Joe:

I agree that, based on the good points of various smart folks, Win Shares is pretty problematic for this purpose.

However, Win Shares would still be worth including on helpful resumes, along with other nifty data. In particular, until B-Reference or B-Prospectus offers the alternative 'light-years' advances in defensive ratings (someday? please!), the Win Shares defensive numbers would be a huge help in evaluating candidates. I gather that the Digital Update includes each season's fielding shares for every player ever.

Oh, and if, say, 1900's top shortstops had a lot more fielding shares than 1990's top shortstops, there oughta be something to tip the reader off to that context change, and maybe a link to commentary on what to make of it.

I think that an 'ideal' resume would have things year by year, so you could contemplate 'peak' however you saw fit.

Games played by outfield position is available on B-Reference, no?

Certainly in addition to Win Shares, I'd want people to be considering Avg/OBA/SLG-above-context as provided by B-Reference. Rather than reproducing the _same_ detailed info, resumes should probably have links to players' B-Ref pages. Maybe career totals, or anything new generated from those numbers (!), could be on the resume. Or maybe some members of the resume task force could help Monsieur Forman in adding cool number crunches to B-Ref...

For a pitcher, it'd be really keen to see the Avg/OBA/SLG context in which he pitched. Though we lack doubles and triples allowed for most of history, I'd love to see the remaining offense-allowed-rates info, maybe even substituting context-average doubles & triples in some way...

Finally, we should all 'lean' on B-Prospectus to be ultra-cool and provide their historical translations again, which resumes could link to. =)

I would think that for the earlier years, Win Shares would be less relevant than in later years (to the extent people want to consider them at all.) First, they don't include National Association stats, which constitutes about 1/6th of the years in consideration. Second, in years with fewer stats available, ultra-precise calculations like Win Shares present an illusion of exactness that is unwarranted.

I would recommend setting up a log for each position(one every few days), along with the names of the likely 10-25 candidates at each position, and then posting the WS data, as it becomes available, under each log. That way, WS aren't given undue priority, and do not delay the process any more than necessary.

That said, of course I would consider the data when posted, and think it's a worthy endevour.

There is no reason that we can't have other rankings or "resumes" of the eligible players. The more information, the better. If Dan wants to have any of his analysis posted at this site, I say great. We're going to be discussing the worthiness of each player, so I think different ideas and analysis would certainly help.

It's fairly easy to figure Win Shares for the NA. I have 1874 completed. I had to bound the OF DER adjustment at 0 and 40 (which is probably evidence BJ should have given this a lesser emphasis), but otherwise, it works. Spalding, if you must ask.

James had a huge advantage in analyzing fielders -- all the time in the world. I have a new version of CAD pretty much finished (some people are just looking over the article), but even with a plug-and-play spreadsheet, it will take much time to figure a league. There are plenty of things at the individual level -- figuring innings, namely -- that take tons and tons of work.

Once I have the data entered (which will take a few weeks), I plan on looking over 1980s fielding/pitching stats to see what they yield for improvements. We have the advantage of the Retrosheet data, which I especially want to use when evaluating catchers' arms.

"I do not think win shares should be used, unless they can be converted into some sort of winshares above average per season. The winshare replacement level is too low as to make it useful in a Hall of Fame discussion. To be a reasonable candidate for the HOM, you should be great, and a more accurate measure of greatness is to see how much value a player accrued over the average player, as opposed to the .250 player."

Dan, I strongly disagree that success measured over that of an average player is the way to go.

For one, average players have value. Below average players even have value. Boston might have made the playoffs if they had slightly below average players at 3B, 2B and SS last year.

Also, you dock players that hang around at the end of their careers, guys like Brooks Robinson. That's not an accurate way to evaluate a player.

I agree that the WS replacement level is too low. So dock the guy 6 or 8 or so WS for every full season he plays, and you'll have WS above replacement level. But this is much better than comparing a player to average.

Also, WS are the best tool we have right now for evaluating the defensive contributions of 18th century players.

"There is no reason that we can't have other rankings or "resumes" of the eligible players. The more information, the better. If Dan wants to have any of his analysis posted at this site, I say great. We're going to be discussing the worthiness of each player, so I think different ideas and analysis would certainly help."

Agreed, 100%, we'll put up anything someone wants to contribute.

As Charles said, calculating WS for the NA shouldn't be too difficult, the hardest part is coming up with a decent RC/XR formula for that league. I'm planning to have WS calced for those years as well.

I've got 3 volunteers, so hopefully we'll have the data up by early next week. I finished the 3B last night, and I'll get the SS's done this week. Each of us took two positions, and we're adjusting the player's WS to 162 game season equivalent.

The top 3B on the first ballot, by a comfortable margin, will be Ezra Sutton, who played in the NA and for the team that went on to become the Boston Braves in the NL. His peak and career value are both solidly ahead of anyone else. He was a heckuva player.

Good one George, you've got me there :-)

Dan -- I don't understand the difference. All of the two hundred will measure up fine on wins above average, wins above replacement, wins above top 25%, whatever. The question is how much value did the players have over the course of their careers.

What I'm trying to get at is that the benchmark shouldn't change based on the quality of players you are trying to evaluate. Wins relative to average just isn't relevant, unless both players are above average in every respect of the game, batting, fielding, stealing, baserunning, pitching. Once you are below average in any one of those categories, it throws the whole thing off, because you still have value, even if you are below average. This doesn't even get into playing time issues. If you compare to average, you are going to overvalue players with short careers.

Like James says in the untitled article on pages 102-105 of the WS book, you are going to rate a .490 player over a full season lower than a .501 player in 1/3 of a season, and that just doesn't make any sense at all. .500 doesn't mean anything. It's an arbitrary number. Replacement level is very real. It's the difference between broadcasting and playing. In almost every single case you are better off rating players by comparing them to a replacement level instead of an average level. I can't think of one scenario where I'd rather use an average comparison.

Rating players by value over replacement at their peak will work much better for what you are trying to do than rating them by value over average (seasonally) for their careers.

Side note: you mentioned SABR, will you (or anyone else in this discussion, reading or writing) be at the SABR convention later this month?

(There is no way that Goodman or Cuccinello are even on the same planet as Barnes in terms of legitamacy as a Hall candidate, yet WAP will tell you otherwise, and Win Shares will probably say that Barnes was much WORSE, even if you docked Goodman and Coochie a few Shares a season.)

I, with a couple of other Primer regulars, have been working with Scruff by converting the Win Shares for many 19th century players into a 162 game setting. When Scruff finishes the National Association Win Shares, Barnes' total is going to be very high. I'm confident he will lap Goodman and Cuccinello easily.

Why not use a combination of career Win Shares and WS per 162 games (as a Fibonacci number)? Wouldn't this solve your problem Dan?

Whatever numbers we use, we have to take into account the standard deviation of a particular era. A player who was 20% better than average with BA, WS, ERA+, etc., in 1876 is NOT the same as a player who achieves that feat this year.

I've got to agree with Dan too. I found the Prospectus article pretty convincing that a strong peak can more than compensate for a greater career value. Looking just at averages over periods of time de-values what may be the most important part of a player's resume -- how much did he contribute toward winning pennants.

