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Introducing XRA: The New Results-Independent Pitching Stat

There are a multitude of ways that we can judge pitchers. Most people look at earned run average to gauge whether a pitcher has been successful, while many old school announcers will still cite a pitcher’s win-loss record. ERA is a nice, easy way of looking at how a pitcher has performed at limiting runs, but it doesn’t come close to telling the whole story. In the early 2000s, Voros McCracken created the idea of Defense Independent Pitching Stats or DIPS, which credited the pitcher only with what he could actually control. Fielding Independent Pitching was born from this theory and only took into account a pitcher’s strikeouts, walks and home runs allowed. It turns out that a pitcher’s home run rate is not terribly consistent, thus xFIP was created by Dave Studeman to normalize the home run aspect of the FIP equation by using the league home run per fly ball rate and the pitcher’s fly ball rate.

In 2015, a new metric was developed by Jonathan Judge, Harry Pavlidis and Dan Turkenkopf called Deserved Run Average or DRA. This new stat attempts to take into account every aspect that the pitcher has control over and control for everything that he does not, thus crediting the pitcher only for the runs that he actually deserves. DRA, however, is still dependent on the result of each batted ball. If the batter hits a ball deep in the gap and it rolls to the wall, the pitcher is charged with a double, but if the center fielder lays out and makes a remarkable catch, the pitcher is credited with an out. When evaluating pitchers, why should it matter whether they have a Gold Glove caliber defender behind them or not? It shouldn’t, and that’s where Expected Run Average comes in.

Expected Run Average or XRA gives pitchers credit for what they actually can control. FIP attempts to do this as well but assumes that pitchers have no control over batted balls. While the pitcher does not control how the fielders interact with the live ball, he does have an impact on the type of contact that he allows. XRA is based on a modified DIPS theory that the pitcher controls three things: whether he strikes the batter out, whether he walks the batter and the exit velocity, launch angle combination off the bat. After the ball leaves the batter’s bat, the play is out of the pitcher’s hands and should no longer have any effect on his statistics. The goal is to figure out a way to measure, independently of the defense and park, how each pitcher performs on balls in play. Since 2015, StatCast has tracked the exit velocity and launch angle of every batted ball in the majors. Each batted ball has a hit probability based on the velocity off of the bat and its trajectory. The probability for extra bases can also be determined. These batted ball probabilities have been linearly weighted for each event including strikeouts and walks to give each player’s xwOBA, which can be found on Baseball Savant. This is the perfect way to look specifically at how well a pitcher has performed on a per plate appearance basis.

Once xwOBA is found, then XRA can be calculated. The first objective is to find the pitcher’s weighted runs below average. To do this, I used the weighted runs above average formula from FanGraphs except I made it negative since fewer runs are better for pitchers.

wRBA = – ((xwOBA – League wOBA) / wOBA Scale) * TBF

For example, Max Scherzer has had a .228 xwOBA so far this season and has faced 487 batters. After finding the league wOBA and wOBA scale numbers at FanGraphs I can plug these numbers into the formula.

– ((.228 – .321) / 1.185) * 487 = 38.22

Max Scherzer has been 38.22 runs better than average so far this season, but now I need to figure out what the average pitcher would do while facing the same number of batters. To find this I need the league runs per plate appearance rate and multiply that number by the number of batters that Scherzer has faced.

League R/PA * TBF = Average Pitcher Runs
.122 * 487 = 59.41

So a league average pitcher would have been expected to surrender 59.41 runs facing the number of batters that Scherzer has so far this season. Now that we know how the average pitcher should have performed we can find the expected number of runs that Scherzer should have surrendered so far this season by subtracting his wRBA of 38.22 from the average pitcher’s runs.

Average Pitcher Runs – Weighted Runs Below Average = Expected Runs
59.41 – 38.22 = 21.19

Based on Scherzer’s xwOBA, he should have only given up 21.19 to this point in the season. If this sounds incredible it’s because this is the lowest mark of any starting pitcher though the first half of the season. Finally, XRA is found by using the RA/9 formula by multiplying the expected number of runs allowed by 9 and then dividing by innings pitched.

