .500 must be the starting point in actual game conditions.

Now, the next step is: "Well, how would the bottom of the barrel had done, given that average environment?" And, for one PA, you can argue that the bototm of the barrel is 80% of league average.

But, the argument here goes, that over the average career of an average 3-yr hitter is 90% of league average. THAT's the guy that you have to beat. It's not the 2-month guy who gets the emergency callup and who has no business being in the majors. It's that guy, that 3-yr guy, who's your bottom of the barrel. Anyone below that is keeping you from finding that 3-yr guy.

It's like if you have a company, and you suddenly got alot of work, and you need someone, anyone. So you hire some schlub. But, if you keep this schlub for 3 years, you know what happens? You start to lose business. You actually lose absolute dollars.

I don't see why the "emergency" baseline is the baseline we need to compare against all the time. Use that to compare against for an "emergency" time period (1 month). Use a different baseline for different needs.

I feel another 108 post thread coming...

Posted 7:22 a.m., June 28, 2003 (#23) - David Smyth
The first part of your posts, Tango, and Patriot's posts, are fine with me. They have nothing to do with what I am talking about. I'm just saying that, since value is *created* on a PA by PA basis, that the most *fundamental* way to *evaluate* it should be on a PA basis, with each PA being independent of all other PAs.

If Sosa misses, say, 40 more PAs this season, but in a random pattern (1 PA here due to getting hit in the eye by a wine cork, 1 PA there due to a hangnail on his index finger, etc.), then each PA will likely feature that .375 substitute. But if Sammy goes out for 8 consecutive games with a strained hammy, the team can use the "consecutiveness" of those 40 missed PAs to lessen the damage, by chaining or signing Rickey. The question is, who gets "credit" for that. Perhaps in a way it should go to Sosa for providing a favorable missed PA pattern to the team. I know that sounds kind of silly, but at least that is a real-world way of justifying looking at each PA independently.

Tango wrote, "Use a different baseline for different needs." Right, and for the common need of a general rating system, ala Win Shares or Total Player Rating, or even Slwts, I think the standard 75 to 80% baseline should be applied to every player.

Posted 9:33 a.m., June 28, 2003 (#24) - Patriot
Not to get too picky here, but if Sosa is missing 1 PA at a time, there's no reason to think that the average player who takes his place will be .375. Part of the idea of chaining, at least as I orginially intended it, was that most teams have bench players who are maybe .425 players. Your best bat off the bench is usually not a FAT player. That is the guy who will get Sosa's PA. And the chaining occurs when the .375 bum has to take his role. But since his role involves 1 PA/G and Sammy's involves 4, the effect on the team is something like replacing Sammy with a .405 player instead of a .375 player.

As for different baselines for different needs, sure. But don't we look at a career and a season as different needs, or at least we consider doing so? The whole idea of pennant value comes from saying that 10 WAR for a career distributed 1/year isn't the same as 2 seasons of 5 WAR. We are basically using a different comparison point for different units. For a season, your replacement will be the 80% guy. But for five years, the replacement will be a 93% guy or something. It seems to me as if the entire idea of peak/career, pennant value, etc. is an admission by most sabermetricians that it is ok to use different comparison points for different but similar questions. The questions of career value and seasonal value are similar, but I don't see why they can't have 2 seperate answers.

I do realize that I am rehashing the same argument we have had many times before.

Posted 9:45 a.m., June 28, 2003 (#25) - Patriot
You can tell me if if I'm way off base here. I'm not even sure I agree with this, but...to me, it seems as if the entire idea of value above a non-.500 baseline is somewhat forward looking in nature, or backwards looking in the "what if" sense. If we look back at the completed record of a season, some combination of players has actually gone out and made 4000 outs for the team, and now it's over. Player A, a .490 with 500 PA, has hurt the team's chances of winning. Period. It doesn't matter, in retrospect, whether he was a better option than the .375 player. The .375 player never played, he's irrelevant. The .510 player with 1 PA has increased his team's chances of winning. Period. It doesn't matter if he at some point was considered less valuable then Player A because he would only get 1 PA. His net contributiom has been positive. If we add up all of the WAA for everybody in the league, it's 0. The league is at 0 WAA, and the sum of it's players are at 0 WAA. Measuring against replacement, once we already know what these guys have done, is saying "what would have happened if Player A had been lost?" But Player A was not lost. It is a moot issue in retrospect.

Now this does not mean that Player A does not have value; anybody who's over 0 has done something positive to help the team. Player A still has value over a .375 player, and that is important for the future. We'd expect Player A to be a more useful part of a team than Player B next season. But that does not change what has already happened.

Since the question of "who is better" usually means "who would you rather have on your team", some sort of replacement baseline is the right choice to answer the question. But for what has actually happened, value comes in being better than your opponent, not than being better than the guy who would replace you ig you got hurt which you didn't.

Posted 1:01 p.m., June 28, 2003 (#26) - tangotiger
I agree with Patriot's good explanation.

I also want to talk about "salaries".

Salaries have 2 components: value relative to average, and playing time. In terms of marginal dollars, each marginal win is worth about 2 million $ in salary. So, an average team (81 wins) will pay the average payroll (70 million$). If you are a player that is +1 win over average, you should get 2 million$ more than average.... but what average?

That's where playing time comes in. If the average regular gets 4 million$, then this player is worth 5 million$. If this guy did +1 as a backup, then maybe the backup average gets 2 million$, and this guy is worth 3 million$.

