Replacing WAR with VOA, Part Two: Calculating an MLB Player’s $/Year Value and Projecting Team Win Totals

When evaluating players, the common baseball fan, and most analysts, use Wins Above Replacement (WAR), a statistic that is meant to capture a player’s overall value. However,  there are rather glaring flaws with WAR, which is why I came up with a statistic that I believe is superior- Value Above Average (VOA). In the introduction to VOA, we covered several topics, such weighting offense versus defense properly, coming up with a $/VOA amount, and creating multipliers to adjust for offense based on the position a player plays. Today, I’ll expand on the statistic even further, analyzing how we can implement positional value into it, and, also, how it should be used to project team win totals.

Calculating a Player’s $/Year Value

In the initial article, I proposed using an adjusted VOA to incorporate positional value. Essentially, the average VOA at each position would be subtracted from each player’s VOA, so producing at a position where strong production isn’t expected would be rewarded. However, after reflecting on the idea, that no longer appears to be the correct method, in my opinion. Not only would this version of VOA be too subject to change based on a consistently fluctuation of talent at specific positions, but it also would confound one from being able to see how valuable a player truly is. After all, if we used adjusted WAR for football, then a quarterback wouldn’t win the MVP every year, and that wouldn’t be correct- they are the most valuable players. That same thinking goes for baseball- positional adjustments shouldn’t confound an award race, and that could happen with the previously suggested version of adjusted VOA.

At the same time, though, positional value needs to be a critical part of a team’s decision-making process; you shouldn’t spend as much for a 4 VOA player at first base than at an up-the-middle position, and that needs to be reflected when evaluating trades and free-agent signings.

Rather than coming up with an altered VOA statistic, we can illustrate a player’s value from a $/year standpoint. We already know that 1 VOA is worth about $6.8 million, as well as the fact that a 0 VOA player should be paid around $8 million. With that, we can calculate a player’s strict $/year amount based on their projected VOA (all of this is covered in the first article). The tricky part would be figuring out a way to incorporate positional value, but luckily for us, we can use a similar model to what I recently used to capture an NFL player’s value:

“It’s clear that some teams are far more efficient “buying” wins from some positions than others, but rather than calculate a player’s worth on the open market simply based on a $/WAR mark, I believe we need to focus on meeting in the middle. As a general manager, you can’t reset the market of each position on your own, and if you only pay players based on the $/WAR scale, you’re team is going to lack impact talent at a lot of positions. Flexibility is key, so taking the mean from the $/WAR scale and the implied market value makes the most sense.”

Now, in baseball, we don’t have to account for the fact that certain position simply can’t produce enough value, as is the case with football. Rather, we’re focused on adjusting to increase the value of players at positions where production is harder to come from, which is the opposite of the football value calculation.

In other words, we’ll take the mean value from the value a player is worth strictly from the VOA and what they’re worth based on the talent at their position. To calculate that, we need to subtract the average VOA at the position by our y-intercept of $8 million, since that value is supposed to capture the value of an average player. After doing that, here is what a 0 VOA player is worth at each position:

C= $8.42296M

1B= $-2.0238M

2B= $4.5592M

3B= $-0.296M

SS= $7.0076M

COF= $-0.4388M

CF= $6.8168M

SP= $5.994M

RP= $12.69404M

Since VOA values offense 5.35 times more than defenses, it’s no surprise that the corner positions have the easiest time accumulating VOA. Meanwhile, players at up-the-middle-positions, which are thought to be the premier positions, appear to be far less replaceable. As for relievers, it’s so difficult to accumulate enough value due to the limited innings they pitch, so a 0 VOA reliever is essentially a top-of-the-market shutdown weapon.

To provide an example, let’s compare the game’s best catcher, Yasmani Grandal, to the highest-rated first baseman, Freddie Freeman:



If you strictly went based on $/VOA, Freeman is worth over $37 million per year, but doing so would disregard the fact that the difference between him and the average first baseman is not worth $37 million. However, saying that he’s only worth $27 million, considering the value he provides with his elite offensive production, would also be foolish- once again, meeting in the middle makes sense. Grandal, meanwhile, is an outlier at a catcher position where offensive production is difficult to come by, so his value only slightly increases, while most catchers have a much higher implied value than actual $/year value.

Using VOA To Project Team Win Totals 

One of my goals when creating VOA was to come up with a statistic that better correlates to wins than WAR, and now, I believe I’ve found the method to do so. Just like with WAR, VOA is an individual statistic that isn’t meant to be added up to project a team’s win total, but we can use the principles of VOA to come up with a simplistic way to do so. If you know a team’s projected offensive runs above average, defensive runs above average, and pitcher WAR, the following formulas (found in this article) can be used to demonstrate how many games they should win, based on those three areas:

Pitcher WAR (x):   Wins= 1.74x + 58.1

Offensive Runs Above Average (x):   Wins=  .137x + 84.7

Defensive Runs Above Average (x):   Wins = 0.0943x + 80.1

Wait, but now we have three different totals, so how do we turn that into one consensus prediction? Luckily for us, we’ve already found out the value of offense, defense, and pitching in the past:

  • 43.5% Pitching
  • 47.083% Offense
  • 9.4167% Defense

Therefore, rather than taking the mean win total projection from those three areas, using those proportions allow us to properly weight each facet properly, so teams with strong offenses and pitching staffs stand out.

Yet, we’re far from done. That win total projection only shows how many games a team should win in a neutral environment, but if there was one word that I’d use to not describe baseball, it’s neutral. The top-end teams see their win totals increase due to the imbalance of talent in the MLB, and the inverse is true for the worse teams; mediocre teams are the only ones that generally have win totals that completely reflect their true talent. Therefore, we need to find out what the average team should win in a natural environment, and from there, the following steps should be taken to properly estimate team x’s actual win projection:

  1. Divide team x’s true talent win projection with the average team’s win projection.
  2. Multiply that number by team x’s talent win projection. The top team in the league may only be a 96-win team based on talent, but if they’re the top team, they’re very likely to overachieve that win total. Over a course of a season, the gap between the top teams and the bottom teams only becomes greater as teams reveal their true fate and prioritize different objectives.
  3. Take the mean amount from the wins calculated from step two and team x’s true talent level- this allows us to take into account the margin for error when projecting each team’s win total.
  4. Adjust for strength of schedule by multiplying team x’s win total by (average team/average opponent)- teams with easier schedules are rewarded generally with a few extra wins.

That’s it! With just four simple steps, you have the ability to adequately predict the results for an upcoming baseball season! Obviously, this isn’t as simple as adding a team’s overall VOA together, but projecting individual statistics to evaluate a team isn’t correct- where the wins are coming from is important.

For a complete deep dive into VOA, I recommend reading last week’s introductory piece. The topics covered today are meant to add onto previously established ideas, and since positional value and correlating with team success are two benefits VOA has over WAR, it’s important that claim can be backed up with some sort of validity. I’m excited to see how VOA continues to evolve over time, but, for now, it’s clear that the foundation of the statistic has firmly been cemented.

2 Comments Add yours

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s