A Retrospective Look at the Price of a Win, Part Two

Yesterday, I discussed an important finding about the use of FanGraphs “Dollars” when evaluating past contracts. Specifically, I found that for all players with at least six years of service time in the past five years, their “Dollars” statistics summed $7.41 billion — but they were paid $8.46 billion. Players were paid 14% more than we estimated their market value to be at the time. This was happening primarily because we used projection systems that over-estimated playing time — with the side note that free agents tend to under-perform projections, anyway. Then there was this caveat: The $8.46 billion in total salaries doesn’t even take into account the value of draft picks surrendered to sign those free agents, which is another $780 million.

Considering these facts, we can compare the approximate “market price” for free agents using Marcel projections and compare that to the actual price paid. For the sake of that comparison, the third column excludes the value of draft picks. The last column tags this cost onto the dollar cost, as well.

Year Estimated Market $/WAR $/WAR Paid Excluding Draft Picks $/WAR Paid Including Draft Picks
2007 $4.1 $4.4 $4.8
2008 $4.5 $4.9 $5.4
2009 $4.5 $5.1 $5.6
2010 $4.0 $4.7 $5.1
2011 $4.5 $5.6 $6.1

This means that in retrospect, the actual price paid per WAR turned out to be 14% higher than the estimate — if you exclude draft picks. It’s 25% higher if you include the picks. This makes evaluating contracts in hindsight a very different science than estimating them for the coming season. These two facts need to be tied together.

LINEARITY

Of course, all of this analysis is useless if we were severely misunderstanding the model that teams use to pay for players. Because of that, it’s important to test some of the main assumptions of the model: The price of wins is linear. One of the most persistent arguments against $/WAR contract estimation is that teams pay a premium for superstars. Many people believe that the price of a six-win player should be more than twice the price of a three-win player simply because of the scarcity of those six-win guys.

What that view misses is that the scarcity of six-win players only matters if wins themselves are so scarce that teams can’t sign two three-win players, instead. In reality, they can and they do. Instead of signing Albert Pujols — perhaps a 6 WAR player — the Cardinals signed Lance Berkman and Carlos Beltran, a pair of approximately 3-WAR players who filled holes in the lineup. Another example is the Washington Nationals. After failing to sign Prince Fielder, the Nationals turned to Edwin Jackson, traded for Gio Gonzalez and kept Adam LaRoche (who the team likely would have traded had they signed Fielder). The Marlins, too, fell out of the Pujols sweepstakes, but the team added talent elsewhere.

This is very common, and it comes down to asking how many vacancies teams have in a given off-season. If you think about some of the teams on the free-agent market, they generally have somewhere between three and six job openings in either their lineup, their rotation or their bullpen. So if a team didn’t want to sign a big name to fill one vacancy, they were able to sign several players to fill several vacancies. We see that the New York Yankees avoided the big names this off-season, but added a number of smaller-scale contributors. The Boston Red Sox have done this in recent years, as well. Simply put, teams don’t have to treat an individual 6-WAR player as a scarce item; they can treat 6 WAR as a scarce set of items that can be bought in parts.

The data supports this concept. I looked at the past five years of free agents and divided players into buckets of salaries.

While most free-agent deals that are less than $5 million come with incentives that are poorly reported, contracts more than $5 million generally are worth the publicly reported amount. So, even though the lowest price deals look like relative bargains, the numbers may be misleading. This contract data doesn’t always contain information on incentives. Because of that, the true cost might be higher than reported for a number of low-base-salary, incentive-laden contracts. On top of that, my list of players also doesn’t include buyouts in minor league deals that could be spent in the process of searching for these types of bargains. The rest of the table gives a clearer picture. For my five-year calculation, the price of WAR for deals between $5 million to $10 million, $10 million to $15 million and more than $15 million have been very similar. That is, once you adjust for the price of draft picks.

Groups of FA-eligible Players 2007 $/WAR 2008 $/WAR 2009 $/WAR 2010 $/WAR 2011 $/WAR 2007-11 $/WAR
All $4.9 $5.4 $5.6 $5.1 $6.1 $5.4
>$15MM $4.1 $5.2 $5.9 $6.1 $6.3 $5.6
$10-15MM $4.7 $5.7 $6.9 $8.2 $11.4 $6.5
$5-10MM $5.9 $6.5 $5.3 $3.9 $4.8 $5.2
$0-5MM $4.5 $4.1 $3.6 $2.6 $3.4 $3.6

Looking at this table, it’s clear that superstars aren’t being paid more per WAR than other players. In fact, the highest-paid group looks to be players paid between $10 million and $15 million. In other words, above average — but non-superstar — players are actually getting paid more per WAR than the very best players. Of course, the differences are small enough that this night not represent anything that’s likely to continue in the future. But hopefully this can put a dent in the claims that superstars are paid more per WAR than other players.

