I’ve been a fan of WAR, or Wins Above Replacement, for quite some time.  For one, it’s convenient, as it seems to offer an answer, or at least an approximation of one, to important questions that people who love baseball care about.  For instance, how integral was player x to the fortunes of team y during z period?  That’s an important question when comparing players or even an individual player’s performances from year to year, and WAR helps us quantify that in a digestible, convenient way.  Mookie Betts had a WAR over 10 last year – so we can conclude that he was Very Important to the fortunes of the 2018 Boston Red Sox.  See?  Convenient, digestible.  Nor, as we will see in this series of posts, is this the only important question about baseball to which WAR offers a possible answer.  In the weeks following, I’m going to talk about WAR, the stat, and ways in which it could be used to highlight certain aspects of or help us pose questions about the Grand Old Game.  In this post, I’m going to talk about how the total number of Wins Above Replacement, of which there are 1000 in a given season, is derived.  I’m going to talk about how you get to the 1000, like, math-wise.  And thinking-wise.

At no point will I be explaining the basic utility or fundamentals of the WAR stat itself.  That ground is covered.  For an excellent primer on WAR, go here or here.  And trust me, any explanation I could offer for what WAR is on a fundamental level or how it’s derived would be redundant, as the above links explain it better than I ever could.  My interest is in using WAR, as presently constituted, as a tool to pose questions and suggest possible answers.

I decided to write about how the total number of Wins Above Replacement in a season was derived because it was a consistent stumbling block for me as I began reading about WAR, and I could find no satisfactorily complete explanation as to its derivation.  In fact, the more I read about WAR, the more the statement that there were “1000 Wins Above Replacement in a given season” popped up, each time in an axiomatic way.  Each time I read it, I thought to myself “great, but how do they know that?”  I never doubted the truth of the statement, mind.  I knew they knew, and I knew it was true (or, as I’d find, near enough to make no matter), but I didn’t know how they knew or why it was true.  That’s what this post is about.

So how are there 1000 Wins Above Replacement in a given season?  Well, if we want to find out how many Wins Above Replacement there are in a given season, we need to find how many total games there are in a season, then how many total wins and losses, and then, once we’ve separated the wins from the losses, how many of the total wins are Wins Above Replacement.  So let’s do it.

So How Many Total Games ARE in an MLB Season?

Imagine an MLB season.  30 teams, each of whom plays 162 games.  Some teams excel, some teams…not so much. Maybe you’re team is in it. Maybe they have a storybook season. Or maybe you’re saying “there’s always next year” by May 15th.

But to find precisely how many total games there are in a given season, that’s easy: 30 teams times 162 games per team, giving us 4860 total games.

Keep in mind that how many total games the teams play in a season and how many game events [read, ballgames that people attend and eat food and cheer and jeer at] there are in a given season are two different things.  In each game event, two teams are each playing a game against each other.  Every time, then, that a team plays in a game event against another team, that counts as one of the 4860, and thus, each game event, each ballgame, gives us 2 out of 4860 total games played in an MLB season.  Thus, it can be said that the 30 MLB teams play a total of 4860 games in the context of 2430 game events.   

So How Many Wins and Losses Are There?

So, with our 30 MLB teams playing a total of 4860 total games in a season, we next need to determine how many wins and losses there are in a season, and then separate out the losses, as we’re concerning with Wins Above Replacement, not losses.  So we realize pretty quickly, then, that in a given MLB season with 30 teams and 162 games, there are 2430 total losses for an average of 81 losses per team.  “But my team won 100 games!”  Good for you.  Someone else’s team won 62.  But if you don’t believe me, add it up.  Go to any season since the league expanded to the current format of 30 teams and 162 games in a season, and you’ll find that the average number of losses is approximately 81. 

Now, in terms of losses, all we need is the total number of losses, as all we want to do is separate the losses from the wins so that we can drill down into the wins to find the Wins Above Replacement.  81 losses per team is an average number.  I’m not saying that each team is going to lose 81 games.  It’s an average.  For some teams, you can think of them as Schrodinger’s losses. 

If you’re still unconvinced at the total number of losses in a given year, think about it this way: each of the 2430 game events in a given year has to generate both a win and a loss.  It’s a ballgame: someone wins, and someone loses.  Has to.  Can’t have a ballgame without someone winning or someone losing, generally.  Forfeit?  Results in a win or a loss.  Game suspended due to darkness?  They resume the next day and it results in a win or a loss when it’s finished.  Asteroid strike?  Assuming anyone is left around to record or care about baseball statistics, it will [probably] result in a win or a loss, or the game will be made up, in which case there will be a win or a loss.  So, after 2430 game events, both the win and loss button will have been punched 2430 times, leaving us, after a given season, with 2430 wins, and 2430 losses, or, more precisely, a number of wins and losses that are both equal (barring ties or game cancellations) to the number of game events in a given season.    

With 2430 losses in hand, we can subtract those from the total games in a season, that being 4860, and we find that, in a given MLB season, there are a total of 2430 wins.    

Getting to the 1000

Now that know how many wins there are in a season, (2430) we need to find how many of these are Above Replacement.  Thanks to the efforts of a bunch of Very Smart People and their Handy-Dandy Formulas, the number of wins we can chalk up to a replacement-level team has been established.  What is a replacement-level team?  It’s a hypothetical team composed entirely of fresh, new young faces from AAA, or, put another way, of replacement players. 

According to the Very Smart People’s calculations, a replacement-level team will win 29.4% of their total games.  So if we take .294 and multiply it by the total games each of the 30 teams play, that being 162, we get 47.628 games that each MLB team is pretty much guaranteed to win, as each MLB team is composed of talent that is at least at replacement level.  To obtain the league-wide number of wins at replacement level or below, we multiply 47.628 by 30, and we get approximately 1429.  Subtracting this number from the 2430 total number of wins every year, we find that, of that total 2430 games, about 1000 of them would be considered wins above replacement level.    

Since the nature of WAR is, like any stat, retrospective in nature, each of these 1000 wins are, to the tenth, apportioned out among the 800 or so MLB players using a Handy-Dandy Formula that, not I, but some Very Smart People, designed.

Why I’m a Fan of WAR

I like WAR as a stat because it’s a convenient tool for comparison between players.  Too, even though the WAR numbers shouldn’t be viewed as precise down to the decimals to which they’re generated, WAR ranges allow us, at a glance, to categorize an individual player’s performance in a given year and to compare that performance to other years in that player’s career.

The main reason I like WAR, though, is because I think it has something to say, or at least illuminate, about the economics of the game, and, to the extent we acknowledge that a WAR has a dollar value on the open market that can be quantified, where the true dollar value on a given payroll might lie and how much dollar value might lie there.  Along these lines, I think that WAR can help us frame questions about whether there are inequities in the compensation system in baseball and in what context those iniquities might lie.  Specifically, we might use WAR to help us ask how much a bargain (or not) young talent is to the various clubs, especially during championship seasons, whether the arbitration system equitably compensates players under club control, or whether the free agency system does a better or worse job of compensation, in terms of WAR and the dollar value attributed to it, than the arbitration system.

In next week’s post, I’ll be taking a look at two champions, the 2018 Boston Red Sox and the 2009 New York Yankees. Specifically, I’ll be looking at where these teams’ WAR came from, how much they paid for this WAR, and whether, and to what degree, the teams received adequate value for the price they paid for those WAR.

But this Thursday? Oh, we’re doing Game of Thrones. Wanna know who finally takes the light from Queen Cersei’s eyes? Check back here in a couple days, because I’ve got THEORIES.