Win Values Explained: Part Six

Over the first five parts of this series, we’ve discussed all the components of what makes up a Win Value. Today, we tackle the conversion of that win value into a dollar value.

First off, a little background. Since we’ve set replacement level at around a .300 win% (or 48 wins per team), that means that there are about 1,000 marginal wins in a major league season. All 30 teams are fighting over these 1,000 wins, each trying to get more than 45 or so to get them in the playoffs.

Every dime a major league team spends above the major league minimum is theoretically spent in an effort to buy as many of those 1,000 wins as possible. A major league team’s minimum payroll is about $12 million, so MLB as a whole has a floor of $360 million in salary per season. Total payroll for MLB teams in 2008 was reported at $2.67 billion. That means that major league teams spent $2.31 billion to try to buy their share of those 1,000 marginal wins. Basic division tells us that the cost of a win in MLB salary was $2.31 million per win for 2008.

However, a huge share of those wins were created by players whose salaries were not determined by a free market system. Every player with zero to six years of service time had an artificially depressed salary due to not being able to qualify for free agency. As well, most players who signed long term contracts that bought out some of their arbitration and free agent years had salaries below market value as well – they had traded some potential cash for the security of a deal several years ago. The amount of money that teams are paying per win for their cost controlled players is far less than the $2.31 million league average.

So, the market of wins available for purchase doesn’t total 1,000. A significant batch of MLB players simply aren’t available for acquisition at any given time. The Cardinals aren’t trading Albert Pujols. The Mariners aren’t trading Felix Hernandez. The Rays aren’t trading Evan Longoria. The wins that these players generate are not for sale.

Who is available? Obviously, players who qualify for free agency in a given season are available. Also, there are players traded from one club to another, so those players are also available for the right price. But what is the right price?

In general, we can say that the market price of a win is the mean of the dollars per win handed out to free agents in any given year. If you approached CC Sabathia this winter and offered him $12.65 million because he was a 5.5 win pitcher and the league average cost per win is $2.3 million, you wouldn’t have gotten very far. If you want to compete in the market for available wins, you have to know what the going rate for a win is, and the easiest way to calculate that is to look at the free agent market. Let’s look back at 2007, for instance.

90 free agents signed major league contracts last winter, ranging from Alex’s Rodriguez $275 million deal to Josh Towers‘ $400,000 contract with the Rockies. The sum of those 90 contracts paid out $396 million in 2008. To figure out what the average cost per win of a 2007 free agent was, though, we need to know how many wins that group was worth.

To calculate this, I did a three year weighted average of their win values, then multiplied that value by .95 to factor in aging and estimate what teams considered considered a player’s true talent win rate for 2008. In total, I came up with 88 wins, or $4.5 million per win. That’s what major league teams were paying for a marginal win last winter, so for 2008, that’s a players dollar per win value as listed on the site. I re-did this for all years going back to 2002, and the dollars per win for each are as follows:

2002 – $2.6m / win
2003 – $2.8m / win
2004 – $3.1m / win
2005 – $3.4m / win
2006 – $3.7m / win
2007 – $4.1m / win
2008 – $4.5m / win

Now, I know there’s some sentiment that teams don’t pay for wins linearly, because a six win player is worth more than three two win players. While I agree with this in theory, major league teams just don’t operate this way. If you just look at the dollar per win costs for the multi-year contracts handed out to hitters last year, the cost per win was $4.3 million for guys with an average win value of 4.4 wins per player. Alex Rodriguez signed for about $3.8 million per win last year. Teams just don’t pay exponentially more for higher win value players than they do for average and below players. You could argue that they should (and I would probably agree), but they don’t. The dollar per win scale is linear.

This afternoon, we’ll look at the opportunities that are presented to teams due the linear nature of dollar per win, and how the smart teams are exploiting this to their advantage.




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Dave is a co-founder of USSMariner.com and contributes to the Wall Street Journal.


44 Responses to “Win Values Explained: Part Six”

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  1. Thor says:

    Dave,

    As a long-time lurker on USSM, I’ve read a lot of your analysis into these issues, and something still bugs me about the linear dollar-per-win finding. Isn’t it possible that the high win-value players are signing longer contracts than low win-value players, and thus we can’t correctly identify the dollar-per-win curve without making strong assumptions about how teams and players value long-term contracts?