FURTHER BACK AND FURTHER FORWARD

Now that we know that we’re using a good model of the return-on-investment for players from 2007 to 2011, we can think about how to estimate market values in other years. Unfortunately, I didn’t have access to contract and service time data before the beginning of the 2007 season, so I couldn’t apply this analysis further back. Luckily, www.bizofbaseball.com has total team payrolls going back decades — and FanGraphs has WAR as far back as I need. The issue is that I don’t have an exact split of how much money was paid to players who were eligible for free agency.

We’re still OK, though, because I have a way around that. It turns out that if you add up all WAR for players over 30 years old and half of the WAR of all players equal to 30 years old, you can get pretty close to the sum of all WAR given out to players eligible for free agency, so I used that as an estimate. To estimate salaries paid for players with at least six years of service time, I take approximately 80% of league total payroll (above the league minimum) as an estimation of dollars spent on free agents. If I add 9.4% for draft pick compensation, I get the following chart:

 

Year Approx. WAR Approx. Salary (Million) Estimated $/WAR
1985 309.8 178.3 0.6
1986 316.5 215.1 0.7
1987 302.0 180.1 0.7
1988 315.7 207.8 0.7
1989 316.3 252.1 0.9
1990 293.6 303.0 1.1
1991 318.5 436.0 1.5
1992 306.5 587.8 2.1
1993 320.4 660.3 2.3
1994 249.6 479.4 2.1
1995 303.3 622.3 2.2
1996 400.0 704.6 1.9
1997 394.9 817.7 2.3
1998 472.5 920.6 2.1
1999 467.1 1075.4 2.5
2000 437.9 1212.9 3.0
2001 433.7 1448.5 3.7
2002 443.7 1499.3 3.7
2003 413.9 1522.6 4.0
2004 400.9 1443.8 3.9
2005 392.8 1561.4 4.3
2006 374.9 1661.6 4.8
2007 383.8 1695.5 4.9
2008 360.6 1766.0 5.4
2009 331.9 1702.5 5.6
2010 348.5 1644.5 5.1
2011 294.7 1647.5 6.1

Now, if we were to guess what the return might be in 2012, we can see that about $1.85 billion has been allocated to players who have six years of service time. Based on historical trends, that group will accumulate about 320 WAR. Add in approximately 9.4% for the cost of draft pick compensation, and we get a rough estimate of what the 2012 price of wins might look like: $6.3 million per WAR.

Using projections to estimate the market’s price is a useful tool. After all, we’ve been able to figure out that the appropriate model for pricing talent is linear — we just need to find the $/WAR constant and multiply by WAR. The important lesson here is that when we look back in time, that actual $/WAR constant will look much different — and smaller — than our initial expectation. Whether teams are actually aware that players are under-performing their projections is an entirely different story, but to compare contracts, a retrospective analysis of that actual return is absolutely necessary.




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Matt writes for FanGraphs and The Hardball Times, and models arbitration salaries for MLB Trade Rumors. Follow him on Twitter @Matt_Swa.


25 Responses to “A Retrospective Look at the Price of a Win, Part Two”

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  1. Not a Dick says:

    I agree

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  2. Jason says:

    Two questions:

    Re: superstars – I don’t see how you addressed the limitation you discussed yesterday that $/win is lowest in the first year of the contract becuase players decline over the life of the contract. My hypothesis is that you would discover a super star premium if you looked at projected wins over the life of the contract rather than just the AAV and the first year production.

    2nd question – Re: draft pick cost. have you taken into account the new CBA?

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    • Matt Swartz says:

      What I have listed above is not the first year of contracts, but all contracts. So that wouldn’t explain the issue– I think it really is just linear.

      I discussed the new CBA here: http://www.fangraphs.com/blogs/index.php/more-than-they-collectively-bargained-for/
      In short, it’s still going to be about the same. They just shuffled who gets arbitration offered to them, but the total number of players will be very similar.

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      • Jason says:

        Re: draft picks… the issue isnt who gets offered arb. Its who has draft comp attached. With type A’s gone, and comp only awarded if the player recieves AAV > than approximately $12.5 million…. I would expect the draft pick “cost” to decline significantly.

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      • Matt Swartz says:

        Jason, read the article. I talked about all of this. I took the list of players who ended up making more than $12.5MM and so they presumably would be offered arb since that would only be an improvement to them. It was a very similar number to the number of players who were offered arb (or re-signed with their team for more than arb would have given them). Read through it, let me know if something’s unclear.

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      • Bryan says:

        Great article, I’ve bookmarked it for future reference.

        Looking at your results, it comes to mind that $/WAR other than >$15m are more volatile. Secondly that >$15m contracts have a more stable ratio, and are consistently lower than the lower AAV contracts.

