Value in Baseball
In the midst of MLB free agency you’re bound to come across an article discussing how much a player is “worth.” Just like any sport, it’s inevitable that certain players stand above others (i.e. Juan Soto or Corbin Burnes this year), with their value further being dependent on factors such as what position they play, how prone they may be to injury, and of course, their overall production on offense and/or defense. As such, in a sport where winning games can come down to marginal differences, even some of the best players in the game may be passed up if they don’t fit a team’s needs or if their personality isn’t compatible with that team’s roster. However, this hasn’t stopped analysts and statisticians from coming up with many stats to find/interpret a player’s value; OPS+ and WRC+ may come to mind as metrics that can measure a player’s offensive production, for example. For pitching, one may look at a pitcher’s ERA, ERA+, their strikeout rate, walk rate, or their WHIP (walks and hits per inning pitched). However, to find a player’s overall value, a metric needed to be invented that took into account all aspects of a player’s game. This is where “WAR” comes into play.
What is “WAR?”
When it comes to determining the value of a baseball player, few stats measure up to the concept of “WAR.” WAR, or “Wins Above Replacement,” uses several variables to measure how many wins a player contributes to their team compared to a replacement level player available to any MLB team, for the minimum MLB salary. In the baseball world, there are two major analytical websites that measure WAR: BaseballReference (BR) and Fangraphs (FG). When a player’s WAR is calculated on BR, it is called “bWAR” (or rWAR), on FG, it is called “fWAR.” Each of these websites use different statistics and variables to calculate their version of WAR.
How WAR is Calculated Part 1: Position Players
The two different types of WAR have different methods of calculations that lead to quite a bit of variance in a player’s value from one website to the other. Calculating WAR on BR and FG is very different for both position players and pitchers. I’ll go over bWAR first. On BaseballReference, WAR is calculated for position players through the following formula:
bWAR = (Batting Runs + Base Running runs +/- Runs from GIDP + Fielding Runs + Positional Adjustment Runs + Replacement Level Runs) / (Runs per win)
As mentioned above, FanGraphs makes use of different statistics for defensive WAR, which means that a player’s value can be drastically different when using bWAR or fWAR. The formula for a position player’s fWAR is as follows:
fWAR = (Batting Runs + Base Running Runs + Fielding Runs + Positional Adjustment + League Adjustment +Replacement Runs) / (Runs Per Win)
At first glance, it seems very similar to bWAR, the only immediately noticeable differences are the addition of “League Adjustment,” and the removal of the variable accounting for GIDP (Ground into double play).
How WAR is Calculated Part 2: Pitchers
The formula for pitching bWAR is extremely simple:
bWAR = Runs Allowed / Innings Pitched * 9
Okay, this is misleading. There’s a lot more factors that go into pitcher bWAR than simply the number of runs allowed over the course of nine innings, but this is the basic formula. I’ll include a link to the BR article that dives deeper into the more nuanced variables that go into a pitcher’s bWAR (such as “Expected Runs Allowed,” “Wins Above Average,” and adjustments made for a team’s defense). This formula is meant to be simple at its most basic level, as pitching is a much more complicated skill than hitting (at least in my opinion). Therefore, the more complicated calculations must be done after this equation in order to account for the thousands of unique situations and matchups that pitchers can find themselves in (i.e. runners in scoring position, inheriting runners, varying strength of offenses). Overall, while the base formula is extremely simple, in order to figure out the whole story, there are tons of other variables that must be measured.
Pitching fWAR is a lot more complicated at its most basic level than bWAR, with the formula being:
fWAR = [[([(League “FIP” – “FIP”) / Pitcher Specific Runs Per Win] + Replacement Level) (IP/9)] Leverage Multiplier for Relievers] + League Correction
The variable with the biggest impact here is “FIP,” or “Fielding Independent Pitching.” Essentially, FIP is meant to answer the question: “how would a pitcher do with no defense to back him up?” FIP is calculated with the formula:
ifFIP = ((13*HR)+(3*(BB+HBP))-(2*(K+IFFB)))/IP + ifFIP constant
Basically, FIP combines the sum of all outcomes only a pitcher can control, and then divides that sum by how many innings he pitched plus a special constant that requires more calculations to come up with. I’ve included the link to the FanGraphs article that dives deeper into these calculations. In its simplest form, FIP is meant to remove “random outcomes” and “luck” from a pitcher’s performance and paint a clearer picture on the pitcher’s contributions to a game/season.