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    • Dave Cameron says:

      Isn’t it possible that the high win-value players are signing longer contracts than low win-value players

      It’s not that it’s possible – that’s exactly what’s happening. The data makes it fairly apparent that the premier free agents on the market don’t negotiate in terms of dollars per year nearly as much they do in total years. Alex Rodriguez was more concerned about a 10 year deal than he was about getting $30 million per season. Same with Sabathia and Teixeira this year.

      Great free agents get long (7-10 year) contracts. Good free agents get multi-year (4-6 year) contracts. Average free agents get short-term (2-3 year) commitments. Below average players get one year deals.

      They all get paid similarly in terms of $/win, but the length of the deal is where the premium free agents are getting their extra money.

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      • toad says:

        But this suggests that the annual salary does not reflect win value for premier FA’s. When you give someone a long-term contract you are not necessarily assuming he will maintain current performance levels for the length of the contract. How do you think A-Rod’s win values will compare with his salary five or six years from now?

        Much more of the money is being paid for near-term performance than longer-term, even though the annual breakdown of salary doesn’t look that way. Long-term contracts, eveluated over their life, would, I suspect, show a much higher price per win than the apparent value.

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  2. Thanks for the explanation, Dave. Much appreciated.

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  3. David says:

    Two questions. In order to find a free agent’s expected value in the 2008 free agent market, what number should we multiply wins by? You just mentioned the 2007 value. And also, what is the going rate for arb. eligible players and pre arb. eligible players?

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  4. TangoTiger says:

    Fantastic stuff Dave.

    I was working on $4MM per year in 2007, with less rigor than you applied to get 4.1. I then presumed 10% growth rate going forward and backward. So, I figured 4.4 in 2008 (you get 4.5). I presumed 3.64 for 2006 (you got 3.7). In 2005: 3.31 for me, 3.4 for you. In 2004, 3.01 for me, 3.1 for you. In 2003, 2.73 for me, 2.8 for you. In 2002, 2.48 for me, 2.6 for you.

    So, I am very very pleased to see additional evidence for the 10% growth rate that I presumed. And that I am centered pretty much where I should be.

    Great stuff.

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  5. Anonymous says:

    Hey guys… I’ve been reading a lot about this win value stuff, and it excites me a lot. I’m really intrigued by the way that you find your data and whatnot. However, after doing some basic researching, I think you guys have something wrong.

    If win values are what they say they are — WIN VALUES, they should be able to predict a team’s won-loss record, right? The Phillies, though, have 29.7 value wins.

    In seeing that, I realized that something must be wrong. This is not wins above replacement… and even if it is, according to your data, the data is not adding up correctly. Replacement level, you say, is 48 wins. 48 + 30 is 78… a below .500 team. Something in that data is obviously not right.

    When in doubt, go to Baseball-Reference… and I went there, and did this simple computation — how many runs are there per win? There are about 2430 wins in a given season (81 multiplied by 30). I divided the number of runs scored per wins (that’s found in the splits on B-R, like right here: http://www.baseball-reference.com/pi/bsplit.cgi?lg=ML&team=TOT&year=2008), and averaged it out for the past three seasons. My total? About 6.5. 6.5 runs is equal to a win.

    I then did the next thing — went back to the 2008 Phillies data, since that is the first page that shows up on the individual teams data of FanGraphs… and re-did the calculations. My total? 46.5 wins for the 2008 Phillies batters. I went to my favorite team, the New York Mets, and calculated again, this time getting 40.1, obviously a very interesting number… being that that’s less than half of their real win total… and their pitching (bullpen especially). There may be some flaws in my calculations, as it was hand-done [someone double check for me, please!]. But there you have it… and those numbers, to me at least, seem to make more sense.

    Obviously, these numbers mess up poor teams, and would essentially have them ranked at not being worth anything. That’s where the more knowledgeable people come in and tweak with my data. But it’s a start.

    Now — two things. How to adequately measure fielding is an issue. I think that there need to be more fielding numbers taken into the equation. I know getting the numbers may be a licensing issue and whatnot, but as much as I love UZR, it’s not enough. There needs to be an almost BCS [college football] type thing — in which 5 or 6 scores are averaged… the highest score is dropped, as is the lowest score, and then you get your number once the three or four remaining scores are averaged. I realize, again, that could be complicated. But boy, wouldn’t it be sweet to see an average of UZR, OPA!, RZR, PMR, and two others?