I mean, Cap Anson may have the most Win Shares over his career, and his longevity at a slightly-above-average level brings up his averages over a good period of time, but the fact is that it's hard to find any sizeable period of time when he wasn't the third best first baseman in the league (in an only 8 team league, no less), behind Dan Brouthers and Roger Connor in the 1880s and '90s.

Being average for a long time may have lots of value for your team, but does it make you one of the "greats". For my money, he doesn't even get considered until his (lower Win Share, comparable rate) contemporary betters are enshrined and only those of comparable value to their teams are available.

Until the Win Share numbers that Scruff is making up changes my mind, I would rank the first basemen as such: Brouthers, Anson and Connors.

These are Scruff's numbers from another thread, taken from NHBA, so excluding NA years:

Name; Total; Top 3; Top 5 Consec.; per 162

Cap Anson 381 WS (30, 29, 24); 123; 27.12

Oops. That chart should be headed "1871", not "1971".

A few things to touch on:

From ChapelHeel -- "Why does it matter what data we put on the "resumes"? They can contain anything in my opinion. It doesn't mean any voter has to use that information in evaluating the HOMers. We all have basically the same data or we wouldn't be interested in this stuff, so we'll all do our own independent analysis."

I see what you are saying, but everyone voting doesn't have the time to do comprehensive individual analysis on the 100 or so players that will reasonably be considered from the beginning.

So it doesn't hurt to present information for our pretty knowledgable electorate to use in their evaluations. Win Shares are already out there, all people have to do is look up the book. But I think they should be adjusted into a 162-game season context for fair evalutation of players during a time where the length of season was in constant flux. Of course voters can account for the fact that the leagues got tougher over time, etc. but giving people reasonable numbers they can have access to is important.

We aren't only going to present Win Shares, this isn't the WS Hall of Merit TM or anything like that. But the defensive numbers are the best we have to go on and as such they are relevant to the discussion. WS might not be great, but I'm pretty sure, in most cases a player with 40 WS had a better year than a player with 30, etc. This is relevant information to consider as part of the process of formulating a ballot. Of course there will be no requirements to use this info.

We'll also present things like offensive W-L records, number of fictional Stats ATHB All Star Teams (or others if they are out there), fictional MVPs, etc.. If anyone has any other data they'd like presented, we'll present that too. But I think giving people that don't have the time to park and league adjust numbers themselves something to go on is a big help.

As for the Anson/Brouthers/Connor thing, let me start by saying all 3 should be slam dunk HoMers, Deacon White, Buck Ewing, Jim O'Rourke and King Kelly are probably the only players on the first ballot that compare with these guys, in terms of a peak and career value combination.

Let me also say that Connor is one of my favorite 19th Century players, so if I have any personal bias, it's towards him.

Here is what the seasonally adjusted WS numbers look like, not counting the NA for Anson (ages 19-23).

Career:

Anson 570

One other thing -- Does anyone have a link to the Prospectus article referenced earlier?

"As for the Anson/Brouthers/Connor thing, let me start by saying all 3 should be slam dunk HoMers".

Ah, but should they be FIRST BALLOT HoMers?

The Prospectus article, to the best of my knowledge, was never put online. It is in their 2002 book (sometimes you gotta buy the book, darn it). I don't have it in front of me, but I think it'd be a relevant read for debating HoMers, clearly taking the "peak" side of the peak v. career debate. The general gist in that the marginal Win over Replacement (I think that's the stat they use) of a great player pushes a team closer to a pennant in a season that he's having a great year, than in a later year when he's just good.

The conclusion (in WS lingo) is that a marginal win share is geometrically more important than the previous one, and that (this may be an exaggeration) a 42 WS season is more valuable than two 30 WS seasons, because those 4 extra wins bunched in one year are more likely to push your team over the top.

(So Anson was only 2.5-4.0 WS per year worse, despite being 5.5 and 6 years older, playing against the exact same competition. Considering this, there is no question he was every bit as good as either one of those players, unless this method is extremely flawed. That, combined with the fact that he played for 27 years leaves little doubt as to which one had the most valuable career.)

Brouthers still averaged about six more WS per 162 games than Anson throughout his career. That's a considerable amount. When you take into account quality x quantity, Dan edges out Cap (not by much).

I do think when you add in the National Association stats, the many games at third, plus his years as a player/manager (are we taking that into account), Anson has to vault to the top.

"Brouthers still averaged about six more WS per 162 games than Anson throughout his career."

John, this is a biased count (and shows why season numbers need to be adjusted to 162 game seasons) for a couple of reasons. First the seasons were longer when Brouthers was the same age as Anson, so in a raw numbers comparison his best years have greater weight. For example, when Brouthers was 27 his team played 112 games. When Anson was 27 his team played 83 games. This bias tracks their entire careers.

Also, Anson played regularly until he was 45, while Brouthers as a regular was pretty much done by age 36, although he had a decent 1/2 season at age 38. Straight "per 162 games" comparisons don't work unless you have two players with similar career length. Players that "hang around" are severely penalized by such a ranking.

I really went into this part of the discussion just looking to answer a question, not knowing what I'd find. I don't really have a bias here, except maybe towards Connor. I'm just not seeing what you guys are seeing.

Matt - I'll try to run down the article in the next day or two.

Bill James did a similar study in the Politics of Glory and reached a similar conclusion. I wasn't as convinced as he was though, when I looked at the data he presented. The more realistic (and less theoretical) he made his simulation, the smaller the advantage became. By the end, we were talking like 1/5 of a pennant over a 20 year career for the Carlton type over the Sutton type IIRC (don't have the book handy right now). A small advantage, sure, but I saw nothing that made me think it justified making my rankings 80% based on peak value or anything. I'm definitely curious to see the Prospectus article.

Scruff:

Yeah John, I guess we are pretty close. NA would definitely put Anson over the top solidly, even if you dock him some for the quality of the competition. Good point on Robinson and Rose as well. Not to keep piling on it (I really do feel kind of bad about stating this over and over), but TPR is good for same season assessments of players at the same position with similar playing time, if you don't care about the quality of defense; that's about it.

Actually, I lean towards Connor over Brouthers. His peak was a little better and he was a better defensive player. I could be convinced either way. If voting, I'd have them tied for whatever spot their in, it's too close to call based on what we know, definitely falls within the margin of error of whatever method one might choose (lots of guesswork in the 19th Century assumptions of these formulas). If forced to choose, I'd go w/Connor for the reasons mentioned at the beginning of the paragraph, but 2T is how I'd rank them in this one.

Glad to see we are back up and running! Scaling everybody's WS up to a 162-game schedule makes a lot of sense. However, we have to be careful how we treat early pitchers' WS. James used an arbitrary (I am not saying it is wrong, just arbitrary) cutoff of 1893; pitchers before 1893 get their innings pitched (and therefore WS) divided by two, those afterwards are treated whole.

