A Primer and Review on Value Calculations – Part 1
One of the things that we’re going to be doing quite often here at Breaking Blue is value calculations. These involve comparing a player’s production (actual or projected) and cost in order to determine how much they are or were “worth”. By comparing cost to production we can place a monetary value on players, and determine where they fall on the spectrum from significant asset to significant liability.
Here is a basic example. In 2007, Roy Halladay provided the Blue Jays with 5.3 Wins Above Replacement (Fangraphs version). If we say that the value of a win was 4 million dollars that year, then Halladay was worth $21.2 million. Since the Blue Jays only paid him $12.75 million, Halladay gave the Blue Jays $8.45 million in surplus value.
Value calculations form the backbone of transaction analysis. We find that the soundest thing to do when analyzing baseball transactions is to begin with a quantification of how much every involved piece is worth, and then layer in other considerations, such as team need or competitive environment, on top of that financial foundation. Thus, it is critically important to have a well-reasoned and well-thought-out method for value calculations.
Unfortunately, there isn’t really a perfect way to do them. At least, there doesn’t seem to be a general consensus. Big name sources of analytical baseball content use methods of value calculation that differ significantly. Here is a comment thread from tangotiger.com that outlines just how Dave Cameron, Fangraphs curator, and Tom Tango and Mitchel Lichtman, co-authors of The Book: Playing the Percentages in Baseball, disagree on a key part of the subject. Specifically, Cameron thinks that a win might be worth somewhere around $6M right now, after using a figure of just $5M last season, while Tango and Lichtman (MGL) seem to be in favor of a loftier figure of around $7M+, calculated independently by Matt Swartz and Lewie Pollis.
The specifics that we choose for our value calculation methodology can have drastic impacts on our conclusions. Here is an illustration using one recent signing. Let’s look at Hunter Pence’s 5 year, $90 million dollar contract with the Giants under a couple of different scenarios. We will assume here that Pence produces 3.1 WAR in 2014 (his current Steamer projection) before declining by 0.5 WAR per year (a back-of-the-envelope decline figure for players past their physical prime).
Method A: 1 WAR = $5M
Method B: 1 WAR = $8M
Method C: 1 WAR = $5M and the cost of WAR grows by 5% every year.
Method D: 1 WAR = $8M and the cost of WAR grows by 5% every year.
|Pence's Produced Value||$52.5M||$84M||$57.55M||$92.08M|
|Surplus Value / Liability Cost||-$37.5M||-$6M||-$32.45M||+$2.08M|
Hunter Pence at 90 million dollars for the next 5 years is either a slight asset, a slight liability, or a significant liability, depending on which figures we choose. And in this scenario, we only tweaked the market value cost of WAR and whether or not wage growth exists. There are numerous other factors that can influence value calculations significantly, such as the rate of player decline, whether or not to consider opportunity costs or discount the value of future assets, and so forth. I’ll talk about those later, but for now let’s focus on what is the most important part of a value calculation: the cost of a win. We’ll begin with how Dave Cameron calculates his figure for Fangraphs.
Cameron recently made a post at Fangraphs that outlined his methodology. If you scroll to the “value” portion of a Fangraphs player page, you’ll see a dollars column right beside their WAR totals. Divide any player’s dollar value by their WAR and you’ll get Fangraphs’ $/WAR for that season. By glancing at Jose Bautista’s page, we can see that the figure was about 5 million dollars in 2013 (21.2/4.2=5.05) and $4 million back in 2010 (26/6.5=4). Cameron reaches this figure by taking the free agent contracts handed out in each offseason and comparing the price tag of these players to their projected WAR. So the $/WAR figure that we see at Fangraphs is not based on what teams actually pay for wins in the free portion of baseball’s restricted talent marketplace, it is based on how much Cameron and Fangraphs think that teams think they are paying wins (the double use of “think” here is because teams probably aren’t using the same projection systems as Cameron). Other sources prefer to look retrospectively at how much actual wins ended up costing.
Last February, also on Fangraphs, Matt Swartz posted a two–part retrospective inquiry into the cost of a win. He found that there are some flaws in using projected wins to estimate the market value of WAR. Swartz showed that if you take every player with more than 6 years of service time (a sample of players that are no longer cost-controlled), and line up their combined actual salaries to their combined “Dollar” values as shown on Fangraphs, their actual salaries come out to a substantially higher amount (from 2007 to 2011, $7.41 billion vs. $8.46 billion). So teams actually paid quite a bit more for a free market win in baseball than the figures from Cameron and Fangraphs would indicate. Swartz indicates that the primary reason for this is that projection systems overestimate playing time by about 16%. Fangraphs sets their $/WAR based on projected WAR, and since projections add more WAR to the mix than will end up there in reality, Fangraphs has been underestimating the cost of a win.
In order to settle on some more robust $/WAR figures, Swartz decided to bring some other considerations into the fold. The cost of draft picks lost in order to sign free agents is not insignificant. Swartz estimates that in addition to the $8.46 billion spent in total salaries on free agents between 2007 and 2011, a cost of around $780 million should be factored in for spent/surrendered draft picks.
Swartz concludes that the actual price paid for WAR in baseball, ignoring the cost of surrendered draft picks, is about 14% higher than the Fangraphs estimates. If we include the “spent” picks, then the actual price is about 25% higher. Jose Bautista was worth 26 million dollars in 2010 under the $4M per WAR paradigm, but with Swartz’ $5.1M estimate, he would have been worth $33.15 million.