    And then, pitching. I was thinking that some type of number could be generated by using wOBA against (similar to how batting average against is used by the “mainstream” media), and FIP converted to runs.

    Those were just my long thoughts… hope you enjoy, and think about it! It might just make sense.

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    • tangotiger says:

      You are on the wrong track in a few places. Try to slow down, and read more. No offense intended.

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    • Now at age 70, I can say that I have been a Mets fan since they started and attended their first game at Shea Stadium, a day game vs the Houston Colt .45s.

      Now we live on a farm in Maine, so I am the Co-Editor for the FANSIDED Red Sox website, the Bosox Injection.

      I was so impressed with your analysis that I am wondering if your might be interested in contributing “baseball” statistical article to our website.

      As you can see, the staff covers the daily Sox stuff and I write a feature [general baseball column] every weekday.

      My thinking is that Red Sox fans are also interested in the game of baseball and can get plenty of “news” about the team from other sources.

      PLMK if you would be interested in writing an article.

      Baseball and “Let’s GO Mets!”
      Earl thethrillofthegrass@yahoo.com

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  6. joser says:

    And — as I suppose Dave is going to mention in his post this afternoon — the fact that higher-value players get their return in years rather than dollars/year can to some extent take care of the non-linearity in dollars as well. After all, the league-wide $/Win value continues to climb over the course of that long deal while the players’ skills generally don’t, and may actually decline, since the players signing those deals are usually in their prime at the start of the deal, not at the end. Take ARod: in 2016, when he’s 40, he’s still going to be paid $28M by somebody whether he’s productive or not. It’s more than a little dangerous to make a straight-line projection of league-wide $/win, what with new collective bargaining deals happening in the meantime (not to mention new attempts to reign in the Yankees’ spending habits or outright economic meltdown, either in baseball in particular or in the economy as a whole), but what the heck: just taking Dave’s calculations of $/Win and projecting it forward (guessing that about every 3 years it jumps by an additional $100K), we can estimate that teams in 2016 will be spending somewhere in the neighborhood of $8.5m-$9m per win. That values the 40-year-old ARod as a 3 to 3.4 win player. That’s the range that encompasses guys like Jacob Ellsbury, Ichiro, and Jason Bay today — guys who get a big bonus from their fielding. It’s possible Arod will still be playing the hot corner at 40, but it’s more likely he’s a 1B/DH by then — making his comparables more the likes of today’s Ryan Howard or Prince Fielder or Milton Bradley. It’s certainly possible to imagine ARod at 40 still being that good; but it’s equally possible to imagine him hobbled by injuries by then, or out of baseball altogether, spending his days as a zero-win player walking Madonna’s poodles to the bank to cash his checks. There’s your non-linearity.

    Incidentally, that projection on league-wide $/win implies that team salaries are going to double over the next decade. Considering the league average payroll went from $40M in 1998 ($1.2B league total) to $82M in 2007 ($2.5B total), that’s not as unrealistic as it initially sounds.

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  7. Dave Cameron says:

    If win values are what they say they are — WIN VALUES, they should be able to predict a team’s won-loss record, right? The Phillies, though, have 29.7 value wins.

    A couple things:

    1. No, they won’t match a team’s win loss record. They’ll be pretty close to a team’s pythag win-loss record, but we’re not attempting to value base-out-score-inning contexts, so the situational stuff gets left out. That’s intentional, not a flaw. We already have a metric that adds up to a team’s record and counts all that stuff – WPA. If that’s what you want, just use that.

    2. You realize that we haven’t included Win Values for pitchers yet, right? The 29.7 wins you’re noting for the Phillies is just for their position players.

    Nothing’s wrong. Our numbers work.

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    • studes says:

      We already have a metric that adds up to a team’s record and counts all that stuff.

      Yup. Win Shares. :)

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    • Anonymous says:

      In response to 1, can I ask — what exactly are you trying to accomplish, then?

      To #2, I do realize that… I included that in my long post above. But, then, did the Phillies pitchers — are they worth 60 games or so? Or is this wins above replacement? I’m just trying to clarify… not to cause a problem. Thanks.

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      • Dave Cameron says:

        1. We’re quantifying the amount of runs scored/runs saved that players give up in relation to each other that isn’t luck.

