Arguments rage on around the baseball world about who should be inducted into the Hall of Fame, but there are still other arguments within these arguments. These inner squabbles focus on the statistics used to measure the greatness of players, and one stat seems to get the most attention. Damian Dydyn explains why attaching a dollar value to this statistic can confuse the true cost of WAR.
In Part One of this series, we covered the basics of WAR and why it isn’t the best tool for directly comparing players in single-season samples. In this piece, we will explore the more complicated concepts of linear scaling and relative value, analytical approaches with both qualitative and quantitative elements, involving factors that do not show up in the numbers and which aren’t accounted for by WAR in any meaningful way.
To start, we need to address the basic idea of “replacement level.” For many park- and league-adjusted rate stats, there is a clearly delineated line for league-average production. In UZR, it’s 0. For OPS+ and ERA+, it’s 100. You can quickly look at an OPS+ of 115 and determine that the player was 15% better than league average. With WAR, however, it is not quite that simple. League average is 2.0. So what is 0.0 and why is league average pushed to 2.0?
0.0 WAR is considered replacement-level production. This is a nebulous concept unique to WAR, adding a second performance baseline to the more widely-used league average. Replacement level purports to pin the value of the roster fodder every team has hanging out on the fringe of their active roster or in the upper minors. These players are fungible and supposedly plentiful. In other words, a league-average player should contribute two wins more in a season than the replacement-level AAAA guy on the very edge of the big league roster.
According to WAR orthodoxy, a perfectly average 25-man team full of 2.0 WAR players with perfect health should see about 50 WAR on the field. That number is then added to what a team of replacement-level players would be expected to win over a season (roughly 43). So a theoretical team of perfectly average players with perfect health would be expected to win around 93 games. Think about that for a minute, a team with no stars, but no weaknesses, would win more games than all but four teams managed in 2015.
WAR is designed to be linear, but this is where the idea of linear value starts to unravel. Relievers, for example, mostly fall well below 2.0 WAR in any given season; only elite bullpen arms tend to get into or exceed that range. Last year, for example, only nine were worth that much according to Fangraphs. fWAR would tell you that Craig Kimbrel was only worth 1.5 wins more than the fodder the Red Sox had floating around near Pesky’s Pole all last season, except Boston likely would have won more than the 1.5 games Kimbrel was “worth” if they had been fortunate enough to have had his 2015 season production in the late-inning mix. He would have extended the pen significantly, allowing both Uehara and Tazawa to stay fresh. He also would have kept players like Jean Machi and Matt Barnes out of some vital high-leverage situations. WAR systematically undervalues top relievers, which is why leverage index has to be included in reliever WAR calculations.
A player who is worth 4 WAR is, in theory, worth 2 WAR more than a league-average player, who by definition is worth 2 wins. That means that the 4 WAR player is twice as valuable as the league-average player, right? Well, that depends on the context. In mathematical terms, yes, he is twice as valuable. Four wins is twice as many as 2 wins. Two times two is four, QED. But in reality, teams face a number of restrictions when looking at player value that don’t show up in an abstract player X versus player Y comparison, but which are critical to roster-building decisions
So yes, Fangraphs’ WAR tells us that Mike Trout, and his 9 fWAR in 2015, was worth roughly twice as much as Mookie Betts and his 4.8 fWAR. In a vacuum and without context, that’s not a terribly unfair generalization to make. If a team had a chance to acquire one Mike Trout or two Mookie Betts, a linear, context-free view of fWAR would say that they were better off with two Mookies. However, rosters aren’t constructed in a vacuum. In the real world, a team can fill only 25 roster spots and play just one center fielder at a time. If one considers those limits, a team would be wiser to spend $25 million on one Mike Trout than two Mookies. Using only one roster spot for those 9-10 WAR, instead of two, leaves the team more room to add additional players worth more wins to help get it to the playoffs. So even if WAR did scale linearly quantitatively, it doesn’t necessarily work in practice when constructing a roster.
The Fallacy of Placing a Dollar Value on WAR
Is there a simple connection between WAR and the salary teams are willing to pay a player? A study by Fangraphs argued that in the 2014 season, the mean (or average) value of one WAR was $7 million, and the median was $5.9 million. In theory, a 5-win player should have been worth $35 million on the market that year. So why did we see Jason Heyward, who was worth 4.87 WAR on average over the previous three seasons (and 6.5 the year before that) sign a contract for eight years and $184 million with an average annual value of $23 million? fWAR would have us believe he was worth $34.09 million per year. Or Chris Davis, who averaged 4.37 fWAR in the three seasons leading up to his seven-year, $161 million dollar contract, also an AAV of $23 million, who fWAR would suggest was worth $30.59 million per year. Then there is Nelson Cruz. He averaged 3.23 fWAR in the three seasons leading up to last winter and signed a four-year deal for $57 million, or just $14.25 million AAV as compared to the $22.67 million 3.23 WAR is supposed to be worth.
There is a disconnect between what WAR is worth in theory and what it is worth on the real market. Part of this is because of the variety of factors that impact a player’s worth in the market in which they exist, whether that be free agent, trade, international free agent, amateur draftee, Rule 5 draftee, or something else. Age, market demand, which skills a player excels at, and how they are valued at the time the contract is signed, the signing team’s need, the existing contracts that the signing team already has on the books and when they are set to expire, where they are in the competitive cycle, and dozens upon dozens of other factors all impact that final agreement and most of them are not accounted for in WAR.
In short, player value is constantly in flux and is affected by a huge number of variables, most of which are easy to overlook and aren’t accounted for in WAR. All of these factors complicate the connection between WAR and dollars. Baseball players and teams don’t operate in a vacuum, and building a real team is different than building a fantasy roster which is all about pure stat accumulation. Real general managers don’t get to enjoy the same advantages that fantasy league managers enjoy. They can’t stack their outfield with three sluggers who only play right field and aren’t good defensively. In the real world, general managers must be concerned with clubhouse chemistry, providing a veteran presence to help younger players grow, taking advantage of market inefficiencies to stay within a budget, and dealing with the limited choices in the free agent market every year.
A 5-win player is a 5-win player, but the market might dictate that he be paid like a 4-win player, or it might lead to him being paid like a 6-win player depending on when, where, how, and why he became available. For example, Kyle Seager posted 5.5 fWAR in 2014 after 4.0 fWAR in 2013 in his age 26 and 27 seasons, and was extended by the Mariners for 7 years and $100 million. He was entering his first arbitration-eligible season, which means that Seattle still had three years of control left on his previous contract, giving the team significant leverage in contract negotiations. He is being paid $14.29 million per season over those seven years, which is much less than the $35 million per year that WAR says he is worth. Value is relative and constantly changing, but WAR is consistent and often lacks context. As a result, it isn’t always a good metric to discuss player value in the real world. As was pointed out previously, it’s a fine jumping-off point, but if your goal is to identify which player is a better fit for a particular club, or which player deserves the MVP trophy, quoting raw WAR numbers is superficial and inadequate – you absolutely have to dig deeper.
Follow Damain on Twitter @ddydyn.