I have written about this several times before, but I think a better system of adjusting pitchers' innings (and win shares) is available by considering the typical load a starting pitcher is asked to shoulder each season, and then adjusting each pitcher's innings pitched relative to this typical load. I realize that win shares is trying to do something different, but to the extent we rely upon WS we should be aware of its shortcomings in this area (IMHO).

Anyway, the peak vs career value debate that Dan Passner and others are raising is certainly important. But everyone probably has their own views on the proper "weight" to give each, and it is difficult to convince others of your own view.

My personal view on this issue stems from simulations that I have done, along with the work of James and Wolverton (the BP 2002 article). I have concluded that a player's pennant-impact value each season is reflected in taking his value above league average and raising it to a power of 1.20. (If you want to add in his value above replacement level, but below league average, you can do this too, but without the exponent.)

Clearly, then, a player with two seasons of 8 wins each is a little inferior to a player with one 10 win season and one 6 win season. The difference isn't all that great on a seasonal basis, though over the course of players' careers it can make a significant difference.

Scruff said:

"I take from this that Anson was every bit as good as either one of those players, unless there is something in the WS formula that would favor Anson over the other two."

I think my biggest problem with Win Shares does not involve its method at all, but it's intransparency. The "Tip 3" numbers Scruff presented above are:

Connor 47 (1886/age 28), 43 (1885/age 27), 38 (1888/age 30)

Matt - RBI have nothing to do w/Win Shares. The clutch adjustments are only applicable after 1987 when stats has the data for AVG w/RISP and HR w/MoB.

In 1881 Anson played in a park that had a 114 run factor in a league average RC was 5.10 runs per G. Adjusting for the park, Anson's environment was 5.41 R/G.

In 1886 Brouthers played in a park that had a 109 run factor, but the league average RC was 5.27 per G. Adjusting for the park, his environment was 5.47 R/G.

Brouthers created 12.61 R per 27 outs; Anson 12.25, in a slightly lower run environment. If you figure an offensive W-L record, you get Anson at 12.4-2.4 (.837) adjusted to 162 games. Brouthers comes out at 12.9-2.4 (.841). The players are extremely close offensively.

I think your RC totals are off. James has Anson at 94 RC for 1881, Brouthers at 150, which would adjust to 102 using the .68 factor. James adjusts outs slightly based on the league average of outs/game (to account for the missing outs in the league), and Anson comes out at 208, Brouthers 218 (321*.68).

What RC formulas did you use? For 1881 NL, it should be:

A: H+BB; B: (1.2*TB)+(BB*.26)+((AB-SO)*.116); C: AB+BB

For 1886 NL, it should be:

A: H+BB; B: (1.21*TB)+(BB*.28)+((AB-SO)*.05)+(SB*.69); C: AB+BB

Your RC calculations are not correct, under those formulas, I get Anson at 98.3 and Brouthers at 153.4 (104.3 after the .68 adj.). So both players were adjusted downward slightly, because their teams underperformed their RC total. Back then, with a relative lack of power, AVG was the most important statistic, and Anson's 30 point edge was big enough to close the gap. 30 extra singles, 10 less outs and 7 less k's are just about enough to offset 6.2 2B, 3.2 3B and 6.5 HR and 18.5 BB. It was a different game back then, and getting hits was just about the most important thing.

So without any adjustments (except the .68), you've got a guy that creates 98 runs using 208 outs in a 5.41 run enviornment, and another guy that creates 104.3 runs using 218 outs in a 5.47 run environment. The players are awfully close, and the WS system agrees. Offensively, Brouthers gets 37.5 WS (adj. to 162 G), Anson 38.4, I don't see how this is that outrageous. Anson picked up 3.3 WS for D; Brouthers, 2.5.

Anson might have nudged ahead of Brouthers because his team was a little more dependant on it's offense for wins or something, but the system rates two essentially even seasons, essentially even (try saying that 3 times fast). I have no problem with it here.

Rob -- I've been mulling over what to do about pitchers, and your idea sounds as good as any I've heard.

I don't necessarily think 1893 is an arbitrary choice, isn't that the year the mound was moved back to 60' 6"?

We definitely need to come up with some kind of equalizer.

I like taking Charles Saeger's number for what the pitching/defense split really should be, and using this number for a backwards adjustment. In one of the early NA seasons, Charles says the split is .77 defense/.23 pitching. James uses .325 D and .675 pitching. So we'd take the WS, and multiply by (.23/.675). This would gradually raise the credit for pitchers, and it's an objective number not a subjective one. This would not only apply to WS, it could apply to anything from Wins to projected wins (based on ERA vs. league in the context of actual decisions), etc.

What do you guys think?

Scruff, you nailed it. The problem shouldn't be dealt with through arbitrary measures; if we are proceeding on the assumption that a win is a win is a win, then a win share is a win share. Where we can tweak the 19th century stats is on the pitching/defense ratio.

You are right, 1893 is when a 60' 6" pitching rubber was introduced (replacing the 50' pitching box). I guess I should have said that James arbitrarily reduces innings before 1893 by two. The "2" is the arbitrary part, not the "1893". As others have suggested, under the assumption that a win is a win, then we should handle the "pitching load" issue via the allocations between offense/pitching/defense.

I am not convinced that the offense vs. pitching/defense is not radically different in the 19th century, especially the early years. That is, not only would I think the split between pitching and defense is radically different back then, I would guess that the split between offense and pitching-and-defense is also radically different.

Although this is not a perfect analogy, in slow-pitch softball offense is far, far more important than pitching-and-defense. Any assumption near a 50/50 split would be way off. It's probably more like 75/25.

I have a couple of comments:

1 - Linear Weights was the first "total" system. Whatever drawbacks it has, it should be presented at the same level as Win Shares. Let the voter decide what he considers relevant as an evaluation system.

2 - Sandy Koufax. People should be consistent in how they evaluate his career, in terms of Hall of Merit, and not make him an "exception case". This is what Dan P was talking about by making the comparison level .500. If you have a guy that is a .550 player, and plays 30 years, is he Hall Of Merit material? If you have a guy who is a .650 player and plays 10 years, is he HOM material? It depends on your basis for comparison. Compare the guys to a .350 level, and the first guy shines. Compare the guys to a .500 level, and the two guys are equal. Compare the guys to a .550 level, and the second guy shines.

When you are talking the best of the best, do you want someone who is better than the bottom feeders the longest.... or.... do you want someone who is better than even the good players in the league. The creme de la creme.

This is for the reader to decide. But the voter should be consistent.

I think there should be less number-crunching, and more thought into how a voter can approach the situations.

3 - Are you comparing players to their contemporaries, or to all players across time? If you compare to contemporaries, then we dont' need to adjsut for games, innings, year-to-year, etc.

There should be as many guys voted in who were born in the 1870s and were born in the 1950s.

4 - What efforts are being spent on the Negro Leagues? If 20% of the stars today are black and will enter the HOM, then 20% of the players back in yesteryear should also go in.

(When you are talking the best of the best, do you want someone who is better than the bottom feeders the longest.... or.... do you want someone who is better than even the good players in the league. The creme de la creme.

This is for the reader to decide. But the voter should be consistent.)

I want a combination of the two, so in that sense I would be consistent.

Great post Tango.