        2. This is wins above replacement. Every component is explained in the series I just finished up writing.

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  8. David says:

    Could someone please answer my question? What is the going rate for players in the current free agent market and what are the going rates for arb. eligible and pre arb. eligible players?

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    • Dave Cameron says:

      Could someone please exercise a little patience?

      The 2008 free agent dollars per win rate is right around $4.5 million per win, much like last year. This is the first non-inflationary spending we’ve seen for free agents in a long time. This could obviously change, however, since there are still a ton of free agents out there.

      Calculating the exact rates for arb. eligible free agents is a ton of work that requires a database with correct service times for MLB players. Feel free to build this database, send it over, and I’ll tell you what the going rate of dollars per win for those players are.

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  9. Kirk says:

    I had actually been wondering why you used a linear value for buying wins, but I don’t really agree with the explanation. Teams don’t pay the going rate for defense that you use, but you still use it.

    So why dismiss an increasing value for elite players just because teams aren’t doing it?

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  10. duffy duff says:

    I’m not sure I like the presentation of having the player’s actual salary next to his deserved salary in free agent dollars. One of the reasons that teams can pay 4+ mil per win to FAs is that they are paying much less per win to non-FAs. There’s an interaction there–if everyone had to be paid as a FA, their $ per win would be lower. In fact, it would be the overall $ per win.

    So I think I’d prefer to see a presentation of actual salary vs overall $ per win (over repl.). This would reflect that FA are overpaid, and non-FA are underpaid–instead of that non-FA are grossly underpaid and FAs are paid correctly.

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  11. Rich says:

    This may be a dumb question, but why did you use “.95 to factor in aging”?

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  12. Bearskin Rugburn says:

    WRT the compensation of exceptional players not factoring in their rarity, do you think it’s to do with the increased risk involved in counting on 6 wins coming from one guy? Seems like 3 2-win players are a far safer bet.

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  13. diderot says:

    As a dissenting voice, I really find this exercise pointless for the typical (or even sabremetric) fan. Win calculations are wonderful…collectively they help tell you how well your team is expected to do, and how it could get better.
    But isn’t adding the cost of those wins important only to the GMs, the players and their agents? If ARod makes $27m/yr., well, goody for him. If the Yankees can afford to pay it, nice for them. But the vast majority of teams aren’t going to be able to get into that bidding war, so what do the fans in Pittsburgh care? Their GM has to find a way to do more with less. Which takes you right back to the issue of wins.
    As long as teams have varying payrollsand there is no salary cap, they’ll have unequal opportunity to acquire the wins represented by various players.
    To me, in terms of relevance and interest, win shares and $ per win are polar opposites.
    But, if you just love doing the math, well more power to you…

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    • tangotiger says:

      If you find this exercise pointless, then this means that we haven’t done a good enough job in presenting the arguments.

      I’d say this is mostly related to the blog format, rather than having a full-blown article / chapter-type of presentation. It is partly related that many of us have had this discussion, and so, people are walking in the middle of a movie, and we’re trying to give them the catchup in a hushed 2-minute recap.

      ***

      Duffy’s point about whether to present the dollar figures along the free agent dollar scale, or the overall average dollar scale (pre-arb, arb, free agent) is a matter of taste. You can make the argument either way, depending on what it is that you are really trying to answer.

      Ideally, MLB would release the service time data to the public, and we’d present the salary data along service-time levels. While we have most of the service time through 2007, the up-keep for each future season is just another obstacle that need to prioritize.

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  14. CH says:

    diderot, I may have missed the point of your post, and if I did, I apologize. But the Pirates should care about $ per win because they have a finite amount of $. Yes, the Yankees and Red Sox can afford to pay (or in some cases overpay) for wins, but the Pirates can’t. $ per win is MORE important for a team like the Pirates.

    The Yankees can afford to make mistakes or be the victims of bad luck with big signings (Carl Pavano fits into one, or maybe both, of those categories) but the Pirates can’t. If you’re a Pirates fan, you should want to know whether or not the little money your team has is being spent wisely, or if it’s being spent foolishly.

    If the Pirates were continuing to pour money into players who weren’t truly earning their money, I think the Pirate fans would want to know that. True, the Pirates can’t afford someone like A-Rod, but don’t you think they at least looked at the relative value of Ryan Doumit before they gave him a guaranteed extension?