Enter replacement level. If this guy, who is +1 over average, he might be +1.5 over replacement (while a regular might be worth +3 over replacement).

Mutliply by 2 million/win, and you get his salary worth (3 million or 6million depending on the playing time).

This is just another dimension to replacement level, and one that is based on really the replacement level being about 80% all the time. One a one-year salary basis, I think this makes sense.

I'll be gone for a week, so have fun!

Posted 8:33 p.m., June 28, 2003 (#27) - David Smyth
Patriot, using the .500 chance of winning a game vs avg opponents, etc., is based on an assumption that starting the game with players who give you a .500 chance of winning implies that those players have no value--that a .500 chance of winning just appears out of nowhere. I assure you it does not.

Posted 10:06 a.m., June 29, 2003 (#28) - Patriot
That's not what I'm saying. Your opponent is .500, relative to the league. It is what you do in relation to your opponent that determines whether you win or not.

Obviously, when the DRays play the Yankees, they have say a 40% chance to win. But their average opponent for the entire season is a .500 team. If they outperform .500, they win. If they underperform .500, they lose.

No one is saying that a .490 player has no value. But they have negative value compared to the opponent. As I said, that 2nd post of mine was just kind of a thinking out loud exercise, and I agree that the baseline we want to use for most things is not .500.

I think the fundamental difference between your view and the Tango/Patriot view(at leas it seems like Tango and I agree on a lot of this) is that you are looking at the player's value within the league, and we are looking at it within the team. Going back to chaining, unless I am misinterpreting your argument, you say that the replacement level or FAT level or sustenance level or whatever we want to call it does not change when one player goes down, and so everyone's value is still measured against this constant line. We're looking at the team and seeing how that specific team is effected if the player goes down. Now it seems to me as if the league approach is the correct one for ability, and the team approach is the correct one for value.

Posted 3:38 p.m., June 29, 2003 (#29) - David Smyth
Patriot, maybe I'm not understanding the application of the sliding repl level concept. Let's say we have two teams. Team A has the same 3Bman for 20 seasons, and he puts up a .500 season every year. Team B has the misfortune of losing the incumbent 3Bman on a career-ending injury ever spring training. Thru good luck and good management, each of the 20 yearly 3Bmen puts up a .500 season.

So the career value for 3Bman for Team A would be based against a 20 yr repl level of about .480, while the career values for each of the 20 1 season 3Bmen on team is based against a 1 yr repl level of about .410. Therefore, the sum of those 20 is also based on .410.

So, even though the performances at 3B are the same for each team, the values are different because of whether there is either 1 face, or 20 faces, under the baseball caps?

So, even though the

Posted 8:17 p.m., June 29, 2003 (#30) - Patriot
Now I think we are confusing sliding or time-dependent replacement level with chaining. I didn't specify that my last post was on chaining. The two can work together, I suppose, but I have not really done that.

But the time dependent approach is to determine a player's career value. That's not necessarily germane to the question of value to the team. The player's career values could be different. Their value to the team in the season, against their chained replacement, will be identical.

Chaining is what I was referring to last post about being from the team perspective. That is my fault for not specifying.

Posted 1:52 a.m., July 7, 2003 (#31) - MAH
David, Patriot and Tango,

After re-reading your posts, the following ideas occurred to me. Sorry for the slightly disorganized (and heretical) thoughts--the hour is late and I may not be expressing myself too well.

In evaluating how valuable a player has been during his career for purposes of all-time rankings or Hall of Fame consideration, maybe we should compare his value *during the time he actually played* against the "90%" 3-year-player (or the 85% 1-year player), and then *penalize* him for his *absences* from the lineup based upon the *likely* replacement value player given the *type* of his absences*.

Here is where Nate's formula becomes so important. (David's Sosa example is the source of the idea.) Certain players have a *pattern* of *sporadic* absences--a few games here or there that add up over the course of a season. It is a "quality" (and I don't mean to make a "character" issue out of it) that has real impact on the success of their teams. Say, Bob Horner. Or Eric Davis. For each such absence, we could *assume* that the 75% "emergency" player is the replacement, who thereby brings down the *team's* *expected* performance by the difference between the 85%-90% "baseline" and the "75%" emergency level.

Contrast the Bob Horner player with a workhorse who plays every game that he can--but suffers a serious injury that takes him out mid-season. In theory, we would assume that the first few games would be played by a 75% replacment player, but that at some point an 85% player will be found and start to play. Again, this is not a "character" issue--but if a workhorse *does* get injured, his teams *are* likely to suffer.

Now let's say that there's a player who persists in playing for a few years at the end of his career when he's clearly below average. Say, Brooks Robinson or Pete Rose at the end of their careers. Those players implicate Tango's example of the employee who's really hurting you. Team management should *know* that the aging player is *expected* to be below-average; they should *foresee* the need for a replacement and *find* the 90% 3-year player. The Pete Roses should be deemed to have a *negative* value to the extent they can't perform better than the 90% 3-year player who is "readily available" with the benefit of a little planning.

The type of career rating system I'm proposing would give credit to durable "average" players, who do have substantial practical value. It takes as its point of departure a "typical" team--i.e., not the theoretical Year Zero expansion team of cast-offs--and asks the question of how much the player is likely helping or hurting such team given the fact that with a little bit of planning such team can usually obtain the services of a 85-90% player before a season begins.

Modeling this rating system would not be practical for all players, but it might be appropriate for making retrospective career evaluations for the type of players evaluated in The New Historical Baseball Abstract.