In the last week or two I’ve had multiple people tell me they’re not too familiar with the statistics I tend to use and ask various questions – mostly about Wins Above Replacement (WAR). I’ve taken to adding a little glossary link at the bottom of each post based on which stats were used therein, but expounding more thoroughly on WAR seems like a fair idea. Luckily, there are numerous great primers on the stat around the interwebs, so I’m going to crib shamelessly from them (and I’m pretty much just sticking with the position player side). If anyone has any additional questions – big or small – please leave a comment and I’ll try my best to explain more/better.

**What is WAR?**

*“Wins Above Replacement (WAR)*is an attempt by the sabermetric community to summarize a player’s total contributions to their team in one statistic. You should always use more than one metric at a time when evaluating players, but WAR is pretty darn all-inclusive and provides a handy reference point. WAR basically looks at a player and asks the question, “If this player got injured and their team had to replace them with a minor leaguer or someone from their bench, how much value would the team be losing?” This value is expressed in a wins format, so we could say that Player X is worth 6.3 wins to their team while Player Y is only worth 3.5 wins.”

The “minor leaguer or someone from their bench” part doesn’t mean a particular player. If Joey Votto was on the Cardinals, we wouldn’t suggest that Albert Pujols isn’t really that valuable because if he got hurt then there wouldn’t be too much drop-off to his replacement. We’re talking about freely available talent – guys that any team can generally pick up off the scrap heap for the league minimum salary at virtually any time. That puts players on all teams on the same baseline (more or less).

Also, the value added – measured in wins (converted from runs) – is the value added from the stats that went into the WAR measure. It’s a frame-work more than a set in stone statistic. If Baseball-Reference’s WAR (brWAR) adds in baserunning and FanGraphs’ WAR (fWAR) doesn’t, then they’re not measuring precisely the same exact thing (so saying they don’t match doesn’t invalidate WAR in general). It also means that WAR – any publicly available implementation, anyway – does not look at intangibles (like leadership). Many things people consider intangibles though – like hustling, for instance – will actually show up in the stats that are generally included in WAR (hustle and you might beat out an extra infield hit – that ups your batting line, after all). The nice thing about WAR is that it “provides a handy reference point”. If player A’s WAR is 3.0 but you think that he really helped the team with his leadership then maybe bump it up to 3.5. As long as you make it explicit and account for it (how did his leadership help? if it was by improving the players around him, then are you going decrease each of their WARs a little?).

I don’t really care about chemistry and whatnot – it’s amazing how good teams tend to end up having great chemistry that we can only identify after the fact – so I stick with the baseline WAR provides.

**How is WAR calculated?**

If you want to know how good a particular baseball player is, what information do you need? How good of a hitter is he; what position does he play; how good of a fielder is he at that position; how much does he play (can he stay on the field)? Those are the big four. You can add in baserunning, double plays, etc., but those are the four things you really need to know*.

** Player A – let’s call him Methuselah Honeysuckle* –* **hit .275/.330/.420 and Player B – let’s call him Lodge Blackman – hit .285/.350/.450. Which one was the more valuable player? Any idea? What if I said both were shortstops? What if I said A was below average with the glove and B was above average? Once I tell you both had the same number of plate appearances, it gets pretty easy to say B > A (ignoring stuff like adjusting for ballparks and whatnot).*

**Part one: hitting.**

We know Methuselah Honeysuckle (MH) hit BA/OBP/SLG (or, more precisely, we have his wOBA*) in X PA. How many runs did he add with the bat over what an average hitter would have done?

* *“So, why should you care about wOBA? What makes it better than OPS or any of the more famous rate statistics that measure offensive value? The beauty of wOBA lies in linear weights. Essentially, every outcome has a specific run value that is proportional to other outcomes – a home run is worth a little more than twice as much a single, for instance. What wOBA does, as all linear weights formulas do, is value these outcomes relative to each other so that they are properly valued.*

*OPS, as you probably know, significantly undervalues the ability of a hitter to get on base. It treats a .330 OBP/.470 slug as equal to a .400 OBP/.400 slug, when the latter is more conducive to scoring runs. wOBA gives proper weight to all the things a hitter can do to produce value, and is a more accurate reflection of a hitter’s value.”*

wOBA is on the OBP scale, so less than .300 is bad and over, say, .360 is good. I like wOBA since it’s conceptually easy to understand, in my opinion. How much is an average home run worth over an out? Around 1.7 runs. Did MH just hit a home run? Credit him with those runs. It’s scaled up to be on the OBP scale and then divided by plate appearances to make it a rate stat, but that’s basically it.

That’s were wRAA comes in:

“*Weighted Runs Above Average (wRAA) *is based off of wOBA, and measures the number of offensive runs a player contributes to their team. How much offensive value did Evan Longoria contribute to his team in 2009? With wRAA it’s easy to answer that question: 28.3 runs. Zero is league-average, so a positive wRAA value denotes above-average performance and a negative wRAA denotes below-average performance. This is also a counting statistic (like RBIs), so players accrue more (or less) runs the more they play.

Calculating wRAA is simple if you have a player’s wOBA value: subtract the league average wOBA from your player’s wOBA, divide by 1.15, and multiply that result by how many plate appearances the player received.”

The 1.15 scales wOBA back down since we scaled the run values up to get it onto the OBP scale*.

** Anyone watched The Cape? Is Scales supposed to have some sort of power, or is he just a weird looking regular bad guy?*

So now we’ve got a measure of how many runs MH added with his bat, relative to the average hitter (so 0 is average) and (hopefully) ballpark adjusted (the same wOBA tells you something very different depending on whether it came at Coors Field or at Petco).

