As baseball analysts shift towards evaluating players with advanced statistics, calculating a player’s overall value has become essential. To do so, the common fan uses Wins Above Replacement (WAR), a statistic that measures a player’s value compared to a replacement-level player- a 1 WAR player is worth about one win above a replacement-level player, for instance. The convenience of a “tell-it-all” statistic like WAR cannot be emphasized enough, and for that reason, I have always looked at WAR when judging a player’s performance in a given season. However, this statistic has been in place since as early as 1982, and 38 years later, its flaws have become more obvious. For that reason, I have developed a new statistic that I believe better captures a player’s value in the modern game- Value Over Average (VOA).
When it was first developed, WAR did a fantastic job of illustrating how much more valuable a player was over his peers. Yet, when it was developed, the strategies of baseball were different. Players placed a priority on making contact, which made league strikeout rates far lower, and, thus, meant that teams needed to be strong defensively. Now, though, there are far fewer balls put in play- in 2010, the league contact rate was 80.7% and in 2019, it was down to 76.2%. To further back up this de-emphasization of defense, in a study conducted at mvpsportstalk.com a few months ago, it was determined that team offense was about 5.35 times more predictive of team success than team defense, but that isn’t reflected through WAR. A player’s offensive runs are only 3.8 times more predictive of a player’s WAR than their defensive runs; if you can’t add a team’s WAR output to predict their success, then the statistic is clearly limited. That’s my major grievance with the statistic, but it’s not the only one. For example, it’s really difficult to picture what is a replacement-level player. Fangraphs defines it as the production that “would cost you nothing but the league minimum salary to acquire”, but those types of players don’t get much playing time, which makes it difficult to visualize. Also, with Baseball Reference and Fangraphs each having different calculations for WAR, it’s difficult to use the statistic when evaluating a player- why use a statistic that can change so much based on the site you use?
That’s where VOA comes in handy. Obviously, there aren’t multiple variations of the statistic, since it is being originated here, nor does there need to be at the current moment. Now, as the game evolves, the calculation of the statistic will change to capture that, but that’s only an added benefit- it won’t have to undergo the same fate as WAR. Plus, since the goal of VOA is to calculate a player’s value over an average player, that’s much easier to envision – there are many starting-caliber players who are considered average. As we’ll get to with the calculation, a 0 VOA player is worth roughly 1.67 WAR, which is about what Kevin Pillar has been worth over the past few seasons; when you picture the added value a player has over the average player, think of Kevin Pillar.
Those perks are gratifying, but what makes VOA superior to WAR, in my eyes, is how it does a much better job taking into account what moves the needle in the modern MLB- it weights offense 5.35 times more than defense, which is what it’s supposed to be. Overall, the calculation itself is much simpler than WAR:
(Offensive Runs Above Average*5.35 + Defensive Runs Above Average)/Runs Per Wins
Offensive runs above average (Off) adds a player’s batting runs above average and baserunning runs above average (BSR) to compute the total amount of offensive runs, while defensive runs above average (Def) adds a player’s fielding runs above average and positional adjustment (weighting more valuable positions more) to demonstrate their defensive value. Since Def already has a positional adjustment, it doesn’t need to be altered at all, but for Off, the following multipliers should be used to weight the value of an offensive run at each position:
First Base- 0.933
Second Base- 1.051
Third Base- 0.99
Corner Outfield- 0.962
Center Field- 0.97
Meanwhile, ten runs are considered to be worth a win, but the amount of runs generated per win varies by the year. Last year, for instance, 10.296 runs were considered to be worth a win, but that number decreased to 9.714 when you look at 2018.
As for pitchers, there are so many factors that needed to be taken into account, such as ballpark adjustments, scaling innings pitched, and leverage for relievers. Luckily for us, Fangraphs’ pitcher WAR model, which, unlike Baseball Reference, uses Fielding Independent Pitching (FIP), successfully can depict a pitcher’s value based on what they have control over. Nevertheless, since we’re trying to show how much more valuable a pitcher is compared to one who is average, we have to use the WAR to VOA conversion:
VOA calculates the added value a player has over the average player, but “average” isn’t the same per position. Therefore, once a player’s VOA is calculated, we need to find out what “average” means at each position, and then subtract that number from the player’s VOA. Based on projections for next season, here is what’s considered “average” at each position:
First Base: 0.4645999657
Second Base: -0.004380717019
Third Base: 0.5004390101
Corner Outfield: 0.2373690752
Center Field: 0.01613601273
Starting Pitcher: 0.03768912636
Relief Pitcher: -0.7875820028
As you can see, the up-the-middle positions are where the bar is lowest for a player to be an average player, which lines up with the theory that those are the most valuable positions. Although relievers have the lowest projected mean VOA, that’s more indicative of the limited value they provide, rather than a lack of talent.
Another benefit of VOA’s simple calculation method is that it’s relatively easy to project future value as well. If you can estimate how talented a player is with a percentile grade (preferably with the stable metrics), you can use the following formulas to estimate their projected offensive runs above average and defensive runs above average:
(x= Percentile Rank)
Future Batting Runs Above Average: 0.632x – 28.1
Future Defensive Runs Above Average: 0.326x – 16.9
Future Base Running Runs Above Average: 0.118x – 5.79 (I like to take their mean BsR from recent seasons)
Starting Pitcher WAR= (.0067x-1.26)
For prospects, projecting future performance is more complicated, and not just for the fact that they are unknown commodities. One of the traditional 20-80 scale’s main benefits is its resemblance to a normal distribution curve, which shows the probability that a chosen statistic will be one, two, or three standard deviations from the mean:
In other words, the 20-80 scale can be converted to a percentile rank:
20- 1st Percentile
30- 5th Percentile
40- 32nd Percentile
50- 50th Percentile
60- 68th Percentile
70- 95th Percentile
80- 99th Percentile
With that in mind, we can get a rough estimate of how many runs a prospect figures to add in the future, which is made clearer with these formulas:
(x=20-80 scale scouting grade)
Batting Runs Above Average: 1.26x – 58.1
Defensive Runs Above Average: 0.661x – 33.6
Base-Running Runs Above Average: .237x – 11.6
Starting Pitcher WAR: 0.13x – 4.12
Now, we can build models that can project a player’s future value, and, also, the millions of dollars they figure to be worth per year. That’s where our next line of business comes into play.