(9 * Expected Runs) / Innings Pitched = XRA
(9 * 21.19) / 128.33 = 1.49

Max Scherzer’s XRA of 1.49 is easily the lowest of any starter through the first half. The second best starter has been Chris Sale who has a 2.15 XRA. Of course these names are not surprising as they each started the All Star Game and are both currently the front runners for their leagues’ respective cy young award.

Here is a list of the top ten qualified pitchers:

Pitcher XRA
Max Scherzer 1.49
Chris Sale 2.15
Zack Greinke 2.26
Corey Kluber 2.33
Clayton Kershaw 2.34
Dan Straily 2.87
Lance McCullers 2.89
Chase Anderson 3.11
Luis Severino 3.17
Jeff Samardzija 3.23

And the bottom ten:

Pitcher XRA
Matt Moore 6.58
Kevin Gausman 6.47
Derek Holland 6.32
Matt Cain 6.26
Ricky Nolasco 6.26
Wade Miley 6.17
Johnny Cueto 6.10
Martin Perez 5.97
Jason Hammel 5.95
Jesse Chavez 5.84

Full First Half XRA List

It is interesting to see that three members of the Giants rotation rank in the bottom seven in all of baseball. In fact, AT&T Park is such a pitcher-friendly park that once you park adjust these numbers, Moore, Cain and Cueto become the three worst pitchers in baseball. It’s not surprising then why the Giants are having such a disappointing season.

One measure of a good stat is whether or not it matches your perception. Therefore, while it is interesting to see Dan Straily as one of the best pitchers in baseball and Johnny Cueto as one of the worst, it is much more assuring to see Max Scherzer, Chris Sale and Clayton Kershaw as some of the very best in the sport. The numbers for relievers also reveal how dominant Kenley Jansen and Craig Kimbrel have been. This is all good evidence that XRA is doing what it is supposed to do, accurately displaying how good pitchers have actually been, independent of all other factors.

Another important characteristic of a good stat is how well it correlates from year to year. While ERA is the most simple and popular way to look at pitchers, it is not very consistent. XRA is much more consistent than ERA and FIP and also compares favorably with xFIP. However, it is not as consistent as DRA. DRA controls for so many aspects of the game that it should be expected to be the most consistent. However, being the most predictive or most consistent stat is not necessarily the goal of XRA. The real goal is to show how well the pitcher actually did, and XRA seems to do this remarkably. While not being as consistent as a stat like DRA, the level of consistency is extremely encouraging and puts it right in line with the other run estimators.

XRA is a stat that takes luck, defense, and ballpark dimensions out of the equation. When evaluating a pitcher, he shouldn’t be penalized for giving up a 350-foot pop fly for a home run in Cincinnati while being rewarded for that same pop fly being caught for an easy out in Miami. With XRA, no longer will people have to quibble about BABIP, since it is results-independent and removes all luck from consideration. A ground ball with eyes will now be treated the same whether it squirts through for a single or is tracked down for an out. Pitching ability will no longer need to be measured with an eye on the level of the defense. It takes a good offense, a good pitching staff and a good defense to make a great team, and with XRA we can finally separate all of these important factions.

Why Doesn’t Mauricio Cabrera Strike Out More Batters?

For many years, the undisputed king of velocity in Major League Baseball has been Aroldis Chapman, with his fastball that averages around 100 mph and regularly reaches higher. Few pitchers have even been able to approach the level of Chapman’s fastball since he came into the league, and none have surpassed him. However, in 2016, one pitcher finally did it. Mauricio Cabrera of the Atlanta Braves averaged nearly 101 mph on his fastball in 2016 and he regularly touched 103; but yet there was still a major difference between Cabrera and the incredible Chapman. Chapman struck out over 40% of the batters he faced last year, while Cabrera struck out less than 20%. Strikeouts are intuitively related to fastball velocity. The faster that a pitcher can throw the ball, the less time a batter has to react, making it harder to make contact. So how does a pitcher such as Cabrera, who throws as hard as anyone in the game, strike batters out at a well below-average rate?

