WAR Diagram: Position Players
Wins Above replacement (WAR) is probably the best known composite statistic that attempts to estimates the entire value of a player to a team in a context-neutral and park-adjusted environment. It is also an incomplete model, and while we’re always trying to make it as comprehensive as possible, that does require updating the formula from time to time; just this past March we added a few more things to try and make it even better.
In an effort to increase understanding of the all the factors that go into calculating WAR, I have created the following diagram to the various player statistics and league average values which have gone into the calculation. Our goal is to always make the process as transparent as possible, and hopefully this infographic can help on that path.
DISCLAIMER: This diagram is meant to summarize the process of calculating WAR, it does NOT contain every detail necessary to accurately perform that calculation. For a full description of the formulas and equations please see the library page, which more fully explains the process.
The very left of the diagram contains the stats which are the basic building blocks of WAR. These include the familiar walks, singles, doubles, triples, and home runs along with the alphabet soup metrics: UBR, wGDP, UZR, and RPP. Most of the latter stats are built on proprietary data, so you won’t be able to calculate our version of WAR from scratch yourself, though you could substitute your own fielding and baserunning metrics.
The right side contains the finished product, a player’s WAR components. The oval shapes represent inputs, while the rectangle shapes represent calculated components which are steps along the way to get WAR.
The WAR diagram is divided into six component areas: Batting, Base Running, Replacement, League, Positional, and Fielding. Four of those six areas also fall under either the Offensive or Defensive region, which are the greatest differentiators of talent. These areas represent different WAR component stats we host on FanGraphs in our Value section on our leaderboards.
The runs from the six areas are aggregated to yield runs above replacement (RAR), which is then converted into wins using each year’s specific R/Win ratio, and that resulting value is WAR.
I build things here.
I love it.
What’s really cool is that you can see the “framework” of WAR, as Tom Tango calls it, at the highest level of the diagram.
For example, if you wanted to scrap the whole “Batting” box with any formula for runs above average (even using, say RBI), you’d still technically be using the WAR framework, just measuring it differently than most folks would. The key steps in the WAR framework will always be (1) estimate how many runs a player has contributed above or below average, in all facets of the game, (2) compare that to the performance level of a marginal MLB player, taking into account positional scarcity, and (3) convert from runs to wins.
Looking at this diagram (which is very nicely laid out, awesome stuff Sean!) leads me to wonder something. WAR is calculated assuming that batting, base running, defense, etc. are each equally as important as the other. But is this really true? Could one of these components be worth more or less than the others? Looking at the WAR equation, there is really no such weighting given to each of these; so I’m more curious than anything.
It is all calculated based on runs above replacement.
In theory, a run saved defensively is just as good as a run earned offensively at the plate, or on the bases.
But I think he’s wondering, as am I now, whether that’s true. Is it worth more to winning if you produce a run at the plate vs in the field? I don’t know the answer to this, but I’d love to find out.
How could it be any different?
A run is a run is a run. It’s the common currency all the other stats are translated into.
If you’re looking for context-specific value for each of these, where there are differences, then you want a stat like WPA, not WAR.
I elaborated more below, but I guess a simple way to look at it would be similar to the wOBA weights. There, a HBP is weighted slightly more than a BB. On the surface, they appear like the same exact thing; the ball becomes dead, the batter goes to 1st, a runner on 1st goes to 2nd, etc. The difference in value seems to be in what tends to come after these events, where after a HBP a pitcher seems to be more frustrated and slightly more likely to give up future runs. I’m wondering if in a similar fashion a batting run has a slightly higher chance to be followed by more batting runs than saving a fielding run has a chance to save more future fielding runs.
Like I’ve said, it’s probably insignificant, but I’m curious.
wildcard wrote: “The difference in value seems to be in what tends to come after these events”
IIRC, it’s the opposite – the difference is in what PRECEDES these events. A player’s more likely to be walked when there are fewer runners already on base; if there are more runners on, pitchers are more inclined to throw strikes. On the other hand, HBP tends to be random, and so is more likely to happen in a situation where it can do more damage.
