How is WAR calculated, really? Breaking down a single play to find out

Tony Quinn/Icon Sportswire

Bryce Harper charged a soft line drive on Sept. 5, fielded it cleanly and fired a strong throw home. The baserunner, Michael Lorenzen, who had started the play on second base, held at third. The trailing baserunner, Jose Peraza, who had started on first base, rounded second and went halfway to third, then backtracked. The catcher, J.T. Realmuto, fielded Harper's throw and snapped a throw to second, where shortstop Jean Segura caught it and dropped a tag on Peraza. Peraza got back to the base before the tag, but his slide took him off the bag. He initially was called safe, but upon video review, the call was overturned, and Peraza was out.

It all took slightly more than nine seconds, at the end of which one thing had changed -- two outs had become three, ending the rally. It can be, like every baseball play, recorded as a simple text description:

Single to RF (Line Drive to Short CF-RF); Lorenzen to 3B; Peraza out at 2B

But those nine seconds, like in many baseball plays, comprise a very complicated story, and converting that complicated story into units of credit is one of the permanent challenges of baseball statistics.

Whose WAR (wins above replacement) goes up on the play? Is it Harper's, because his strong throw home set everything up? Or Realmuto's, because his throw to second led to the assist? Or Segura's, because his acrobatic tag finished the out? Or is it even more nuanced than that?

We're going to break down this play, which is ordinary enough to pass unmentioned but extraordinary enough to watch 30 or 40 times without wringing it all the way dry. And we're going to eventually try to answer the central question: Who gets credit for what happened and how much?

You can watch it here.

What happened

Two important things occurred before the pitch was ever thrown. Eight minutes, 40 seconds earlier, Philadelphia Phillies pitcher Nick Pivetta was removed with a runner on first base and one out in the inning. Cole Irvin, a lefty, replaced him.

And 1 minute, 28 seconds before the pitch was thrown -- when the Cincinnati Reds' batter who hit the line drive, Alex Blandino, was digging into the batter's box -- Harper took one big step back from where he had been playing for the previous batter, Peraza. Harper set up 281 feet from home plate. This qualifies as shallow positioning. The league plays the average right-handed batter 292 feet away. The league played Blandino, on average, 285 feet away, with some teams setting up as far as 290 feet away. Even two innings earlier, Harper had been standing one foot deeper for Blandino -- 282 feet -- but here he was a foot shallower.

He is 281 feet back on the first pitch of the at-bat, and he doesn't budge as the count progresses to 1-2.

Just before the pitch is thrown, the pitcher, Irvin, takes a long look at Lorenzen, the lead runner, on second base. Lorenzen is fast: His sprint speed is in the 85th percentile of all major league runners, according to Statcast. The runner on first, Peraza, isn't being held on at first. He is pretty fast too: His sprint speed is 70th percentile. Irvin delivers, and the play begins.

1.0 seconds after Irvin begins his pitching motion:

The pitcher has fired with a quick delivery -- not quite a slide step, but with a low leg kick you might see a pitcher use to keep runners from getting a big jump. Irvin is very good at holding runners on: In a bit more than 40 innings this year, nobody will even attempt a stolen base on Irvin. Realmuto has an elite arm behind the plate. Between Irvin's delivery and Realmuto's reputation, neither runner gets more than a cautious secondary lead. Irvin's pitch is a fastball, low and out of the strike zone.

2.0 seconds:

Blandino has chased the low pitch and made contact. He doesn't hit it hard -- just 79 mph, a flare more than a line drive -- but it falls into what Statcast researchers call the fly ball donut hole: If it were hit harder, better, it would be carry to the right fielder for an out; but at this exit velocity, it travels just far enough to get over the infield, but not far enough to reach the outfielder. It's a nearly certain base hit, according to Statcast-derived expectations. With two outs, both baserunners are off on contact. Harper gets a good jump on the ball.

3.0 seconds:

Just as the ball is about to land in right field, 210 feet from home plate, the first baseman already has left his position to get in place as the cutoff man. The second baseman, Cesar Hernandez, has begun running to first, where he'll position himself in case the batter, Blandino, takes a big turn around that bag. Lorenzen is about 25 feet from third base, and his body already is orienting itself to go home. The third-base coach, J.R. House, hasn't made his decision yet. House is backpedaling down the third-base line, perhaps 70 feet of the way to home plate as he observes the play developing, his hands still down at his side. The runner on first, Peraza, is running to second base, and he is watching the play in right field. The shortstop, Segura, has walked a step or two in from his position at the edge of the infield dirt and is watching. The pitcher, Irvin, has taken off in a sprint to back up a throw home. Harper is charging hard.

