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

Posted By Matt Swartz On February 15, 2012 @ 10:30 am In Daily Graphings | 25 Comments

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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