**Part two: fielding.**

There are a multiple metrics trying to measure player defense; fWAR uses Ultimate Zone Rating (UZR) and brWAR uses Total Zone, for example. That is – again – because WAR is just a frame-work. When looking at future WAR, I try to use all of the available metrics to (perhaps) get a better handle on a player’s fielding ability.

More on fielding stats here:

UZR, Total Zone, Defensive Runs Saved (DRS), Fan Scouting Report (FSR)

Basically though, we want an idea of how many runs MH will save or cost his team defensively compared to the average player at his position.

**Part three: position.**

Position matters. An average fielding shortstop is – all else equal – more valuable than an average fielding second-baseman. If the shortstop moved over to second, after all, he’d very likely be an above average fielder at that position. It’s this idea that’s used to develop the position adjustment:

“Since players move around (albeit infrequently) from position to position, and we have decent defensive measurements, we can compare positions more or less directly. Well, most positions: we have the problems of dealing with infield to outfield and the issue of left handed players not being able to play third base, shortstop, catcher, and second while being favoured at first. But these things can be taken into account by tweaks to the calculations, and after some work you (by you I mean Tom Tango) end up with the following values for our positional adjustment (in runs per 600 PA):”

C: + 12.5 runs, SS: + 7.5 runs, 2B, 3B, CF: +2.5 runs, LF, RF: -7.5 runs, 1B: -12.5 runs, DH: -17.5 runs

“Please, please note that these values are not set in stone. You could tweak a lot of the numbers up and down by a run or two and nobody would bat an eyelid. This is a guideline, and while it’s close it’s not perfect by any means. The second thing to pay close attention to as that those are run values per 600 plate appearances. In reality, while plate appearances will obviously dovetail pretty closely with defensive chances, it’s not an exact match. We’re also exposing ourselves to a significant selection bias by only looking at players considered capable of moving around the diamond. Furthermore, these adjustments look at the sum of raw defensive ability – they don’t take into account how an individual position stresses different tools (arm is more important in right field than left, for example). None of these points are enough to recommend not using the above values, but as with everything we look at, the holes in the model are instructive.”

fWAR and brWAR use slightly different positional adjustments I believe, and the adjustments have changed over time. Still, it’s a solid general guideline.

So once we know MH’s position, we can debit or credit him depending on how “hard” it is to play.

**Part four: playing time.**

This isn’t just playing time, but also replacement level adjustment (based on playing time). With wRAA (batting), UZR/TZ/DRS/FSR (fielding), and position (scaled to playing time at the various positions), we’ve got a run value for MH. This run value is relative to average though, and that’s not necessarily the most useful reference point overall. If we have an average hitter (+0 runs) playing average defense (+0 runs) at second-base (+ between 0 and 2.5 to 3 runs), how valuable of a player is he? Well, it depends on how much he played!

This additional adjustment compares the player to our theoretical replacement level player instead. fWAR and brWAR use difference replacement levels, and the adjustment is different for the AL and NL (since the AL has been the tougher league recently, so an average AL player is better than a replacement level player by more than an NL player – though fWAR doesn’t make that distinction), but generally an average player is 20-25 runs better than a replacement level player over a full season. So a WAR of 2-2.5 indicates a guy who’s about average.

This addition is scaled to playing time, so if MH gets 600 PA he gets the full value of saving his team from needing to go to the bench, and if MH gets 60 PA he only gets 10% of the value, since the rest of the time his team would need to use a replacement level player (theoretically)

So now we have offense, defense, position, and playing time. In runs. One last step.

**Part five: runs to wins.**

Runs are great, but they’re just the step along the way to wins, right? So to move forward, we need to convert our measure from runs to wins. The conversion rate; 10 runs is ~1 win.

How do you get that? From the Pythagorean Win Percentage formula.

“It was Bill James who first noticed the non-linear relationship between runs scored, runs allowed, and wins. It turned out to be relatively easy to predict a team’s win-loss record using a simple formula, which very closely resembles trigonometry’s Pythagorean Theorem:”

Runs Scored ^{2 _____________________________} Runs Scored ^{2} + Runs Allowed ^{2}

Now that’s not exactly it – you can mess around with the exponent based on run environment – but it’s pretty good.

So if a team scores 700 runs and allows 700 runs, their expected winning percentage would be .500 and they’d be expected to win 81 games over a full season.

What happens if you add 10 runs to the scoring? That would take you up to 82 wins. Instead, subtract 10 runs allowed. Also 82 wins. It’s not a perfect ten-to-one, but it’s close.

So you take MH’s runs above replacement level and divide by ~10 to get… Wins Above Replacement. Ta da!

Hope this helped somewhat.

Referenced:

http://www.fangraphs.com/library/index.php/misc/war/

http://www.fangraphs.com/library/index.php/offense/wraa/

http://www.fangraphs.com/blogs/index.php/the-joy-of-woba/

http://www.fangraphs.com/library/index.php/misc/war/positional-adjustment/

http://www.fangraphs.com/library/index.php/misc/war/converting-runs-to-wins/

http://www.insidethebook.com/woba.shtml

More:

http://www.insidethebook.com/ee/index.php/site/comments/how_to_calculate_war/

http://www.insidethebook.com/ee/index.php/site/article/mike_silva_chronicles_part_2_war/

http://www.baseball-reference.com/blog/archives/6063

http://www.beyondtheboxscore.com/2009/6/12/906943/war-lords-of-the-diamond-position

http://sports.yahoo.com/mlb/blog/big_league_stew/post/Everything-you-always-wanted-to-know-about-WAR?urn=mlb-211211

There’s more than this as well – everyone feel free to post other useful links in the comments.