4.0 seconds:

The umpire kicks away Blandino's bat, and Realmuto straddles the plate while he tracks the baserunner coming around third. The center fielder, Adam Haseley, has jogged a few steps toward right field, but he stops and stands in right-center. Lorenzen reaches third base on a sprint, with his body almost directly facing home. By this point, the third-base coach is nearly at home plate, and Lorenzen picks up House's stop sign. Peraza is slowing as he reaches second base, watching Harper. Harper fields the ball cleanly, belt high on one hop.

5.0 seconds:

Harper is just about to release the ball. Lorenzen has stopped around third base and is watching to see Harper's throw. The third-base coach has both arms raised in a stop sign. Peraza has taken one or two steps past second base, his eyes still on Harper. Segura, the shortstop, is still standing almost at his original position, 50 or 60 feet from second base, watching.

6.0 seconds:

The third-base coach has dropped his arms back down to his side and is watching Harper's strong throw come toward home. The throw is 94.9 mph, a rocket. Harper has one of the best outfield arms in baseball: His "max effort" throw is, at 94 mph, the 10th fastest among 95 qualifying outfielders, according to MLB Advanced Media data. This throw is even harder than that, at 94.9 mph, and it's low and on target. Blandino has reached first base. Lorenzen has come to a complete stop, about 25 feet around third base. But Peraza, the trailing runner, has seen the throw going home and taken off on a sprint to third base, unaware Lorenzen is still there.

7.0 seconds:

The first-base coach, Delino DeShields, is pointing at the bag for Blandino to stay put, in case the throw home gets cut off. The first baseman, Hoskins, feints like he is going to cut the ball off -- and he probably should have cut it off, since Peraza is almost 40 feet toward third base -- but he lets the throw go through. At this point, shortstop Segura, catcher Realmuto and third-base coach House all realize Peraza has gotten himself into trouble: Segura takes off toward second base; Realmuto points to second base; and the third-base coach puts up a new stop sign, this one for Peraza. Peraza also realizes he is in trouble, and he stops. Realmuto prepares to receive the throw home.

8.0 seconds:

Realmuto has fielded the throw on one hop, just before it bounces again. (The throw is strong and fairly accurate, but it is slightly to the wrong side of the plate, and Realmuto has to extend a backhand to field it before it bounces a second time. Had Lorenzen been trying to score, it wouldn't have been in a great place for Realmuto to make a tag.) Realmuto's left knee is on the ground as he takes Harper's throw, and he springs up to fire to second with a quick arm stroke. Segura is still a ways from second base, but he has gotten the jump on Peraza, who is now also in full retreat toward second base.

9.0 seconds:

Realmuto, who has perhaps the game's strongest throwing arm from behind the plate, fires to second base. The center fielder, Haseley, realizes late there is going to be throw to second, and he belatedly breaks to back the throw up. The first baseman, Hoskins, standing near the middle of the field, leans back slightly to avoid getting clipped by the throw. Realmuto's throw reaches second base about four feet above the ground and about four feet to the third-base side of the base, which requires Segura -- just arriving at the base -- to reach back over the baserunner. The throw isn't quite in time. Peraza's foot is on the bag when Segura catches the throw, right over Peraza's shoulder. Segura has had to partially leave his feet to reach for the throw and to avoid Peraza.

9.3 seconds:

Segura catches the ball, and his firm tag drops on Peraza's back as he falls over the baserunner. Peraza's slide is a bit awkward: He starts it a little late, and he has too much force as he jams into the bag. His leg jolts over the bag, clearly separating from it for more than a split-second. Segura, landing with his momentum taking him toward third base, manages to hold the tag on Peraza's back in that moment. The call on the field is safe -- the second-base umpire, on the outfield side of the play, doesn't see Peraza's leg lose touch with the bag -- but it is overturned on review. It's definitive. The left fielder, during all of this, has barely moved.

This is what it looked like using Statcast's radar tracking:

Who gets credit

We've observed almost every actor's role in the play, some of it consequential to the final outcome and some of it not. Most of this is recorded. Much of it is ultimately wrapped into stats that give credit, though often in unexpected ways.

In the most traditional way stats are recorded -- the back-of-the-baseball-card stats -- two players get credit: Blandino gets the hit, and his batting average goes from .143 to .250. The pitcher, Irvin, gets the out, and his ERA drops from 7.46 to 7.39. Harper gets an outfield assist, even though he didn't make the final throw. (For that matter, he didn't even throw in the direction of second base, where the out was made, but Realmuto's throw is basically treated as a relay of Harper's throw.) It is Harper's 10th outfield assist of the year, and he will finish the season with a career-high 13, leading all major league right fielders in 2019.