Therefore, while bWAR may account for the more luck dependent factors in pitching, fWAR seeks to remove this factor. It’s for this reason that many consider bWAR to be better for pitchers, as while luck can be an annoying factor to account for, it’s integral to baseball, and must be considered in a player’s performance. It can also be argued that players should be able to learn how to mitigate “unluckiness” as they gain more experience.
Take Freddie Freeman’s 2024 World Series performance as an example. Freeman is a seasoned hitter with a well established expertise in contact hitting. Throughout the entirety of the World Series Freeman was able to maximize his potential to make good hits by seeking out one type of pitch specifically: inside fastballs. His historical walk off grand slam in game one? He hit it off of an inside fastball. His 2-run single in the top of the 5th inning of game 5? He hit it off of an inside fastball. Off of Gerrit Cole no less, who is another veteran with lots of playoff experience. By refining his hitting to be able to make consistent contact on a specific type of pitch, Freeman was able to minimize the involvement of luck in his hitting during the World Series, and he used that expertise to earn a World Series MVP Award. Thus, it should be said that while FIP has its uses, it would be disingenuous to take a pitcher’s FIP and use that to argue whether they pitched well or poorly.
The Difference Between bWAR and fWAR
We can finally discuss the difference between these two measurements, when it comes to determining a position player’s value. As I said before, the main difference in these calculations lies in the way that Fielding Runs (defensive value) is calculated for bWAR compared to fWAR. BaseballReference uses a stat called Defensive Runs Saved (DRS) as the main variable to calculate Fielding Runs. DRS has existed in baseball since 2003, so there are a lot of precedents and samples to draw from when comparing DRS with players across the league and across multiple seasons. There are 8 main factors that go into DRS, however only 5 apply to position players that aren’t pitchers or catchers. These factors are what you’d expect: how good an outfielder’s arm is, infield play outcomes such as double plays, misplays (errors), good plays (like robbing a home run), and a fielder’s overall range based on league averages. The average DRS is zero, anything above that is considered to be pretty good, while some fielders can even reach a DRS of 15-20 in one season. Say a batter hits the ball to a spot in left field.The left fielder is able to make a relatively difficult play and catch the ball to record the out. DRS uses data from Baseball Info Solutions to determine how often this catch is made. The catch frequency is subtracted from 1, and then the number is adjusted to take into account how many runs the potential hit is worth. So, if this catch is usually made 30% of the time, the first calculation is 1 - 0.30, then this number (0.70) is adjusted to take into account the amount of runs this play essentially prevented. Therefore, there are a lot of factors that influence DRS calculations. This is important because fWAR takes a very different approach to defensive value.
FanGraphs uses OAA or “Outs Above Average” to calculate defensive value. The website used to use a metric called UZR (Ultimate Zone Rating), but this stat became obsolete when Outs Above Average was invented in 2016. The calculation for OAA is pretty simple. Picture this: a line drive is hit to a shortstop at about 97 miles per hour. The player has to make a diving play to catch the ball, and he’s successful in doing so. From a spectator’s standpoint, this is a great play, and the stats agree: the hit had a catch probability of 15%. This is where the calculation for OAA comes in; from a value of 1 (representing a 100% catch probability), .15 would be subtracted, as the play had a 15% probability of happening. From this we get a value of +0.85 OAA, which is added to the player’s total. Of course, a vast majority of plays will not be this valuable, especially as we see more elite defensive shortstops in today’s game. Players with a high OAA include Bobby Witt Jr., Francisco Lindor, and Ezequiel Tovar.
This leads us to the difference between these two measurements: the value of defense over time. fWAR tends to place more emphasis on a player’s defense, as OAA is a better metric to use to compare real time outcomes with that of the rest of the league and replacement level players. DRS is a great metric to use for any player, but the factors it uses may not even apply to most position players (only 5 out of 8 apply to non-catcher positions), and the factors that do apply tend to be highly observational, and cannot be compared to other players at the same position as easily. For pitchers, bWAR is considered to be more accurate due to the fact that randomness and luck are accounted for in more advanced calculations of WAR, unlike in fWAR which removes random outcomes through the use of FIP.
Sidenote: FanGraphs uses separate defensive variables for catchers. Anything from framing skills, game calling, fielding bunts, hits, blocking, and misplays like passed balls is fair game. These calculations can get quite messy, as the catcher position is extremely complex.