There is a minor issue though. You cannot win a game -1 to 0. If two players represent the same overall value I’d always take the more offensive oriented player.
But you can never lose a game when you allow zero runs, so I think the opposite consideration is more important, actually–there are diminishing returns on runs scored that you don’t see with runs allowed.
Well, I think the “weighting” comes into how many runs each is considered to be worth. Or is your point that a run from baserunning or defense shouldn’t be worth the same as a run from hitting? I think it can be accounted for by the fact that the best hitter in the game will be able to produce more total runs than the best baserunner or defender will produce. But again, whether a run from batting is worth the same as a run on the bases or on defense is another story.
Weighting occurs on the front end of the calcs: (wOBA, wRAA, UZR, wSB, etc.). Once we get into Fielding Runs, Battings Runs, etc. everything is equal to WAR. Where things get interesting is how much uncertainty is associated with each category of runs. Batting Runs are generally more certain vs Fielding Runs, hence everyone gets up in arms when someone has a high WAR total based on non-offensive runs.
Thanks Sean, that’s what I had thought. Curious if anyone’s ever delved into differences in value, if there are any, to a batting run vs a fielding run vs a baserunning run? I’m sure that would get into sequencing probabilities and the like, but I think it could be interesting.
This makes a lot of sense. Thank you, Sean!
Runs are the currency we’re dealing with here. The question of whether one type of run is worth more than another seems to me to be like asking whether a dollar earned from selling your kidney is worth more than a dollar earned from working or more than a dollar that you found on the sidewalk.
I don’t see why it should matter where a run came from. The endgame is having more runs than your opponent.
Yeah, I get that a run is a run no matter where it comes from. But I’m wondering if there’s any value difference such that maybe a batting run begets more additional future runs than saving a fielding run begets your team saving more future runs. There probably isn’t anything significant there, at least not that we’d be able to find right now, but I was just curious if it had ever been looked into.
Sean, you’re the man. This is pretty awesome. I want to print it out and hang it in my cube.
Ditto
I did omit weights and a few minor math-related things, the idea of the diagram is to understand what goes into WAR at a high level. I do want to make an interactive that allows the nitty gritty calculations, but I need to clone myself.
The infograph is awesome love it!
It brings up a question for me, why are intentional walks not counted anywhere? They still bring positive value to the team just in theory less them allowing them to bat.
Intentional walks are not really a good evaluation of the player’s skill, though. A great player cannot draw an intentional walk; it is the strategic decision of the other team to put the player on base rather than pitch directly to him. Now, obviously some great players (Barry Bonds) have been intentionally walked a ton (a TON!) of times, but these are consequences of the OTHER factors which make that player great.
I’ve always disagreed with this thought.
The benefit of the INT walk to the defense is directly related to the expected out come of the batter’s plate appearance. Teams only INT walk when the expected outcome of an at bat is greater than a walk.
Barry Bonds is a perfect example. If you threw him a strike he was going to hit the ball over the fence. If teams had simply chosen to INT walk him every single time, would we say he added no value to the team?
Intentional walks are counted in a player’s run production, they just don’t change his wOBA. If a batter has, say, a 0.400 wOBA, it will remain the same after an IBB. But an IBB counts as a PA, and wRAA are proportional to PA, so every time a hitter is intentionally walked, his batting runs increases.
So in effect, an IBB counts as an average run producing event for that batter.
This is all very intuitive, which is great. But it doesn’t seem to work quite the same way for pitchers – it’s clear that RAR isn’t the only thing being used. There are players with identical RAR but different WAR – as of right now, Scherzer and Gray have the same RAR but slightly different WAR. What else is happening in that calculation?
That’s a very good question. Turning RAR into WAR is just a matter of dividing by a constant. That constant represents how many runs it takes to produce a win, on average. It varies season-by-season depending on the run environment. When runs are more plentiful, it takes more runs to produce a win. The constant was 9.5ish, last I looked.