Many of the participants who did their jobs properly aren't recorded at all. Rob Thomson, the Phillies bench coach, will never be credited (besides here, right now) for positioning his team's right fielders shallow for Blandino, assuming it was him who did it. But had the Phillies been playing Blandino five feet deeper, as the rest of the league did this year, Lorenzen quite likely would have scored from third, or at least tried. In that scenario, Peraza probably would have run unimpeded to third. Those were five very consequential feet. Irvin and Realmuto kept the runners from getting good secondary leads -- Irvin by paying close attention and delivering the pitch quickly; Realmuto with the reputation of his arm -- and if the pitch had been taken, each would have received tiny bits of credit by Baseball Prospectus' advanced metrics, which track how often baserunners attempt to steal against each pitcher and catcher. But because the ball was put in play, the pitch does not go into that baserunning data set, so Irvin and Realmuto get no credit. The second baseman who ran to first base, the pitcher who backed up the play at home and the first-base coach who pointed for Blandino to stay on the bag at first base get no acknowledgement.

Some of the participants who arguably didn't do their jobs escape statistical notice. Center fielder Haseley stood watching the play and wasn't in position to back up the final throw to second base. There is no stat for that. Hoskins didn't cut the ball off when he had a play on Peraza at second base, but that isn't recorded. The third-base coach gets no statistical credit or blame for holding Lorenzen at third base, but we will never even know whether that was the right decision or not, whether he deserves credit or blame.

There are parts of this play that are recorded but don't ultimately get calculated as part of a player's WAR. Irvin gets credit, in his chase rate, for inducing the swing on the pitch out of the zone. That is generally treated as a positive skill, frequently cited when trying to assess how good a pitcher is, but it's not part of his WAR. Blandino's chase rate goes up (generally bad), but his contact rate goes up (generally good), though neither of those goes into any stat that attempts to estimate his value.

And then there are the ways the credit gets a bit jumbled up. Peraza made the out at second, but it is the batter, Blandino, whose win probability added takes the hit, because WPA credits the entire play to the hitter. In that recording of events, Blandino cost the Reds 4% of a win by hitting his single and ending the inning. Irvin gets the corresponding credit to his WPA, 4% of a win he earned the Phillies by allowing the single.

Similarly, Blandino's average exit velocity drops on the weak contact, which might be cited against him. But because his hit fell into the donut hole, Statcast gives it credit for being a nearly certain base hit; indeed, it is Blandino's most certain hit of the year, by Statcast's expected batting average stat, and that lifts his expected batting average, or xBA. Neither WPA nor xBA is part of any of the current mainstream WAR models, but an MVP voter might well factor in each. (I consult WPA in filling out my ballot.)

And then there are the parts of the play that do go to a batter's WAR, but the credit is dependent on how different sites code of all what we just watched. Lorenzen's baserunning value gets knocked, because he didn't score from second on a two-out single to the outfield. It might well have been the correct call -- he might have been out at home had he gone -- but 88% of lead baserunners scored from second base on two-out singles to the outfield in 2019. Lorenzen, by holding, is considered to have failed: Baseball Reference docks his WAR by 0.14 runs. It docks Peraza's even more, since he made the crucial baserunning out: 0.51 runs.

But at Baseball Prospectus, Lorenzen -- by holding at third -- absorbs all the lost credit, because he is the lead runner. In that site's formula for baserunning value -- part of the player's WARP -- trailing runners are considered to be "pulled along" by the lead runner. So Lorenzen, who ended the inning safely on third base, is docked 0.6 runs. Peraza's baserunning is not treated as its own event, but only part of Lorenzen's, so Peraza's WARP takes no blame.

The trickiest part of the play, though, is deciding who should get defensive credit: Is it Harper, who made the strong throw home, holding the runner at third and getting the ball quickly and accurately for Realmuto's "relay" -- but who never actually had any intention of getting the runner at second base out? Or is it Realmuto, who alertly saw Peraza's bad baserunning and snapped a quick throw to second -- but whose throw was too late to actually get Peraza before the runner reached the base? Or is it Segura, who made a difficult catch of Realmuto's throw, then crucially kept the tag on Peraza? Couldn't we argue Peraza wasn't even thrown out -- since he got back to the bag safely before any throw arrived -- but was actually tagged out in a separate play altogether, removed from Harper's and Realmuto's throws entirely?