Anthony Volpe: fWAR vs bWAR in action
The Kid. The second coming of Jeter. Volpe is an interesting player. At such a young age he’s had so much hype around him, as he is expected to reach and even perhaps surpass the heights of his personal hero Derek Jeter. So with all this hype, is he good? The short answer is yes. Volpe has accrued 6.7 bWAR and 5.3 fWAR in his first two MLB seasons, a very good mark, but it doesn’t give us the full picture. Take for example Volpe’s WAR metrics in 2023: 3.3 bWAR and a 1.8 fWAR; both his bWAR and fWAR were 3.4 this past season.
Why is his fWAR in 2024 so much higher than in 2023? For starters, his offense improved. Despite the fact that his wOBA (Weighted On Base Average) actually decreased from 2023-24, his batting average improved significantly, his on-base saw an improvement, and he struck out less while also locating his hits much better (+0.44 BABIP from 2023-24). He also became a much better baserunner in 2024. He stole a few more bases, but he was also the fastest everyday player on the Yankees’ roster, not to mention the best at understanding when to reach for extra bases or try to score on a close play. Then there’s his defense. In terms of fWAR, Volpe became a top Shortstop in the league defensively, as his OAA skyrocketed . Therefore, it can be reasonably concluded that Volpe’s fWAR increased due to two factors:
His hitting and baserunning saw massive improvements from ‘23-24.
According to Baseball Savant, his Baserunning Run Value doubled from 2 to 4, and his Batting Runs Value increased from -15 to -9.
His OAA increased drastically, going up from 1 in 2023 to an astounding 15 in 2024.
This brings us back to his bWAR. The stagnance in his bWAR is due to his worsening in terms of DRS. In 2023, Volpe accrued 15 DRS, in 2024 he accrued 6. This means that despite his improvements on offense, Volpe’s bWAR stayed relatively the same because according to bWAR, his defense worsened. Of course, his role at shortstop means that his defense has a more significant weight, so that would explain why he has such a positive WAR on both websites despite being a well below average player offensively. Volpe’s amazing DRS mark in 2023 led to him achieving a much higher bWAR. His 1 OAA in ‘23 meant that according to fWAR he was an above average fielder, but only ever so slightly. As a result, his fWAR was much lower than his bWAR. In my opinion, his fWAR over the past two years paints a clearer picture of how he’s played, especially when it comes to his offense. Since his DRS decreased by a lot and his OAA increased by so much, his bWAR is actually undervaluing his defensive prowess, and short-selling his offensive improvements. Basically, his stagnance in bWAR makes it look like he’s barely improved as a player, much less as a hitter.
Some noticeable improvements in Volpe’s offensive numbers. Especially in Batting Average and BABIP. His SLG% had decreased, but as a whole, his hitting improved.
Closing Thoughts
From Volpe’s example we can see how fWAR and bWAR stack up when applied against each other. In this example specifically, bWAR doesn’t indicate that Volpe improved, and therefore I believe that fWAR has done a better job at tracking his value so far in the MLB. Yet, both metrics fall short of accurately showcasing his defensive value. As mentioned above, Volpe’s Statcast defensive metrics (OAA and FRV) were both among the best players in the MLB this season. Fielding Run Value takes OAA and combines it with other factors like how many runs a player saved with good throws, and/or blocking and framing prowess for catchers. Neither WAR metric takes this into account. So, WAR isn’t perfect, but it is still a great way to see how much value a player brings to their team. The differences between fWAR and bWAR may seem miniscule, but as shown with Volpe, it can lead to vast differences in player value between the two websites.
Works Cited:
“Anthony Volpe Stats, Height, Weight, Position, Rookie Status & More.” Baseball, www.baseball-reference.com/players/v/volpean01.shtml.
“Anthony Volpe Stats: Statcast, Visuals & Advanced Metrics.” Baseballsavant.Com, baseballsavant.mlb.com/savant-player/anthony-volpe-683011?stats=statcast-r-hitting-mlb.
Lichtman, Mitchel. “The Fangraphs UZR Primer.” FanGraphs Baseball, 7 Jan. 2013, blogs.fangraphs.com/the-fangraphs-uzr-primer/.
McLeod, Jack. “Sabermetrics 101: Understanding the Calculation of War.” Samford University, 11 Apr. 2023, www.samford.edu/sports-analytics/fans/2023/Sabermetrics-101-Understanding-the-Calculation-of-WAR.
“Pitcher War Calculations and Details.” Baseball, www.baseball-reference.com/about/war_explained_pitch.shtml.
Slowinski, Piper. “War for Position Players.” Sabermetrics Library, 2 Apr. 2012, library.fangraphs.com/war/war-position-players/.
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