As to your question about which player is better, I don't know. It depends on the situation. Extreme peak players with short careers are very valuable for their run. Players who are pretty good for a very long time are also quite valuable, even if in any one year they don't push a team over the top, during those 20 years there will probably be a year or two or three where their team is very close to a pennant and they'll push them over the top also. The question isn't Carlton or Sutton? If the two pitchers had similar length and production, the peak guy wins.

The real question is Koufax or Sutton? Sure Koufax was great for 4 years, but Sutton contributed to his teams' success for almost 20, though not nearly as much each year. If I were starting a team I honestly can't say which guy I'd take, if I knew their trajectories up front.

Eric Enders is going to help a lot w/the Negro Leagues players once they come on the ballot, and we'll get as much info up there as we can get our hands on. They'll be in the same pool for election, I have confidence that the electorate will listen to the knowledgable posters and make informed decisions when they rank their ballots. It's like a jury. The judge explains the criteria, you trust the jury to follow the expectations and include and account for things they might not believe in. If you are filling out a ballot you are agreeing to give Negro Leaguers full, fair consideration. We're going to have issues if a 10-man ballot comes in that doesn't have Josh Gibson or Oscar Charleston on it. Hopefully we'll be able to recognize the accomplishment of some lesser know guys that were damn good, including Cristobal Torriente, etc..

That's why we'll have to clarify expectations as we get this off the ground.

To clarify your other question, players will be compared to their contemporaries at first, but the first ballot will have 30 years worth of careers in it, and the games aren't similar, even for this first group. Anson and Brouthers is a good example, and they were only 6 years apart. I do think some kind of "timeline" adjustment is reasonable, and RobertDudek is working on coming up with some hard numbers, a straight line adjustment like James used is definitely not appropriate. We've already worked this in a little by lowering the number of electees slightly in the early going and picking them up over time, although no one ever drops off the ballot. We also are starting the elections earlier than our original plan (1906 instead of 1915) to guarantee that several players born in the 1850's and 60's get in.

But this will be up to voters as well. I'll lobby for it, but if someone thinks what he did against his competition is all that matters, that's fine.

I think players should be given reasonable allowances (based on normal conservative career projections, etc.) for time missed for military service. And I will lobby extremley hard for this. It's probably the strongest 'controversial' opinion I have on the whole thing actually.

But again it's up to the individual voter, but through discussion we can lobby for our beliefs. I'm sure I'll even change several of mine before it's all done.

A good discussion on Koufax v Sutton can be found on fanhome starting here:

I also posted this elsewhere. While I talk about "Koufax", I am talking about guys of his type (Pedro if he were to retire today, etc), and not necessarily him. Same thing for "Sutton".

*****************************This is an opinion, which I do not support.

As I've said in the past, I'd rather have a 200-100 player than a 300-240 player.

Compared to various baselines, here's what their "value" says:

====================================

Baseline... 200wins... 300wins

The whole issue of what "baseline" you use in your evaluations (either implicitly or explicitly) is very important, of course. It is essentially another manifestation of the compare-to-league-average methods and the compare-to-replacement-level methods. This issue has received a great deal of attention over the years.

I have come to a view that I believe properly reconciles the two views. In any one season, I believe that the replacement level is the more appropriate baseline. However, over time teams can do better than simply filling in a vacancy with the replacement level every year. Drafts, trades, development, free agency, moving players to different positions, etc., cause the replacement-level-over-time to approach the league average.

I wrote a short piece on this subject in SABR's By The Numbers awhile ago. I even developed a simple formula, with suitable parameters, that estimates the additional value a player who played X years provides his team over a player who played Y years. I don't have the formula in front of me, but I will post it later when I find it.

The formula is an analytical way to enforce consistency, a definite benefit, no matter what your underlying beliefs, as suggested by tangotiger, John Murphy, scruff, and others.

Scruff wrote:

"What RC formulas did you use?"

I didn't use any formula. I copied it off baseball-reference.com, like I did for all the other stats. I think Sean uses the simplest of the RC formula.

I also had a chance to look at the BP article again last night. It's called something like "The Problem with Peak". Just having Babe Ruth on a random team for 22 years adds about 3.5 pennants to your team over that period. Of course, the Babe could drop out a couple of his best seasons and still be among the best of all time. The focus on peak seems to help pitched Ed Walsh to most (pushing him into the Top 20 pitchers of all-time).

He (Wolverton) only analyzes players who played their entire careers after 1903, so doesn't touch on the A-B-C debate here.

Rob, elsewhere on fanhome I argue the same thing. That the one-month replacement level might be .300, one-year might be .400. The longer you need to replace someone, the more you approach .500.

Coming up with something quick, I'd create a formula like:

Tango -- the Koufax-Sutton thread was excellent.

I'm not on board with the rising replacment level thing.

If the Red Sox lose Pedro in a plane crash tomorrow, why are they more likely to eventually come up with a .500 player in place then they would have been otherwise, if Pedro were there?

If this .500 player were to magically appear (I'm not being sarcastic, if it sounds like I am, I'm serious), and Pedro were still around, the .500 guy would be replacing some other replacement level guy? The .500 player is or isn't coming anyway, whether or not Pedro is there. So the loss of Pedro doesn't allow mean he'll be replaced with a .500 player over time. It means some other replacement level player WON'T be replaced by the .500 level player. The net 'gain' if you lose Pedro is still a replacement level player.

Let me know if that didn't make sense, but I know what I'm trying to say in my head. Please explain this concept to me, because as I understand it now, it doesn't make any sense to me.

And lowest level regular position players (say 28-30) are generally in the low .300's in terms of OWP, sometimes a few are in the .200's. Makes me think this is where the replacement level is for a season, not .400.

Again, I'm not being sarcastic, I need help with this concept. Thanks!

I am glad that Tangotiger and I (and doubtless many others) have come to the same belief that the time element can reconcile the replacement level vs league average baseline debate. Scruff, the concept is pretty simple.

If Pedro were scheduled to start tonight, and he was hit by a bus this afternoon, the Red Sox would have few alternatives and they'd probably start some middle reliever in tonight's game. However, the GM would immediately begin to scramble to find a better alternative for future games. Six months from now there's no way that they'd still be starting this terrible middle reliever in Pedro's spot in the rotation. In the interim, they would have made trades, brought up some youngsters, moved other pitchers into the rotation, etc. A year from now one of their Triple-A prospects might be ready for the major leagues. Five years from now a phenom who is now in high school might be pitching in "Pedro's spot".

The fixed replacement level approach suggests that the Red Sox would pitch this terrible middle reliever in place of Pedro for the next 10 years, say. Of course, they wouldn't.

One of the factoids that convinced me that this reconciliation is actually the correct way to think about things was the aftermath of the 1997 Florida Marlins' world championship. Theie owner dumped all the good players in 1998 and they wound up with a .333 win pct in 1998. But then through "natural" evolution (development, trades, etc.) they got better the next few seasons. In 1999 they were .395, and in 2000 they were .491. So, teams don't stay down in the dumps for very long these days. This makes me think that the replacement level concept is best thought of as a dynamic target moving up over time.