I first thought that maybe his perceived velocity is not as great as his actual velocity, and sure enough Cabrera does gets very little extension toward the plate when he delivers the ball. He only extends about six feet toward the plate before he releases the ball, which is a full foot shorter than fellow reliever, Zach McAllister, and several inches shorter than average for fastball-heavy relievers. This lack of extension means that the velocity that the batter perceives is slower than the actual velocity coming out of Cabrera’s hand, because it has farther to travel before it gets to the plate. However, this is only a minor difference, as Cabrera’s perceived velocity is still above 100 mph. This is not a huge drop, but it does bring him closer to the pack, as many relievers get good extension that increases their perceived velocities above their actual velocities. Chapman, for instance, gets great extension toward the plate on his already incredible fastball, which results in his excellent perceived velocity of over 101 mph. Cabrera’s lack of extension is likely a contributing factor to his low strikeout numbers, but it does not seem to be the main culprit.

Next, I wanted to see if there was something about the spin rate on his fastball that doesn’t lend itself to strikeouts. Spin rates correlate quite strongly with strikeout rates. Pitchers with high spin rates on their fastballs typically generate more swings and misses, and thus more strikeouts. It turns out that Mauricio Cabrera does have a low spin rate on his fastball. His fastball spin rate of 2300 rpm is well below average for fastball-heavy relievers, which is probably a major reason why he doesn’t miss many bats.

While it makes intuitive sense that something like the amount of spin on his fastball could be the reason for his low strikeout totals, it is still puzzling to see that his spin rate is so low, because spin rate is typically correlated with velocity. For most pitchers, the harder you throw, the more spin you will put on the ball. Aroldis Chapman, for example, has one of the highest spin rates in the sample. In order to single out the spin rate from the velocity, I divided the spin rate by the velocity to find the Bauer Unit, named after Indians pitcher Trevor Bauer. Cabrera’s average Bauer Unit of 22.85 is one of the lowest in the entire sample of fastball-heavy relievers. This means that he has some of the lowest spin per MPH in the game. There must be something inherent in how Cabrera throws a baseball that just doesn’t allow him to generate the amount of spin that is typically commensurate of how fast he throws.

Cabrera’s low spin is not all bad, though. Just as high spin rates lead to strikeouts, low spin rates lead to ground balls. An average spin rate is really where you don’t want to be, as those are the pitches that get squared up more often. While Cabrera actually has an above-average spin rate for the entire population of major-league pitchers, his spin rate is one of the lowest in the league compared to his velocity. This effectively makes him a low-spin pitcher, and last year’s batted-ball numbers bear that out. Nearly 50% of the batted balls Cabrera gave up last season were on the ground, and he didn’t surrender a single home run all season despite giving up the hardest average exit velocity in the game last year on his fastball. Cabrera got away with that extreme exit velocity by only allowing an average launch angle of 5.9 degrees, which was one of the lowest among the fastball-heavy relievers. It is hard to do much damage on balls hit on the ground, even if they are hit 95 mph. While the myth that the harder the ball is thrown the harder the ball can be hit has largely been disproved, it is interesting to see that the pitcher who throws the hardest also gave up the highest average exit velocity.

Of course, strikeouts aren’t just about swinging strikes; you have to get called strikes as well. Throughout Cabrera’s minor-league career, he struggled to throw strikes consistently. So much so that many thought his strike-throwing ineptitude might prevent him from ever even reaching the big leagues. However, once he started pitching in the majors, he suddenly discovered how to find the strike zone. Of course, walking four and a half batters per nine innings is still poor, but that mark represented his lowest walk rate since rookie ball in 2012. Even with the high walk rate last year, he actually threw strikes at an above-average rate. His Called Strike Probability, according to Baseball Prospectus, was 47%, which is slightly above league average. For a guy like Cabrera who has always struggled with control, it is probably a good thing to see him filling up the strike zone at an above-average clip. However, the tendency to pitch within the zone could result in more contact and thus bring his strikeout numbers down. Since he doesn’t command his pitches well, he cannot nibble at the corners or trust himself to throw his pitches just off the plate to generate swings and misses. This allows hitters to either lay off pitches that are safely outside, or lock in to the pitches that are squarely in the zone. This could be another significant cause for his lack of strikeouts.