    If all you care about as a fan are wins and losses, then I guess you can ignore the salary data. But those wins come at a price, and a lot of fans want to know exactly how much of their ticket price is going toward tangible results on the field.

    I’m not trying to attack you or your opinion, I’m just trying to shed some light on why people other than GMs, players and agents should care about this.

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  15. duffy duff says:

    Tango, I think it’s a bit more than a “matter of taste”. This is essentially choosing a baseline to compare to, similar to what is done with batting. The default position should always be the average, to be changed only when convincing arguments are presented (as has occured with replacement theory).

    In this case the default position is the overall avg $ per win. I have seen no real persuasive argument (or really, any argument at all) as to why the FA baseline is preferable. And I don’t believe it is.

    BTW Tango, duffy duff is DS (think Baseball Boards).

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    • BIP says:

      Well, I think the reason the FA scale is used is because FAs are the only type of player who can be acquired exclusively with money. When looking at a given player’s value, to me the question is, “What is this player worth if a team wanted to acquire him solely by spending money?” As Dave pointed out, pre-arb and arb players can only be acquired via draft or trade. While draft picks and assets given up in trade have present-day monetary value, teams spend them with an eye towards some future value that we simply don’t have the information to calculate.

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    • tangotiger says:

      duffy: yup, I knew it was you, but I didn’t want to “out” you.

      You make a good point that it might be a bit more than a matter of taste. But as the next reader pointed out, the guys you really care about would be the free agents. Nothing is really stopping David A from showing BOTH (the free agent dollars, and the overall average dollars). He shows plenty of other data, so one more won’t hurt. We can all have our pizza and beer.

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  16. Justin says:

    You have to use a FA scale…………they are the ones we all talk about year after year, and they determine market values for the next year, etc. We are not talking about Player A who is 4 years away from FA and still pre-arb, but we are talking about Player B who is a FA. pre-arb and arb money is all based on scale, and the arb years based on past performance.

    I think that is shows their ACTUAL salary vs. how much they are actual worth. Not all FA are overpaid, and many of the FA can be underpaid as well………and many players who have had their arb years bought out have been underpaid. I really do not see any huge flaws that would make huge differences in their actual worth.

    This is an excellent feature to have, and to have their actual salary vs. their actual value is very useful.

    Tango, your positional adjustments are wonderful and w/o them, this would not have been possible.

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  17. Justin says:

    Also, for all small market teams, a good point is brought up that the fans should want to know how their team is spending their money, and to see if it is being spent wisely.
    This does not just go for small market clubs, but I think for all clubs. After the Yanks wasted huge money on FA in the past, and really put a stranglehold on their team the last 8 years, fans should want to know how Cashman is wasting/wisely spending. Granted, they can make MORE mistakes than most teams, but after what has happened this decade, I am sure Yankee fans do not want to see them do the same things again (even though they did just spend 420+M on 3 players, but the Teix and CC signings seem good signings at the forefront, and the Burnett one was a year or 2 too long and about 2-3M too much per year).

    As for a team like the Red Sox, we have been giving out smart contracts since Theo has taken over, and it is nice to see his genious shine a little brighter when looking at his players actual values. For example, the Drew signing, many people were upset and thought he was incredibly overpaid. He was just worth 5M his 1st year, but you could expect such a thing from Drew, but last year, he was worth over 20M (and he only played in 109 games), and I expect him to worth over his salary next year as well. Just avg. a few projections for O, add about 20-30 games to about 130-135, take his UZR for about 130 games which should be around 12, and he will be worth close to 20M again next season.
    For fans, this is just a justification mechanism for players, and it shows the actual value. It is one thing to just look at RAA, UZR, VORP, WAR, WARP, but to have it all laid out for you is a tremendous tool for just the average sabermetric fan (and this is beyond any classical joe morgan fan…long live FJM)
    One cool interesting stat which this relates too—if you look at the team stats and actual worth, the Yankees were worth about only 88M last year and the Red Sox were worth 155M. I may be wrong, but this is just from the hitters values since the pitchers have not been calculated on this site yet……Just goes to show how wisely the GM is spending the money, and every fan should care about this.

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  18. Brent says:

    Dave, is the 2008 dollars per win ($4.5 mil) for last season?