But Rob, isn't the Sox GM trying to find better players right now anyway? If Pedro weren't hit by the bus, he could be trying to fix the problem at 2B or something, but now he's got to use his resources to fill a pitching slot. Sure the Marlins players developed and they didn't stay down in the dumps, but instead the Orioles went in the crapper. Just because one team doesn't stay down long, doesn't mean a team eventually replaces everyone with average players. It means they'll have a replacement player at another roster spot that they couldn't replace, right?

I guess what I'm saying is that even if the phenom develops, the team would be better with Pedro and the phenom, not the phenom and whoever their new 5th starter is (in place of Pedro), which most likely won't be an average pitcher on a typical team. That's where it falls apart for me.

Scruff, I see your point. My mental model is that GM's are constantly trying to improve their teams. But their options are more limited in the short run than in the long run (obviously). Think of it this way. GM's try to "churn" anybody who is a below average player at his position. Every off-season, say, they throw all their players who are below average back into the pool of non-regulars. Then they draw somebody else (they may "draw" the same person again) from this pool, including minor leaguers, new players acquired via trades (and maybe free agents), allowing for development of existing talent.

Studies have been done that show that the long-run average performance of a player "chosen" from this pool is just slightly less than league average. This was quite surprising to me at first, but the more I think about it the more sense it makes. Many, many major league regulars were at one time in this pool, so choosing from this pool is not such a bad thing. The saving grace is that if you get a "lemon", you can discard him quickly and choose again. Eventually you'll land yourself a decent player. Again, this gives another explanation of why the replacement level approaches the league average over time.

Scruff:

You are probably right in theory: assuming infinite options and perfect decision making.

I think you also have to consider that, in practice, a (non-Yankees) team cannot always afford an "average" or better player at every position. In practice, if you've got Pedro and a whole in second base, your options for second base are limited. If Pedro gets hit by a bus, maybe insurance picks up the contract and you can go out and get someone better.

So, the A's lose Giambi. Short term, their performance drops as they are forced to stick in their best available option at the moment. Maybe Pena's the answer. Maybe he's only a replacement level player, and you try for better next year. One would therefore not be surpised if the A's (or any other team who loses a player they are trying to re-sign) got replacement level performance at first base in '02. But now, with 10s of millions of extra dollars, you can make up a lot of the difference between Giambi and replacement.

Similarly, if Scott Rolen gets injured now, there's only the utility infielder to pick him up. There are free agent third basemen on the market every year. None of them would even have considered Philadelphia 2 or 3 years ago. Why would an average 3B go to Philly, when they have an above-average guy there for the foreseeable future? This off-season, Scottie moves on. You try minor league prospect Chase Utley. If he bombs, Travis Chapman's in AA. If they both stink, in the next two years or so some decent free agents come onto the market in time for the new stadium in '04 that you can buy with the $14M you're not paying Rolen anymore.

Scruff wrote:

"Sure the Marlins players developed and they didn't stay down in the dumps, but instead the Orioles went in the crapper. Just because one team doesn't stay down long, doesn't mean a team eventually replaces everyone with average players."

Another thought. This may be exactly the point. When the best player in baseball goes down, he would be placed by a player who is approximately replacement level (or he will be replaced by a utility player who is replaced by a replacement level player, which is effectively the same thing.)

The overall quality of the major leagues has decreased by the difference in play between the best player and the new replacement level player.

But soon (next week, the trade deadline, the off season, three years later), players will start to move. The replacement level player will be replaced by a free agent or a developed prospect. At a cost to some other team, of course (the overall quality of the league stays the same), but over time the diminution in player skills will diffuse over all 30 teams.

Since replacement level theory deals with a player's value over the next best option available to his team, that replacement level should rise as the number and variety of players available to his team rises.

Another tack:

The Red Sox assumedly have signed the 25 best players in the universe who are not signed by any of the other 29 teams (in either their major or minor leagues). When Pedro gets injured, he must be replaced by player 26 on the Red Sox depth chart, who is (let us assume) exactly at replacement level. (Assume also all GM's have perfect knowledge, so no other team will take player 26 in a trade for someone better).

Next week, the Mariners who (let us assume) have an above-average system, and the Orioles who (let us assume) have a below-average team, need to cut someone (or put them through waivers) because Edgar Martinez and David Segui are back from injury and ready to play. The Red Sox look at the 2 players who are cut, let the one the Orioles cut (who is below replacement level) go play in an independent league, and decide the sign the one the Mariners cut (who is slightly above replacement level) and cut player 26, who is exactly at replacement level.

Assuming these transactions happen regularly, one would assume that a perfect judge of talent could expect a slightly-above-replacement-level player to show up within a fairly short period of time.

Now, it's the off season. There are more free agents. Contracts expire. Can you do better than the Mariners' cast off? Probably.

With each upgrade, the replacement level increases, and the lost value from losing Pedro decreases.

I have unearthed the formula I previously published on this topic. Let N be the number of years it would take a team of replacement level players to reach .500 through "natural" channels (development, trades, free agents, etc.). Let R be the number of wins that a league-average player would contribute to a team of replacement level players in the first year.

Then the cumulative additional value above replacement (but below league average) that a player who plays Y years is given as:

A = ((Y*R)/(2*(N-1))) * (2*N-(Y+1)) ; for 1 <= Y <= N

where I have assumed that the team improves linearly over time. A is capped at the value of the formula when Y=N, since by construction the team attains .500 after N years.

I think a reasonable value for R is about 3 wins. I am not sure what would be a reasonable value for N, maybe around 10 years.

For example, if one player (Koufax) played 9 years, say, and another player (Sutton) played 20 years, Sutton would get an additional 10 years of cumulative additional value above replacement. Under the R=3 and N=10 assumptions, this additional value is 15 total wins. Hope this makes sense.

The Arizona Diamondbacks went from not existing at the major league level in 1997 to stocking a team solely through the expansion draft (replacement players) and free agency in 1998 (and going 65-97)to going 100-62 and winning the division in 1999.

The closest thing to a replacement level team any recent era was the 1962 New York Mets (40-120). They won 100 games and the World Series 7 years later. And they didn't have free agency to stack the deck in their favor.

What makes you think that a good, resourceful GM (or even an average one) would take 10 years to reach .500 from replacement level? I'd put the number much lower.

Matt is probably right that the number of years a team of replacement level players (say an expansion team without any good players) would take to reach .500 is less than 10 years. In the absence of free agency and salary-burdened players, I would say it's probably closer to 5 years. Free agency and other modern factors have served to speed up the "churning", making a faster transition possible nowadays.

Under the assumptions of R=3 and N=5, using my formula for the Sutton/Koufax example, Sutton would receive an additional 7.5 wins for playing more years than Koufax.

Tieing this to a previous post, I am an advocate of crediting peak performance in a non-linear fashion to reflect the high-peak player's team's more than proportionate chance of winning the pennant. As I posted earlier, I have come to believe that an exponent of 1.2 is appropriate on wins-above-average figures. Of course, this adjustment would help Koufax vis a vis Sutton.