Another reason Cabrera doesn’t strike out many batters is because he doesn’t possess a bat-missing secondary offering. His secondary pitches are all used primarily to get hitters off of his fastball. He throws the hardest change-up in baseball at 91 mph, and a mid-80s slider with good depth. The change-up got squared up pretty often in 2016, which makes sense, seeing that he throws the pitch with the velocity of a league-average fastball. The slider also does not get many whiffs, but hitters were not able to do much damage off of it in 2016. Batters only slugged .136 off of his slider last season, and the pitch generated the highest rate of fly balls of any slider in the game. Perhaps what is even more significant is that hitters had an average exit velocity against his slider of 85 mph and an average launch angle of 30 degrees. For reference, hitters that hit the ball with an exit velocity of 85 mph at a 30-degree launch angle went 4 for 72. His slider may not be a swing-and-miss offering, but it sure seems to be a good out pitch for him.

It looks like Cabrera’s low spin rate on his fastball relative to its velocity is the main reason for his lack of strikeouts. However, it is also likely that that same low spin rate allows him to induce an extreme amount of ground balls, which helps him limit the damage from the opposing batter. His lack of extension toward the plate and his tendency to live in the strike zone are also contributing factors. He also doesn’t have a secondary offering that gets many swings and misses. His slider, however, does produce a great deal of pop-ups, which is another way he limits damage on his batted balls. A major reason for his success last season despite his low strikeout totals and high walk numbers was that he didn’t give up any home runs. While a complete lack of dingers is very unlikely to persist, the types of batted balls he allows on his fastball and slider make it difficult for batters to hit it deep off of him.

Cabrera walks too many batters, and while I wouldn’t be surprised to see some progression in his strikeout rate, I don’t expect him to ever strike out batters at the same rate as someone like Chapman. He should be able to persist for several years as a good late-inning reliever, but he probably will never reach the elite levels that his fastball might suggest.

Two of the Most Similar Pitchers in Baseball

In baseball analysis, we often use comparable players or “comps” to discuss what we think the player is likely to do in the future. Prospects are the most comped players because the general baseball public does not know much about minor leaguers. Comparing these young players to major leaguers allows fans to imagine what these prospects could someday become. Comps are also often used in projection systems. Data analysis has found that similar players often perform similarly throughout their careers. Thus, using former players who compare well with current players aids projection systems in forecasting what a particular player is likely to do in the coming years. Comparable players are also used in contract negotiations and arbitration battles. Players at similar ages with similar careers can expect to get roughly the same contract. In fact, the arbitration process is almost solely interested in comparing similar players and their wages.

Sometimes, players aren’t viewed as being similar when in reality they are actually quite alike. Recently, I found that Julio Teheran and Jose Quintana top each other’s similarity score lists on Baseball Reference. I had usually thought of Quintana as one of the game’s best pitchers and a true ace, while Teheran was at least a rung below that and probably more of a number 2 or 3 starter, so I did some research and found that these two pitchers are more alike than many probably realize.

Both pitchers are from Colombia and they were actually born only miles apart. Colombian-born baseball players are actually quite rare as there have only been 19 such players in MLB history, and this includes at least one set of brothers and a set of cousins. In fact, just this past season Teheran and Quintana became the first Colombian-born pitchers to ever start against each other in the same game. The two are apparently also quite good friends off the field and even work out together in the offseason. They each have also decided that they will pitch for Colombia in the upcoming World Baseball Classic. That will make for a formidable 1-2 punch for the Colombian pitching staff and will be hard for any other team in the tournament to match up against.

These two pitchers also match up quite well statistically, as their numbers look quite similar in a multitude of categories.