        You may be onto something when you said that >$15m contracts provide the best value – an inefficiency that unfortunately only big market teams can consistently take advantage of. It might be possible that these players were underpaid by virtue of their lack of suitors, compared to players who would get lower AAVs. The fact that there have been a number of >$15m busts like Burnett and Lackey, and potential busts like Werth and Crawford – which bring that $/WAR down, shows how advantageous it is for big market teams to be able to stockpile such contracts since their still getting good value for money from their better performing stars.

        I still think $/WAR is non-liner given the opportunity costs and roster constraints that Andrew and RC described, as well as the possible inefficiency I referred to above.

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  3. Jesse says:

    I’ve always been a believer in non linear valuation, and when I look at the comparison between the 10-15 AAV earners and the superstars, what I see is that superstars evidence that truely elite talent is more likely to be a good investment. It is a murky number though.

    Perhaps driven by the splits between pitchers and batters? Fewer pitchers getting the tip top dollars, lots of busts in the upper echelons?

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    • Matt Swartz says:

      I used to believe in non-linear valuation too. I’m certainly very comfortable making those types of formulas– I’ve been accused of being overly complicated with non-linearities if anything.

      But it looks like it really is just linear. Speculating about whether they meant to pay more per WAR but just didn’t because they underrated above-average-non-superstars is starting to get pretty close to wrapping data around a theory you want to be true, when it just isn’t.

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      • Jesse says:

        Matt, i totally agree that your data and everything else i’ve seen suggests that people aren’t paying non linerally for wins.
        Whether they’re actually worth non linear amounts is something that frankly is pretty hard to test, and thought experiments don’t really cover it.

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  4. Mr Punch says:

    I think Jason is right. The length of a contract is a major issue, and in a complex way. A team may be willing to give a top player more years on the assumption that he’s more likely to retain his value, and may even be a bargain as salaries rise; the player may hedge against decline or injury by opting to go long. These are really a different kind of deal, available only to stars (and occasionally Tim Wakefield).

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    • Matt Swartz says:

      That’s all true, but the effect is that they still pay more per WAR with some long-term deals working out well and some working out poorly, and each more or less canceling each other out.

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  5. wilt says:

    I’m not sure about the logistics of the ‘beltran + berkman = pujols’ argument as there is a limited number of position openings. If the teams payroll fits just right

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    • Matt Swartz says:

      I’ve looked into this actually. The vast majority of teams have between 3-6 position openings between their lineup, rotation, and bullpen, and they typically fill less than this. Nearly every team has at least room to upgrade in their rotation or their bullpen, which is why you always see teams trying to make moves at the deadline on top of the moves they already made. Very few teams finish the offseason without a lineup spot suboptimally attended to.

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  6. Michigan Matt says:

    So does this mean the Prince Fielder deal looks less terrible for the Tigers?

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  7. RC says:

    My biggest issue with the linear assumption is that I don’t even believe that $/WAR value is consistent from team to team.

    When you look at a team like the Nationals, replacing a 6 WAR player with two 3-War players is a reasonable idea. For a team like the Yankees/Red Sox/Phillies/etc, its not.

    If a 6 WAR player walks on a good team, they can’t replace him with two 3-war players because there aren’t positions available for these guys. Derek Jeter was the only (full time) position player the Yankees carried that was below 3 WAR.

    So If Curtis Granderson walks, they can’t replace his 7 WAR with a 4 War guy and a 3 WAR…They’d have to replace his 7WAR and Jeter’s 2.3. IE, they’d have to find two 4.7 WAR players just to break even.

    Essentially, the better the team is, the more valuable WAR is…. essentially, with good teams, their “replacement level” is much higher.

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    • Matt Swartz says:

      A lot of people have tested whether teams differ in terms of their willingness to pay $/WAR. The results say that they pay similarly, even the Yankees. And that makes sense when you consider why– free agency is an auction process. You need to be willing to pay more than the Yankees to sign a player. Last year, 58% of new free agent contracts went to teams with 85 wins or more IIRC. The truth is that even though the VALUE per WAR is different from team to team for any given free agent, the value per WAR of the team that signs him is pretty similar. The Royals only outbid the Yankees for players their willing to sign at market price.

      Your example looks only at their lineup. Question: How many spots in the Yankees rotation could use some improvement? When you look at it team-by-team, nearly every team has several areas where they can add talent come November 1.

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      • RC says:

        The fact that they pay evenly doesn’t mean that they have equal value. The assumption that the market is rational despite the fact that we know otherwise is ridiculous.

        The same issue stands with the Yankees rotation. In WAR, their starters were 7.2, 2.9, 2.7, 2.2 and 1.5.

        You can’t replace CC’s 7.2 War with two 3.6 WAR guys. You need to replace CC’s and Burnett’s WAR, IE, you need two 4.4 WAR guys.