Matt/Rob -- thanks for the explanations, I was away this weekend, I'm finally now getting to respond.

I can see the 1.2 exponent thing, because of the pushing a team over the top in any given year factor. I'm on board with that one.

I'm still not on board with the .500 replacement level over time thing. Is this commonly accepted or has anyone else disputed it? I don't want to make you guys have to keep explaining it, but is a light-bulb going to off for me here at some point? I'm not sure what else you guys can say to convince me.

How much of that 1.2 is replacement going to .500 over time, and how much is pushing a team over the top in any given year? That's where I'd set my exponent.

I guess I still say the .500 player is coming whether Pedro, Koufax or Sutton is there, so I don't see why Koufax gets credit for that while Sutton doesn't.

Scruff, I am not sure if this is a light-bulb issue or not. I imagine that you are understanding the argument, but that you just don't buy into the argument.

Let's separate the 1.2 exponent issue from the replacement level vs league avg baseline issue. To me the two issues are distinct. The exponent issue pertains to the non-linear impact that above average players have on their teams winning pennants. That is, the relationship between pennants and games above average is non-linear. The baseline issue pertains to what the proper baseline to use to evaluate players' (games above average vs games above replacement).

At the risk of repeating myself, here is how I think we should think of the baseline issue. Suppose you are trying to evaluate two players, call them Koufax and Sutton, Koufax played for 9 years and Sutton played for 20 years. From a games above average perspective, let's say that Koufax is higher than Sutton over their respective careers. Would you conclude that Koufax was the better player from a "career value" perspective?

That would be the immediate right answer if average players grew on trees, so to speak. For the following reason. After Koufax retired, his team (call it the Dodgers) had to replace him with someone else for the next 11 years (that Sutton was still active). If the Dodgers could easily replace Koufax with a league average player for those 11 years, then the immediate calculation is sufficient.

Of course, that is not correct since teams cannot easily replace every player with a league average player. So our task is to estimate what "value" the Dodgers could be expected to receive from their "replacement(s)" of Koufax during those next 11 years.

Using 11 years of the expected one-year replacement level player is tantamount to assuming that the Dodgers would have to replace Koufax each year for 11 straight years. This is not a reasonable assumption, since they could well come up with one or two decent players in those 11 years. (I think we all agree with this statement.) If you accept this premise, then a steadily increasing baseline concept makes sense.

This steadily increasing baseline represents the baseline to which Sutton's "extra" 11 years should be compared to. Think of it as a roster reservation price. Having Sutton on your roster for those extra 11 years may prevent you from acquiring good, or even great, players during that time.

Anyway, the concept of a reservation price varying over the time period over which the reservation is in place is quite common in economics.

I think Matt makes the simplest explanation. Starting with nothing, in fact, already being down 150$ million of expansion money, the Diamondbacks went from no wins to the World Series in very little time.

While the replacement level issue is about "cost-free talent", every team has SOME money that they can use to buy talent. Whether through the draft or trades or whatever, you can always get some talent.

Starting from scratch, you can buy yourself into a .500 team. Not alot of money, just "Average" money. If you have no money, all you can get is a replacement-level team.

So, why is it we have to compare a player to a replacement-level player, when with just a little money that is already available, you will eventually get yourself a .500 player?

While I agree with tangotiger's conclusion, I am not enamored with the argument. Once you emphasize the money angle, you lose me. If some money can get you to .500, why not spend even more money and get above .500 (say .600)? Does that mean that we should use .600 as our evaluation baseline? Of course not.

The proper baseline approaches .500 over time because .500 is the league average. Nothing to do with money. Over time, the average player utilized from a "replacement pool" performs nearly at the league average. Time is the essential ingredient, not money.

I would recharacterize tangotiger's argument as follows. Nearly every team (with the notable exception of Connie Mack and a few others) has sufficient wherewithal to take advantage of the "replacement pool" vehicle, so that over time their "replacement" players approach the league average. But it is the time dimension that is key, not the money.

I'm not so sure Rob. Money is not an issue for the first few years. When they become arbitration eligible and free agent eligible, money does become an issue.

Let's say that you are an expansion team, and you get to stockpile your team the usual way. You'll get a whole bunch of .400 players that will be aged from 25 to 32, all making 500,000$ (essentially replacement level $).

At the same time, you get to draft players every year, which costs you 4 million$ every year. As the players age into 22, 23 years old, you bring them up. Some players will start off at .400 level, and progress to .500 by age 27 or 28. Others will start off at .400 and peak there, and be out by age 25. Others might start off at .450 and peak at .600 by age 29 or 30.

On average, you probably get a .450 team in any given year, just by going through the draft. That is, just behind a stupid GM, you should be able to field a .450 team, since a monkey can field a .400 team.

However, GMs also have money. Since the very smart GMs will be able to exploit the money, they'll be able to field a .550 or .600 team.

While time is an important element in this discussion (because players age and churn), money is important as well.

Don't forget, what a player is is an asset. If Piazza gets 91 million$ over 7 years, this is because the Mets expect him to generate say 140 million$. If they sign a player for 1 million$, they don't expect him to generate more than 2 million$.

The concept of "freely available" is fine, until you think about this. Do you want a free couch that will sit one person uncomfortably, or do you want to spend 500$ for a couch that will sit 3 comfortably. There is a payoff in getting better talent. You pay for it, but in the end, you also get the money back in extra revenue.

I don't buy the freely available, because they give you as much as you pay for them. Almost nothing.

scruff, I'm with you. I don't buy the .500 replacement level argument.

I buy the part about a potential value difference between the emergency stop-gap player needed NOW (possibly below true replacement) and the patch applied after exploring options.

I don't buy the long-term rise. Viewing the picture MLB-wide, the injury to the top-level player still results in one additional marginal player getting to play who wouldn't have otherwise. This is true 5 years later and 20 years later. No potential .500 level player makes a career change decision to baseball because a roster spot has become available.

A particular organization may be able to apply its resources to do better than replacement for themselves, but this just transfers the replacement problem to another organization. Any overall rise in the MLB-wide replacement level would then derive from the hypothesis that these talent redistributions result in player development that wouldn't otherwise have happened (better competition makes better players). I need to be convinced that that is what happens.

Okay, I now can better appreciate your money argument, tangotiger. My time-is-king argument is most valid under the old reserve clause, or at least in an environment in which teams did not think about losing their players to other teams. The money issue becomes more important as the number of years players are tied to their teams decreases, such as in the free agency & arbitration era.

Light bulb. I think I got it.

100 years from now, what is the best guess at team X's W-L record? .500, right? That would represent the expected replacement level at each position on the team.

20 years may be too short a time frame to get there (correlation studies of team records between year Y and Y+N are needed) and there may be individual franchise qualities that interfere with that prediction (the Yankees may actually be higher than .500 due to their economic advantages which show no sign of diminishing).

jimd: yes, exactly. In 100 years, after many generations of baseball players come and go, you will expect that a team will average .500.

Maybe 20 years is too short, I don't know. But I don't think so. Look through every single expansion team from 1962 to 1993. Tell me how many years it took them to get to the .500 level. You'll get some teams at 5 or 6. Some at 12, 17, etc, etc. What is the average number of years that an expansion team takes to get to the .500 level?