These are not just difficult questions to answer in the abstract, but in the specific. But to the best of our ability to untangle it all, this is how the major WAR systems credited the play:

At FanGraphs, Harper gets some credit for Lorenzen holding at third base. Keep in mind, Lorenzen had the stop sign before Harper ever threw the ball. It was Harper's positioning, his fielding of the ball and the threat of his arm that held Lorenzen. It was his reputation, more than the act itself, that altered the play, and for that he gets credit. Harper could have made a limp throw home that bounced six times and carried 30 feet up the third-base line, but if Lorenzen didn't try to score -- on a play where, in the aggregate, nearly 90% of baserunners do -- it goes to the right fielder's credit.

At Baseball Prospectus, Harper gets some credit for the assist, but most of the play escapes the measures of the site's defensive metric, fielding runs above average, because the out was so unorthodox. The Phillies' team baserunning defense is credited with 0.6 runs prevented -- about the same as Lorenzen is docked -- but not all of that gets distributed to the individual fielders involved.

And at Baseball Reference, where human observers (employed by Sports Info Solutions) credit the defenders on each play, Realmuto gets credit for what SIS labels a good fielding play. That's worth 0.2 runs to his WAR. Harper gets some credit for Lorenzen holding at third, and some for the outfield assist. It's worth about 0.33 runs to his WAR.

Segura, across the board, doesn't get credited by anybody. One could argue he made the most important play in the sequence and the most difficult. One could also argue he stood watching the play for far too long, and his late awareness that he was supposed to be covering second base is what ultimately made the play so difficult for him. Maybe he doesn't deserve any credit!

Irvin's WAR improved very slightly at FanGraphs (for the out), improved by a little more at Baseball-Reference (for the runs not scoring) and probably took a slight hit at Baseball Prospectus (for the single). Blandino's WAR improved everywhere but probably least at Baseball Prospectus, because landing singles on weak flares is one of the least stable skills a hitter can have. Harper's WAR, among the defenders, improved at all three sites.

One clear statistical winner of the play is somebody who wasn't even on the field at the time: Pivetta, the pitcher who left the game with Lorenzen on first base earlier in the inning. That would have been his run at the front of everything, but thanks to Irvin -- and Harper, Realmuto, Segura, Lorenzen and Peraza -- it didn't land on his ERA. He left the game in a state of uncertainty, but the rest of his team completed his outing for him.

The Reds began the play with two on and two out, a run expectancy of 0.47 runs. When Blandino singled, the run expectancy jumped, to somewhere between 0.72 (bases loaded with two outs) and 1.52 runs (one run scoring, plus runners at first and third). When Peraza was tagged out, it dropped to 0.0 (inning over).

I've had a few hours with this play, and after all that study, here's how I'd personally assign credit:

  • Peraza: -0.75 runs

  • Irvin: -0.5 runs

  • Lorenzen: -0.2 runs

  • House: -0.1 runs

  • Pivetta: -0.1 runs

  • Hoskins: -0.1 runs

  • Realmuto: 0.25 runs

  • Segura: 0.3 runs

  • Blandino: 0.6 runs

  • Harper: 0.6 runs

But I have no idea if that's fair. Those are just opinions, and they took hours to come to. There were more than 100,000 batted-ball plays in major league baseball this year, many of them involving half the players on the field in direct or indirect roles. There were, furthermore, three-quarters of a million pitches, scores of thousands of stolen base opportunities, thousands of pitches in the dirt. To give credit on all of them means building statistical systems that can make assumptions that hold true in as many cases as possible -- and that don't require hours (and that don't rely on personal opinions) for each of them. The act of assigning value for all these possible plays is a titanic act of research and coding that took years of work, trial and error and ever-more-specific tweaks by generations of analysts -- all to be reasonably prepared for an oddity like this play.

Here's a final ironic twist: Irvin's FIP -- an ERA estimator based entirely on his strikeouts, walks and home runs allowed, stripping out the effects of the defense -- went slightly down when Segura tagged out Peraza. That play at second base obviously wasn't a strikeout, a walk or a home run -- and, in fact, didn't involve pitching at all. But FIP is calculated by dividing those three events by innings pitched. When Peraza came off the bag, and the out was recorded, Irvin's denominator went up by a third of an inning, and his FIP dropped slightly. FIP stands for fielding independent pitching. But in a major league baseball play, nothing is ever totally independent of the fielding.

Thanks to Lucas Apostoleris, Jonathan Judge, Matt Meyers, Sean O'Rourke and Mark Simon for research assistance.