The difference between Scherzer/Gray could simply be a different constant for the AL vs the NL. But now I’m wondering if Fangraphs is using different constants depending on the run environment of each *team*. For instance, even though they’re in the NL, the Rockies actually play in a higher-run environment than even the AL.
Or, when you’re only dealing with a single decimal place, and a 0.1 difference, you can always blame rounding.
R/W is one constant for the entire MLB for each year found here:
http://www.fangraphs.com/guts.aspx?type=cn
Park factors are adjusted before Batting Runs. Basically, RAR is a context-neutral, park-neutral, position-neutral, and league-neutral run value. You can debate on how effective the implementation is, but this is what we are doing.
Thanks for the clarification.
Any explanation for how two players in the same year can have the exact same RAR but different WAR?
But unless I’m just not getting it, that doesn’t answer my original question. To use the example I cited above, if RAR has been fully neutralized, then why are two players with identical RAR (Scherzer and Gray) showing different WAR? There are a couple examples of this if you check the WAR pitcher leaderboard, where the ordering of WAR and RAR don’t quite match up. The differences are subtle, but there’s clearly something else going into the WAR calculation.
Pitching is a different beast, which will present its own problems when I diagram it. But the R/Win does change for pitchers for each pitcher because of his impact on the run environment. Here is an explanation of what’s going on:
http://www.fangraphs.com/blogs/pitcher-win-values-explained-part-five/
?GDP should be included into “Batting” category. Even though avoiding a GDP is mainly speed skill, it occures BEFORE the batter’s PA comes to an end. Other speed-related events like infield hits, triples and ROE are usually categorized as batting. Until the end of his PA, he is a batter and all events he makes are batting. After that, if he’s on the base, then he becomes a runner and some baserunning events (SB, CS etc.) may follow.
Well, I think the reasoning is that as soon as the first force-out is made at 2nd base, the PA immediately becomes a Fielder’s Choice, thereby concluding the PA. The second out at 1st base comes after the result of the FC.
Sexy
I really get the impression that a lot of the people asking questions in this thread have never read “The Book” by Tango et al
In fairness to them, I had discovered Fangraphs before I had bought The Book, and it’s amazing how many questions it answered for me. It’s an absolute essential for anyone who’s serious enough about baseball to spend time on this site – easy to read and a great reference to have on hands.
I’ve been meaning to ask this question for a long time but never could find the right time or place, and this looks like a good place to ask.
I’ll admit that I’ve read a lot about WAR and the calculations and don’t quite get everything, so please correct me about any wrong statements, perhaps that’s all there is to my question. This diagram, while great, still don’t answer my question. I see the math and equations, just not sure how it would answer my question, or if it does. Perhaps you can guide me.
My question regards fielding defense. My understanding about the concept of replacement level players is that the average player is worth 2.0 WAR, it is mathematically set to that via the formulas. I always see this concept with relationship to a hitter’s batting line or OPS or EqA or wOBA or whatever batting metric that WAR equation uses. But when I look over the discussions of fielding, I see no such replacement level concept.
For example, my understanding from fWAR is that 0.0 UZR means an average fielder. I see the positional adjustment to equate positions, but nothing about a replacement level for the position itself.
So, is this concept captured in the diagram above, regarding fielding, and I’m just not getting it? Could you please clarify this for me?
Thanks in advance.
Replacement for fielding is captured by the Replacement Runs, which is separate from Off and Def, since applies for both batting and fielding.
The only case where there’s an imbalance where player bats but doesn’t field (or vis-versa) over a long enough course of time is a DH, but there’s a large negative positional adjustment accounting for the fact he doesn’t meet a replacement fielders defensive contributions.
I hope that helps.
Oh, OK, so what you are saying is that the box for Replacement Runs covers both offense and defense.
So if I got this straight, the computations calculates the number of runs above average for hitting, baserunning, and fielding, then there is a formula that spits out the replacement runs covering these three areas. Is that the basic idea?
And thanks for your answer.
Yes, it basically corrects runs above average to runs above replacement.