I'm going to take a wild guess and say it's 9 years. I guess I should go look it up....

4 Col

Right. I think where people get hung up is in failing to separate the team factors from the league factors.

When a star retires, that opens the door for a marginal player. But ten years, down the road, what are the odds that the marginal player (or his marginal replacement) is still stinking up the field for the team the star retired from? Probably about 1 in 30. The rest of the time, he's playing for Pittsburgh or Tampa Bay.

So, if Mike Piazza retires today, the Mets probably get replacement level catching for a while, but in a few years, they've done some deals and tried some tries, and probably have about league average catching over the next ten years. (I think the conversation got muddled using pitchers as an example, because it's not so clearly an either/or debate. You can have both Johnson and Schilling on your team, but you can't have both Piazza and Posada.)

I wouldn't be surprised if the difference between .500 and "approaching .500" is 1/30th of the difference between .500 and a one-day replacement level player.

Money is only a factor because you've got to assume the team has "average" financial resources. So, while their short term replacement will be the best of the freely available talent, the loss of a star player will permit the team to devote more resources to a replacement than the proverbial "freely available talent".

If the A's lose Giambi, they've now got more money to pay someone else, so can take on some other losing team's salary dump if they find themselves in contention at the trading deadline. The value of Giambi's replacement goes up, and the marginal player is transferred to (usually) Kansas City. The marginal player is still in the league, but to the extent he's not playing for Oakland, he doesn't represent the value lost by not re-signing Giambi.

Tango,

I think all of your numbers are off by one. The California Angels started in 1961 and were above .500 in 1962. I'd consider that taking one year to reach .500, not two.

You are right. I should have said "8th year" and not "in 8 years" as the average time it takes for an expansion team to reach .500.

Free agency started in 1976. Therefore, let's only look at the 8 teams in expansion between 1960 - 1969.

The average year in which they hit .500 was .....their 8th year.

Flo, Col, SEa, and Tor, the 4 free-agency teams averaged .500 in their .... 8th year.

(Arizone is not part of this study, and neither is Tampa)

Here are some correlation studies of winning Pct at Year Y versus Year Y+N:

01) 0.75 02) 0.65 03) 0.61 04) 0.55 05) 0.48 06) 0.43

Well, well, well. That is certainly a very interesting study.... Good job!

I was going to say something about the issue being clearer with regard to position players than pitchers, but Matt beat me to it.

JimD, what was the time period for your study? Did you go back to the entire 20th century?

I wonder if the baseline incline (the number of years for a team of replacements to reach .500) was longer back in the early days. Since we will be discussing players from the beginning of MLB, we shouldn't come up with an estimate that only applies to post-1960 ball. My thought is that nowadays scouting and development is far superior to what it was 100 years ago, so I would guess that the incline would have been longer back then. Any ideas?

I have the Lahman database installed, and I have made a copy of the teams database in which I've modified all the team names to their modern ones (e.g. 'ATL' then runs from 2000 back to 1871) so it normalizes franchise shifts.

So this study includes all MLB team seasons from 1871 onwards. The 1 year comparison was 2227 pairs, the 30 year comparison 1332 pairs.

JimD, thanks mucho. I guess I am wondering if the correlation within franchise win pcts from year to year were higher 100 years ago than it is today. This is kinda the flip side to the parity issue. My belief is that teams long ago enjoyed more sustained success (and failure) than they do today.

Could you re-run your analysis splitting MLB history into different eras? Thanks again.

http://baseball.fanhome.com/forums/showthread.php?threadid=1004932&pagenumber=4#post4716068

So, it looks to me from jimd's numbers that about 30% of what keeps a team down is "bad ownership/ management". That should be taken into account in figuring out how long an average team goes from "one year replacement level" quality to .500. Specifically, teams that ever approach that level of badness are probably more likely to have "bad ownership". So, if it takes an "average bad ownership team" 7-8 years to reach .500, it would take an "average team" only 5-6.

Hijacking this thread by continuing tangotiger's thread here...

Alright, here's your 19th century teams, same rules

Pre-50's 20th century teams:

(1) 1900-2 NL New York Giants - 2 years

Post-WWII 20th century teams:

(9) 1946-8, 7-9, 48-50, 49-51, 50-2, 1-3, 2-4, 3-5, 4-6

This list is similar to the one I posted on fanhome. Again, I see no reason that we should continue to use the "freely available" definition as a basis for comparison.

In-season, sure that makes sense, because your hands are tied, your money is tied, and your players are tied, and you need a quick fix just to keep playing, and any good move you make might cost you something somewhere.

But, taking a long-term view, if you continue to play that .430 player, it's going to hurt. And since we now know that in 8 years you can turn out a team of players who average .500, why do we need to value a player's CAREER against the "freely available" line? Why not value a player's career against his opponents (.500)? If you continue to keep playing a .470 player YEAR AFTER YEAR, you know what, he's going to cost you because his peer is a .500 player.

The value of a player's career is NOT the sum of player's seasons.

Rob, I heard that you wrote an article a few years ago about this progressive replacement level that I'm talking about. Can you email or send me that article? I'm thinking of writing an article on this subject as well. Thanks....

Tangotiger, I just emailed you the article you requested. Let me know if you have any questions. I encourage you to write an article on this topic, especially if you provide empirical evidence on the "increasing baseline" (how long it takes really bad teams to reach .500) throughout baseball history.

By the way, I really like the fact that you and JimD have been looking at this data. However, I would caution that estimates from this method probably under-estimate the length of time we are looking for. Virtually all the bad teams that you have listed were truly bad teams, however they were not as bad as a team made up exclusively of (one-year) replacement players. I'm not even sure that the expansion teams were truly made up of 100% replacement players -- although maybe the 1962 Mets were :) .

Rob, I agree that these teams are not made up of replacement-level players. After all, a team made up of such players will play at a .300 level.

These teams however are sub-400 teams, and if we think of it in linear terms, and assume that these teams averaged .375, then it takes 7 years to add .125 wins. A .300 team needs to add .200 wins, and so it would take such a team 11 years to reach .500 (at the same linear rate as the previous group, which is no guarantee).

I don't think it impacts much on the analysis, though I will make sure to take this into account.

Thanks...

Okay, so it looks we have gravitated to a number around 10 years for a replacement level team to reach .500. And, if I am interpreting the various historical posts correctly, this number generally applies throughout baseball history.

Lost amidst the clutter of the data I presented was my main point.

It didn't take 8 years to get from .400 to .500; it's more like 4 years. Most of these pre-free-agency bad teams stayed bad for years, clueless. Then, suddenly, something changed in the organization, and they went over .500 in 2-4 years.

There were 27 such teams this century between 1900 and 1973. 5 of them went from under .400 to over .500 in 2 years; 9 of them took 3 years; 8 of them took 4 years; 4 of them took longer (5-7 years); 1 team took 12 years. The average is 4 years.

If we accept that under .300 is a replacement level team,

Here you go, Rob Wood.