    Then you said, “The 2008 free agent dollars per win rate is right around $4.5 million per win, much like last year.”

    I think you meant 2009 but I’m not sure.

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  19. studes says:

    There is a lot of room for misrepresentation in this data. For instance, I believe your growth in free agent salary per win between 2006 and 2007 is very low.

    http://www.hardballtimes.com/main/article/2007-net-win-shares-value/

    Plus, the interpretation and specific application of salary information to individual players is very complex. You might want to put a warning label next to this information: “Use with caution.”

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  20. TangoTiger says:

    “Use with caution.”

    Great point. I think adding a provision stating that it’s free agent dollars that requires heavy discounting for non-free agents would be useful. You don’t want to put something out there that may be misinterpreted right off the bat by those who are not knee-deep in this as much as others.

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  21. studes says:

    One month later…

    I was just looking back at this post and comparing it to work I have done. FWIW, I came up with a figure of $5.1 million paid per free agent WSAB in 2007, a full million higher than you did. It could be that your lower replacement level accounts for some of the difference, but I think the margin for error here is huge and I just want to say again that the potential for misinterpretation of this sensitive material is huge.

    It’s the only thing Fangraphs has done that I would disagree with.

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  22. McCoy says:

    Say you got 30 teams and every year 3 of their players become free agents. Then let us also say that 10 teams have 30 million dollars in extra payroll to sign 3 players, 10 teams have 20 million dollars, and 10 teams have 10 million dollars. That is 600 million dollars for 90 roster spots at an average value of 6.67 million per roster spot and if we use the 2.67 billion dollar payroll number the other 660 roster spots have an average cost of a little over 4 million dollars.

    In otherwords by using free agents dollars for all players you are using a relatively closed off supply of players to set the price for all players. Mark Texiera doesn’t set the price for all players because Mark isn’t competing against all those other players for free agent dollars. He is competing against other free agents. In the past we have seen weak free agent crops still get top dollar simply because they were all that was available and the teams had the money. If all the players were available or a greater supply then those players would not have signed for so much.

    I would think a better option would be to compare 0-3 year service time players salaries to one another, look into the arb year players to see how they should be broken down, do free agent dollars, and then use those numbers for players based on where they are at in terms of service time.

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  23. McCoy says:

    Sorry meant to add this

    Think about this in terms of roto-ball. In the initial bidding process when all fantasy players are bidding on baseball players for the most part the bids are restrained and conservative because people have to fill the roster with many players. But then after the season starts everybody is allocated a free agent payroll and when the bidding commences on free agents you get really whacky numbers when compared to the initial draft. You suddenly get a small handful of guys who might contribute a little to your team getting paid huge % of your free agent payroll. This happens because there is a small supply of these free agent players and an even smaller supply of them are of any value to a team and the bidders no longer need to fill the roster with 20 or 30 players. They are only on the lookout for one or two players and have a large budget to use to get them.

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    • toad says:

      But the comparison is inaccurate. The non-FA’s salary is not set under auction conditions, at least not this year’s auction. It’s either capped artificially, or based on a contract negotiated earlier. It does not reflect current values te way a FA contract does.

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  24. McCoy says:

    I’m not saying the non-FA salary is set under auction conditions. I’m saying because non-FA have their salaries set under different conditions using FA dollar values for them is wrong.

    Some 4 year guy isn’t worth 15 million dollars because no 4 year man is ever going to hit the FA market. His dollar value should be tied to what 4 year arb eligible guys are currently getting not what some 8 year veteran is getting when he shops his services around to 20 different teams.

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  25. Interesting article. Were did you got all the information from…

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  26. Interested Observer says:

    I’m new at this but is the cost of a win a linear function? Seems to me additional wins at the high end might be harder to get than the ones at the bottom.

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  27. flatjacket1 says:

    Does anybody know exactly how to calculate previous years WAR? Like between 1990-2010? That would really cool to know

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  28. Brendan J. says:

    Long overdue, but found this to be an entry point to a conversation.

    http://www.foxsportsohio.com/10/24/12/A-conversation-with-the-Indians-Mark-Sha/landing_indians1.html?blockID=809163&feedID=3724

    Shapiro states a win is about $9 million for no other reason than “we have our own analytics.” It seemed a bit concerning since we’re pretty far off from that figure here at fangraphs.

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