Another issue with WAR is that it’s very difficult for people to agree on a set $/WAR amount. Based on free-agent contracts, the general idea is that 1 WAR is worth about $8M-$9M, but that appears to be skewed by some poor decisions by teams- there are far too many examples of players not living up to the contracts they were given. In a study done in 2018 by John Edwards at Fangraphs, teams tend to pay $5 million for 1 projected WAR, based on contracts given to hitters and starting pitchers between 2006 and 2017. That would appear to be much more in line with what teams are paying for players at the time of the contract, and using our VOA to WAR conversion equation, we’ll use that $5M/WAR premise to come up with a $/VOA calculator:
$= ($6.8M*Projected VOA) + $8M
Since a 0 VOA is considered average, a y-intercept of (0,$8M) means that an average player is worth about $8 million per year on the open market. Meanwhile, a player who provides five extra wins above average is worth around $42 million per year. Using our projection system, here is what my model indicates the top of the market should be at each position. Remember, this is based off a projection system that uses stable metrics to predict future performance, since teams aren’t supposed to be paying for past performance:
Catcher- $23.83798266M (Yasmani Grandal)
First Base- $26.97718631M (Max Muncy)
Second Base- $29.82622123M (a healthy Jed Lowrie)
Third Base- $30.64269269M (Alex Bregman)
Shortstop- $28.47523397M (Marcus Semien)
Corner Outfield- $43.41007591M (Mookie Betts)
Center Field- $40.04194305M (Mike Trout)
Starting Pitcher- $32.90748396M (Justin Verlander)
Relief Pitcher- $16.72685502M (Liam Hendricks)
As we mentioned previously, the same can also be done with prospects. For example, Wander Franco ($27.7041222M), Gavin Lux ($26.37794068), and Adley Rutschman ($25.70478148M) are the only three prospects that project to be worth over $25 million per year for the first six years of their career. Also, we can use the $/VOA models to judge some recent trades. With that in mind, let’s judge a trade that Rays and Padres made this past offseason:
- OF Hunter Renfroe: $12.7364062M per year x 4 seasons= $50.9456248M
- INF prospect Xavier Edwards: $12.69243795M per year x 6 seasons= $76.1546277M
- OF Tommy Pham: $22.96487306 x 2 seasons= $45.92974612M
- INF/RHP prospect Jake Cronenworth: $16.06526478M per year x 6 seasons= $96.3959968M
Without taking into account future contract values, which can be used to calculate surplus value, the Padres gain about $15.22549042M worth of assets in this transaction, though, with a player to be named later in the trade and Pham’s projected arbitration raise next offseason, it would appear that both teams accomplished the objectives they intended to meet. Furthermore, all three players who signed massive contracts during the 2019 winter meetings- Anthony Rendon, Gerrit Cole, and Stephen Strasburg- did so for much more than their projected $/year worth, which speaks to the fantastic job that agent Scott Boras (link past article) did leveraging his clients’ career years into contracts worth over $35 million per season.
Recently, MVP decisions have lined up nicely with what a player’s WAR is, but do those decisions still look correct in the eyes of VOA? After looking back through recent MVP decisions, a few stand out.
- In 2019, both MVP races were not reflected properly by WAR. In the National League, Cody Bellinger and Christian Yelich each had a 7.8 fWAR (Fangraphs WAR), but Yelich (5.783748644) was worth about an extra win over Bellinger (4.991274478) based on VOA.
- Meanwhile, Mike Trout barely won the AL MVP over Alex Bregman, which made sense since the two were separated by only 0.1 WAR. Yet, Trout’s VOA was about 1.3 wins higher than Bregman, which indicates that the Angels’ superstar center fielder should have won by a landslide.
- Speaking of Trout, he lost the 2018 AL MVP award to Mookie Betts, who led the MLB with a 10.4 WAR. Nevertheless, it was Trout who had the highest VOA (7.104519405), as he was better offensively than Betts.
There aren’t many past gaffes in terms of MVP decisions, but that’s mostly because voters didn’t start relying on WAR until recently. Assuming this trend continues, more of these decisions will reward players based on their defensive value, even if that “value” doesn’t move the needle the way WAR would indicate it does.
At the time it was developed, Wins Above Replacement (WAR) effectively captured a player’s overall value. However, baseball has shifted towards more of a “three-true-outcomes” game, and offense is now much more valuable than WAR would indicate. That’s why I decided to come up with VOA, which not only better adjusts for the modern MLB, but also has a much more simple calculation method; judging a player based on their extra value over an “average” player is far less confusing than attempting to define what a replacement-level player is. Add in its ability to reflect positional value, easily project future value, and also interpret how much money a player is worth on the open market, and it appears that VOA has clear advantages over WAR. It may be hard to believe that a statistic that is considered “new-age” has already become obsolete, but that just shows how quickly sports tend to evolve.