The eras were chosen as follows:

If one subscribes to the "increasing baseline" argument, a challenge exists as to how to incorporate the concept in player evaluations. Since the baseline is not constant, you cannot simply take a player's seasonal stats (such as win shares or WAA) and adjust them to reflect his value relative to "replacement".

A simple example will suffice. Suppose A played 10 years, B played 11 years, and C played 12 years in their respective careers. Consider the A-B comparison. Since B played one more year than A, B should be given credit for one more year of playing relative to replacement. Let's say the one-year replacement adjustment (vis a vis league average) is 3 wins. So B should be credited with 3 extra wins for playing that extra year relative to A. Same thing for C's extra year relative to B.

However, C's extra years relative to A are a little trickier. Here C played two more years than A. The increasing baseline argument suggests that the additional value C should receive for playing the 2nd year is less than the first year. Let's call it 2 wins for simplicity. Thus, C should be credited with an extra 5 wins (3+2) relative to A.

But you can now see the "problem". These extra credits violate the transitive law of addition. C is credited with 5 wins relative to A, C is credited with 3 wins relative to B, and B is credited with 3 wins relative to A. That is, there exists no set of constants that can be added to each player's career total that are consistent with these extra credits. And the problem becomes even more an issue when you are talking about comparing dozens or hundreds of players.

I am hopeful that there is a straightforward solution to this problem. In the article I wrote on this topic a year or so ago, I suggested that the counting of the increasing baseline begin in the player's first year of his career. In this way, you can simply add in the proper amount to his career relative to the longest career anyone has ever had (say 25 years).

Now that I think about this approach, I am not at all happy with it. For it implies that, under the assumption that it takes 10 years for a team of replacements to reach .500, there is no extra credit for a player (such as B and C above) who plays more than 10 years and plays more than another player (such as A above).

Any ideas?

Rob, if it takes 10 years (just to use a number that we can discuss) to find or develop a player to get to .500, then I see no reason why you need to give player extra credit for playing the 11th or 20th year.

If a player continues to play at a .470 level while he is 35, should he be replaced right away? Not necessarily. After all, there is a tradeoff in time just to find a guy to even play at the .470 level.

So, where does that leave us? Well, rather than developing a curve that goes up to year 10, and flatten at .500, why not develop a curve that goes up to year 10, AND THEN BACK DOWN. That is, if you have a guy who starts at .400, and gets to .500, and is back down to .450, he will continue to be employed.

I would even say that the midpoint should not be .500, but something HIGHER. After all, if you knew that the best this player will do is have 1 year where he'll be average (you don't know which year), would you have this guy on your team for many years?

All I'm doing here is modeling a player's aging pattern, and drawing a line .100 wins (or whatever) below this.

Tangotiger, this is a neat idea that I toyed with too. Something about it troubles me, but I haven't been able to put my finger on it.

Yes, I think there are issues as well.

What I don't believe in is comparing a player against a "freely available" line. Except for in-season moves, no GM in baseball acts in this manner. They all have money and budgets and plans.

Therefore, I believe we are on the correct track with a varying comparison line. We just always have to use expansion teams as our guide.

I read Rob's article/compilation in BTN, and it's very interesting.

I believe that we have to make a distinction between freely available talent, and minor league available talent. While the freely available talent level may be .400, the minor league available talent is far higher than that. Somewhere close to .500.

What I am suggesting is that there are far too many bad players currently playing, and the good players are locked up in the minors. Teams are not aggressive enough.

That in actual fact because teams are not perfect talent evaluators they are not maximizing their risk/reward.

The freely available line and the minor league line should actually coincide. And I believe that this level should be somewhere around .450.

I will attempt to do more research on the matter, but so far my research is giving me some very interesting results.

Interesting ideas tangotiger. Two related comments. In almost any situation in which decision makers do not have perfect information (perfect foresight, etc.), they are apt to be "conservative" in their judgments. Information is not costless, as this discussion makes clear. Thus, some GM's or managers would rather play a known quantity (say a .400 player) than play an unknown quantity with higher expected value but more variance, especially on the down-side.

The concept of a certain equivalent may be relevant here. Under a general set of assumptions, the value (i.e., certain equivalent) a decision maker ascribes to an uncertain outcome (L) is given by:

CE(L) = M(L) - 0.5*R*V(L)

where M(L) and V(L) are the mean and variance of the uncertain outcome distribution, respectively, and R is the decision maker's degree of risk aversion. R is 0 for a risk-neutral agent and R is positive for a risk-neutral agent. Clearly, the riskier is the lottery (e.g., an unknown player), the less willing the GM or manager will be to play him.

I don't know if this concept is useful in our discussions, but I throw it out there for what it is worth.

Oops. In the last post, I meant to say that R is positive for a risk-averse agent.

"What I am suggesting is that there are far too many bad players currently playing, and the good players are locked up in the minors. Teams are not aggressive enough.

That in actual fact because teams are not perfect talent evaluators they are not maximizing their risk/reward."

This is probably true, but I've got three points to add to put a different spin than just incompetent teams leaving better talent in the minors:

First, talent is not evenly distributed. The A's and Mariners likely have minor league talent better than half of the current Devil Rays and Brewers, but that doesn't mean those minor leaguers are better than the A's and Mariners current major leaguers. If the A's have a .475 guy in AAA, and the Rays are playing a .400 guy at the same position in the majors, then replacement level line dips below the minor league line. This is not because teams are making bad choices as to what players to put on the field, it's just that the right player just might not be on your team.

On the other hand, if I'm the Rays and I've got a .400 guy on my team and I've just drafted a college guy who's 23 and .450, I can swap them immediately, or I can leave the new guy in the minors for a while to catch more of his peak years before I lose him to free agency or a high arbitration price. Once again, the minor league line climbs above the replacement line, but not because anybody in making a wrong decision.

Finally, (and contrarily) if I've got choice between a 23 year old rookie playing .425 and a 6-year minor league free agent playing .475, there are reasonable reasons to keep the kid up and "see what he can do" rather than ship him to the minors a la Carlos Pena or Hank Blalock, especially where my team is not contending this year.

So, overall, maybe I'm saying that in practice the replacement line SHOULD be below the minor league line because, just as a player who plays for ten years shouldn't be compared to a one-year replacement level, a team that will continue to exist for ten years should not be judged on how it distributes its talent in one year.

I agree with both your last posts. Good stuff...

Because it takes time to evaluate talent, a GM is probably going to say that Brandon Phillips is, at this moment in time, a .350 to .550 player. He might say that Montreal's backup infielders are .400 players.

So, he has a choice. Should I leave Brandon down there so I can determine what his true talent level is within a .100 range level instead of .200? Or, do I take a chance with him, give him FEWER AB as I leave him on the bench, and take an extra chance that maybe he is actually a < .400 player?

However, in "true replacement fashion", if Vidro or Cabrera goes down, Phillips comes up right away.

Therefore, we shouldn't think of the "freely available line" as the line of comparison. There are many reasons why the MLB freely available line is BELOW the minor league available line.

I continue to see no reason why we need to compare to the freely available line. A standard .450 comp point seems to me like the best/easiest one at this moment.