        The only teams that can replace an X WAR player with 2 X/2 WAR players are teams with a roster littered with replacement players. IE, teams that suck.

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      • Matt Swartz says:

        The market is rational-ish. But is your argument really that the market is rational in that it undervalues superstars? Because if the data says superstars are paid the same $/WAR as everyone else and you say superstars should get paid more, that’s the logical conclusion. I’ve studied irrational markets– undervaluing the glamorous is the opposite of what I’d argue is irrational.

        But take your Yankees example anyway. Say the Yankees don’t sign CC. ZiPS projects A.J. Burnett as replacement level. So the Yankees could have added say C.J. Wilson and Edwin Jackson, or they could have shored up a weak spot in their lineup or pen. Or they could have traded for Gio. There are lots of options on Nov 1.

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  8. RC says:

    Also, what we should really be looking at is not $/WAR, but $/expected WAR if we want to find what the VALUE is.

    The Red Sox spent $20M on Carl Crawford’s .2WAR last year. That doesn’t mean the VALUE of a win to the Red Sox was $100M/Win. That means the COST of that .2 WAR was $100M/win.

    COST and VALUE are not the same thing.

    The VALUE in this case, is that the Red Sox were looking at Crawford as a 5WAR player, and were expecting to pay $4M/Win.

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  9. Andrew says:

    I think what RC is referring to is the opportunity cost inherent in using two roster spots to get 6 wins, given that there are only a finite number of roster positions (25). Any time you can only use one roster spot and get a bunch of extra or marginal wins from it, you are better off because you still have the ability to add more wins in other roster spots.

    Let’s say you had 5 SPs who all posted a 2 WAR in 2011. One of them becomes a free agent, and you then sign a 6 WAR pitcher to replace him. That’s 6 wins coming in and 2 wins going out, so you now have 4 extra wins.

    If you signed two 3 win SPs, it clearly is not the same because you need to use 2 roster spots to accommodate them, meaning you are replacing two 2 win guys. That’s 6 wins coming in, 4 wins going out and only 2 extra wins.

    Of course you could trade a 2 win pitcher off and get 2 wins back in return, but it only improves you by 2 wins if the player you get back is 2 wins better than someone in your current starting lineup.

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  10. peachesnnuts says:

    2 notes, the first is the I assume the table with salaries ranging from 0 to 15 grouped in four buckets represents the AAV of the FA contracts signed? If that is the case I would love to see a breakdown of the average length of those contracts. This is purely anecdotal on my part but very few players in the 15+ bucket got less than three years and so their $/WAR is lessened by the amount of risk the club assumes on the back end of those 15+ deals. Likewise, the 10-15 and 5-10 buckets are populated by 1-3 year deals where the team is most likely to have the AAV match the expected production.

    The second comment is on the second chart. I find it interesting that FA WAR peaked in the late 90s and early 2000s. It speaks to the recent trend of teams utilizing more cost controlled players.

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    • Matt Swartz says:

      Good call on checking length of contracts, though I don’t think it’s too much of a difference:

      All: average length 2.4 years, year number of contract considered 1.8
      0-5: 1.4 year-deal, year #1.2
      5-10: 2.4 year-deal, year #1.8
      10-15: 3.7 year-deal, year #2.6
      15+: 5.5 year-deal, year #2.9

      The reason that I think FA WAR peaked in the late 90s/early 00s is that was an era dominated by power, which is a skill that doesn’t disappear as much with age.

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      • pft says:

        I wonder if FA WAR peaked because teams figured out that the FA route was getting way too expensive and started buying out their own top young players FA years with extensions that pay below FA market rates. So while the number of FA may be the same , the overall quality of the FA available each year may include fewer elite/good players, or they are older and in their declining years when they do become FA due to the extensions.

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  11. pft says:

    Basically, it looks as if teams are willing to spend more for an incremental W on guys making 10+ million, which makes sense since there are fewer players in this category so the supply is limited. It would be interesting to see if large market teams dominate the spending on these upper tier FA. If so, a case could be made that the value of a W is worth more to these teams, which seems plausible since potential revenue gains (losses) is higher.

    It also may be that the $/WAR is higher because these players may significantly under perform compared to non-elite players. That makes sense since the gap between a replacement player and elite/good player is much higher than a replacement player and average/bench player. More downside potential with players in the upper tier. Only takes a few players like Adam Dunn, Jason Bay and Carl Crawford to skew the numbers.

    For example, if you look at FA players signed to be DH the past couple of years, teams paid about 10 million/WAR produced (significantly more than expected).

    Also interesting to seem the divergence between the estimated market $/WAR and what is actually paid for the WAR produced under contract. This suggests teams may be more revenue flush than is being reported (perhaps due to ownership in regional cable stations), or that more contracts are turning out bad, or some combination. If the latter, it would suggest that projections have a way to go.

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