Julio Teheran 4.8 129 3.21 3.69 4.13 1.05 7.5 1.1 2.0 8.0 4.07 39.1% 10%
Jose Quintana 5.2 125 3.20 3.56 4.03 1.16 8.3 1.0 2.2 7.8 3.62 40.4% 9.5%


You might be able to find two pitchers with more similar numbers, but it wouldn’t be easy. They were both virtually 5-win pitchers according to Baseball-Reference, and the difference there likely comes from Quintana throwing a few more innings than Teheran. Their ERA, FIP, and xFIP are all almost identical and they both achieved their numbers in similar ways, too. Neither pitcher allows many baserunners, and they both strike out about eight batters per nine innings. In 2016, they both also had nearly identical ground-ball rates, and they suppressed homers to the same degree. Both pitchers had incredible seasons in 2016 and were both deserving All Stars, and while Jose Quintana did have a slightly better year and has been the better pitcher for the past several years, Julio Teheran has considerably closed the gap on his fellow statesman.

After seeing how closely the two pitchers’ 2016 stats aligned, I wanted to see how closely their styles of pitching matched up as well. While the approaches are not quite as similar as the statistics, you can see by the pitching styles how the stats could end up so similar. Using PITCHf/x data from I found that the biggest similarity in their repertoires is their four-seam fastballs. They both rely heavily on this pitch while throwing them about as hard and with similar amounts of movement.

Player Four Seam Usage Four Seam Velocity Four Seam Horizontal Movement Four Seam Vertical Movement
Julio Teheran 46.4 92.0 -5.1 8.2
Jose Quintana 41.1 92.6 4.6 9.5


These fastballs are not particularly special for two pitchers with such pedigree. They are each thrown with just average velocity and with roughly an average amount of downward and horizontal movement. They produce roughly the same amount of ground balls as the average pitcher and miss about as many bats as the average fastball. The most unique aspect of either of these pitchers’ fastballs is that Jose Quintana induces an exorbitant amount of pop-ups, which are basically as good as a strikeout. This allows his otherwise average fastball to play up better than the average starter.

After the four-seamer, their repertoires begin to deviate quite a bit. Quintana relies heavily on his sinker and his curveball as secondaries and mixes in a changeup occasionally. He throws his sinker just as hard as his four-seamer, but he gets more movement from the sinker. Julio Teheran uses his slider as his main secondary, throwing it over 26 percent of the time, while he mixes in a sinker, a changeup, and a curveball as his tertiary offerings. His slider is a plus pitch and he uses it to miss bats, while the other pitches are basically used as change-of-pace offerings to keep hitters off of his fastball and slider combination. Both of these guys get by with just average or better stuff, but command of their arsenal coupled with their mastery of the art of pitching have made them two of the upper-echelon pitching talents in the game.

It would only make sense that two players this similar would have similar contracts, but these contracts go way past similar — they are borderline identical. They are each under team control for the next four years. Teheran will make $37,300,000 and Quintana will make just a few hundred thousand more at $37,850,000, assuming that their respective option years are picked up, which is a pretty safe bet. Their yearly salaries are basically identical as well:

Year Julio Teheran Jose Quintana
2017 $    6,300,000.00 $    7,000,000.00
2018 $    8,000,000.00 $    8,850,000.00
2019 $  11,000,000.00 $  10,500,000.00
2020 $  12,000,000.00 $  11,500,000.00
Total $  37,300,000.00 $  37,850,000.00


Neither player’s salary ever deviates more than just a few hundred thousand dollars in any year under these current contracts. It only makes sense that two players with so many similarities would be compensated so similarly, but should they actually be valued the same?

Probably not; while they did have virtually the same season statistically this year, Quintana’s track record for this level of success is longer. Teheran does also have a successful track record, but he did struggle in 2015, and Quintana just seems to be the surer bet at this point. Steamer projects Quintana to be worth over a win more than Teheran in 2017. However, I do believe that their values should be a great deal closer than public perception. Teheran is two years younger than Quintana and could just be hitting his prime, he is signed to the same contract as Quintana, and his stuff may actually be better. Quintana is currently being aggressively shopped and the asking price is said to be roughly the same as the Chris Sale package. Julio Teheran is not worth that kind of package, but it might be closer than you think.