This is Matt Swartz’ second piece as part of his July residency at FanGraphs. A former contributor to FanGraphs and the Hardball Times — and current contributor to MLB Trade Rumors — Swartz also works as consultant to a Major League team. You can find him on Twitter here. Read the work of all our residents here.
I first began estimating the average cost per WAR on the free-agent market after the 2009 season, but have not done so since my three–part series at the end of the 2013 season, leaving three extra seasons during which the market for free agents has evolved. In the first piece of my residency, I discussed the labor implications of using this framework. Many of my subsequent pieces in this series will look for which types of players are undervalued or overvalued by the free-agent market.
But first this piece will explain how I actually calculate average value — the reference point for whether players are undervalued or overvalued. It is also the appropriate reference point when considering the opportunity cost of any other number of baseball moves. For example, when a team is considering the value of acquiring a young player who will produce a large volume of team-controlled WAR, the reference point for valuing him is the cost of acquiring that amount of WAR on the free-agent market. This is an important concept for team construction.
The fundamental idea behind my approach to the free-agent market is that we need to consider the entire market for all free-agent-eligible players’ WAR rather than looking across a limited amount of players. This avoids any number of selection biases that come across when limiting the players under consideration. Specifically, this includes looking at those players who signed contracts buying out free-agent years in anticipation of reaching free agency and players past their first year of multi-year deals, since both such players signed their deals in the shadow of an expected market price for talent — which is not only a moving target leading up to the offseason, but also throughout the offseason free-agent market itself.
One key difference between the approach I take to Dollars per WAR analysis and that of other analysts is that I eschew individual projections. I only look at actual cost and actual WAR created by free agents collectively. This is because I have found in the past that projections tend to overshoot actual WAR on average. While I suspect that some of this may be corrected as public projection systems have improved over time, it would not account for the fact that players who reach free agency may be more likely to miss their projected WAR as compared with players who sign extensions in advance of free agency. This comes back to the idea of selection bias discussed earlier. Further, players age throughout the course of a multi-year deal, which is controlled for when using all players with six years of service time rather than just the ones who reached free agency in a given year.
Another important difference in my approach of estimating the cost of WAR in free agency is that I incorporate not only the dollar cost but the draft-pick cost, as well. This is especially important because draft-pick compensation has changed twice during the period of time over which I’ve analyzed free agency using this approach, a development that has (predictably) had consequences for player salaries. Any attempt to estimate the growth in the cost of free agents over time must include some consideration of what happens when the draft-pick portion of this cost changes. I will come back to the details of this momentarily.
Let’s start off by looking only at salaries (net of the league minimum) of players with at least six years of service time over the last 12 years (including 2017) and WAR by those players over the last 11 years (excluding 2017), since I only have service time detailed annually starting with the 2005-06 offseason.
Note that the WAR earned by free-agent-eligible players (those with six years of service time) has gone down over time — which makes the $/WAR ratio go up. This is a function of available talent and is not simply a product of the average player age dropping. If you are familiar with the details of the business cycle in recent years, you’ll note that the dollars spent goes up based largely on the state of the economy. My third article in the three-part series linked above goes into detail on that, and below I will discuss why I expect this growth to be lower in subsequent years.
|Year||Net AAV (billions)||% Change Net AAV||WAR||% Change WAR|
If I used only the annual version of $/WAR (even including the draft-pick adjustment), then I would pick up a lot of noise. Sometimes a single season fails to fully capture the market; there’s a lot of fluctuation year to year in the WAR earned by players with six years of service time (although far less than the fluctuation in WAR earned by actual free agents, which is a smaller sample).
By way of example, look at the change in $/WAR from 2010 through 2012, for example. It doesn’t seem to be due to actual price changes intended by the market actors, but rather a sort of random variation caused by the paucity of the sample size.
|Year||$/WAR unadjusted||% Change|
Obviously the change in total WAR among players with six years of service time fluctuates. Teams didn’t sign contracts expecting this value to drop from 299.5 in 2010 to 249.2 in 2011 and then up to 316.7 in 2012. To smooth out the effect of this year-to-year variance, the best approach appears to be averaging three years of “free-agent-eligible WAR” together at a time, including the WAR actually created by free-agent-eligible players in the year in question itself. I calculated the 2016 Dollars per WAR estimate, for example, using the 278.0 average WAR of free-agent-eligible players (anyone with six years of service time) from 2014 through 2016. (I cannot do that calculation exactly for 2017, or for 2006-07 for that matter, but numbers are based on averaging available years.)
This smooths out annual changes in Dollars per WAR considerably and better represents the actual market, in the sense that it reflects the amount of WAR that teams were trying to buy. We get an average of 8% average growth in salaries from 2006 to 2017, far exceeding Nominal GDP growth during that time. It actually averages 9% from 2012 to 2017, while only averaging 7% from 2006 to 2012, partly because of the stagnating economy during the early period and partly because of changes in available WAR on the free-agent market during these time periods.
|Year||$/WAR estimate||% Change|
My previous research on the drivers of salary growth indicate that we would generally expect salaries to exceed Nominal GDP by about 2.1% per year on average, and since the Federal Reserve’s most reccent forecast of Nominal GDP is about 3.8%, we should expect salary growth of about 5.9% per year going forward. This would lead to Dollars per WAR estimates going forward as follows:
While the last few years have clearly seen growth in Dollars per WAR in excess of that rate, I believe that this was largely a function of the declining WAR share of players with six years of service time. I’m skeptical that such a development can continue indefinitely, and I think that, as the WAR share of such players flattens and salaries grow continuously, we should expect salaries to grow at about this 5.9% rate. After all, free-agent spending net of the league minimum only grew 5% per year since 2006, with the remaining growth in Dollars per WAR coming from the shrinking WAR in the denominator.
Having established this framework, we now have a basis with which to consider whether players are undervalued or overvalued. Some of the subsequent articles in this series will analyze exactly that; however, the next two articles will explain some background on the logic behind these calculations, including the linearity of Dollars per WAR in practice and the correct discount value to use when doing draft pick compensation. Since these are fundamental and could potentially change as the market shifted, it is important to consider these before doing further analysis using this framework. Once these approaches are confirmed, the rest of this series will focus on reviewing previously discovered market inefficiencies and whether the market has corrected for them.
Matt writes for FanGraphs and The Hardball Times, and models arbitration salaries for MLB Trade Rumors. Follow him on Twitter @Matt_Swa.