Swartz also shows us how to create a “dipstick” for WAR markets when we do not have complete data. Here is a summary of that toolkit:
This will come in useful when we want to know more about $/WAR growth. For now though, let’s look at another piece of recent research that corroborates what Swartz has done.
Leaving the Fangraphs bubble, much to our benefit, Lewie Pollis recently immersed himself in the subject of how much wins cost at Beyond the Boxscore. Pollis conducted this research as a precursor to his senior thesis. His method is much like that of Swartz, in that they both look at actual retrospective wins as opposed to the projected wins that Cameron uses. Their methods differ in one key aspect, however, as well as several points of minutiae.
The major difference between the research of Pollis and Swartz comes in how they apply money spent to specific years. Swartz applies the entirety of each contract to the year that it was handed out, so the money spent on wins in a 5 year contract handed out before 2012 would apply entirely to the $/WAR market figure in 2012. Pollis instead chooses to group player seasons by the year in which they took place, not the year that said contracts were handed out. Pollis summarizes the differences nicely:
A subtle difference in the question under examination, but it could have significant effects on the results.
Swartz and Pollis also differ on some more minute methodology. For example, Swartz includes the monetary value of draft picks surrendered to sign free agents, while Pollis does not. Pollis includes minor league signings that were later promoted to the majors, while Swartz does not appear to. Pollis uses RA9-WAR for pitchers, while Swartz uses fWAR. The latter difference should not affect the calculations in general, but the former two differences could have small impacts.
I think it’s time for a picture. Let’s have a look at historical $/WAR figures from our three sources. Pollis calculates $/WAR from 1996-2013, Swartz gives us from 2011 back to the mid-80’s with his “dipstick” measurement, and the Fangraphs/Cameron figure is easily derived from any Fangraphs player page from 2002 onward.
As we would expect, Cameron’s market measurements using projected wins indicate that teams have consistently been getting more bang for their buck than the market estimates of Swartz and Pollis show. I find it interesting that Pollis and Swartz’ figures agree well until 2006 and then take a fairly noticeable divergence. I am not sure what the reason for this would be. Swartz does not give us calculated $/WAR figures for 2012 and 2013 in the article that we are sourcing, but he gives an early (at the time) estimate of $6.3M for 2012 which I have included in the figure and which agrees almost exactly with Pollis’ calculated figure for that year.
With this data, we can divide any given year by its preceding year and find out what our three different market measurements think that year-to-year $/WAR inflation or deflation has been (inflation is probably not an absolutely correct term here, but the term still illustrates what is happening in terms of wage growth). Here is that information from 1997 to 2013:
Our three sources seem to generally agree on market trends. The average inflation in $/WAR among all three sources is +9.81% per annum. Pollis’ market measurement appears to be the most volatile, with a couple of big inflation spikes in there that his peers don’t quite find. If we remove Pollis data from the sample, the average yearly inflation is +7.44%. The three data sets agree strongly on market trends since 2008. The average measured inflation since 2008 is +3.98% per year.
I agree with the Pollis/Swartz general method of calculating the cost of a win. Dave Cameron’s measurement answers a specific question, but I do not think that it is the question we are most interested in. In the humble opinion of me, a retrospective measurement of $/WAR with some reasonably expected inflation or $/WAR growth applied to it is the best estimate of the current value of a win in any ongoing offseason.
Since Matt Swartz’ study did not extend to 2013, we will use Pollis’ 2013 $/WAR figure of $7.03M as our base. The current value of a win will be this times some rate of $/WAR growth. In the last six seasons $/WAR growth has been fairly low at just +3.98% per year according to our sources, but there are some very good TV deal reasons to think that the price teams pay for available wins has already increased drastically. Indeed, a very early look into $/WAR growth by Cameron, within the source already linked to, finds an increase in the +20 to +25% range. Let’s assume that $/WAR growth this year has been the same as the mean per annum increase across our entire sample, +9.81%. This gives us a current cost per win of $7.72M. We will drop this to a nice, round figure of $7.5M. For subsequent seasons of long term contracts, we will apply $/WAR growth of +9% per annum.
These will be the value calculation figures that we will use at Breaking Blue for all transaction analysis: $7.5M $/WAR in 2014 with 9% $/WAR growth per future season. We think that, given the available information, this model might even be quite conservative. If the market has Cameron’s figure jumping from $5M in 2013 to $6M this season, then Pollis’ $7M number would jump to the $8.4M mark. If the market actually ends up jumping that much then we will have to adjust our formula. If you think that this figure and growth rate seem a little bit high, consider that Indians President Mark Shapiro said a year ago that the cost for a win was $9M. Take that for what it’s worth – maybe the Indians have a different internal measurement of replacement level, maybe Shapiro was intentionally leaking a higher than true figure, or maybe they know something that our sources don’t.
I hope that there were at least a few nerds that enjoyed this summary of research on the cost of a win, and our reasoning behind choosing our figures. The $/WAR paradigm and the rate of $/WAR growth form the backbone of value calculations, but a whole lot more goes into the calculus than just those two things. Transaction analysis as a whole requires many other considerations. Part 2 of our primer and review on value calculations will delve into all (or most) of these other considerations.