The Stats We Use: OPS+, wRC+, and ERA+

In previous installments of this series we’ve covered the basic offensive, defensive, and pitching stats we use when discussing player production. Those familiar with the statistics will recognize what it means when we say a player has a .355 wOBA. Those who aren’t, though, might have a bit of trouble determining exactly what that means, even if they’re familiar with the workings of the statistic. To make things easier, we have a number of stats which compare production to the league average. We’ll dive into these today.


Baseball Reference has changed the way we view statistics. The site makes everything presentable and easy to access, so we can look up our favorite players and see exactly what they did. One statistic that B-R founder Sean Forman created was OPS+. OPS, as you likely already know, stands for On-Base Plus Slugging. Since the ability to get on base and the ability to hit for power represent two of the most important things a batter can do, mashing the two stats together made enough sense, even if it double-counts singles — not to mention combines two stats that have different denominators.

The other problem with OPS is that it deals with two statistics on different scales. The maximum OBP is 1.000, while the maximum SLG is 4.000. The answer, then, is to weight the statistics when combining. Forman went with (1.2*OPB) + SLG, and then placed that figure on a scale where 100 was league average. That made the stat easier to understand. Instead of having just a number, OPS+ put the number in context by comparing it to everyone else in the league. Now we know that when a player has a 120 OPS+ that he’s well above league average. We might not have been able to discern that by just seeing a, for example, .870 OPS by itself.

Improved as it may be, OPS+ is not perfect. For instance, Tom Tango believes that OPS+ still undervalues OBP, and that the calculation should be (1.8*OBP) + SLG. Even so, OPS+ is an improvement over straight OPS, not just because of the 1.2*OBP calculation, but also because of how easily it tells us what we want to know. But, perhaps there’s a better stat for this.


Uh oh. Another stat with a lower-case letter. For some this might mean trouble. It’s not, though. In fact, it works right along with wOBA to provide us with a scaled view of player production.

The story of wRC+ doesn’t go back too far. In December Alex Remington wrote a wOBA primer, and Tango made a comment about one of Alex’s lines regarding wOBA in relation to OPS and OPS+. Later, in the comments, Tango said that he did not want wOBA+, but rather wRC+ — weighted Runs Created on a league scale. He used the BaseRuns formula to demonstrate how easy it would be to implement, and FanGraphs proprietor David Appelman (a great guy, really!) implemented it. The whole process took about a day. No joke.

The basics of wRC+ can be found in the wOBA primer. It uses the same system, basically, but instead of outputting a rate stat it outputs a counting stat, weighted Runs Created, or wRC. The number is park adjusted and scaled to the league. Like OPS+, 100 is league average. I prefer wRC+ to OPS+ not only because of the slight flaw in the OPS+ calculation, but because it assigns a proper value to each component, whereas OPS+ still uses the arbitrary measures of two for a double, three for a triple, etc.


Like OPS+, ERA+ can be found at Baseball-Reference. This one won’t take but a paragraph to explain. Like OPS+, ERA+ is on a scale where 100 is league average. You can compute it right from home, too. Just take two minus the player ERA divided by the league ERA and multiple by 100. In other words: 100 * (2 – playerERA/leagueERA).* That’s literally it. The advantage, of course, is that you can determine how much better than average a pitcher was, no matter what the run environment.

* They did change ERA+ just yesterday. It produces the same results, in that the players are ranked the same. The formula change just makes ERA+ linear. That is, a player with a 122 ERA+ is 22 percent better than league average. The old way didn’t handle it like this. Sean Forman, proprietor of Baseball Reference, explains: “With the new formula, the equation is linear, so if the league ERA is 4.50 and you have one pitcher at 3.50, one at 3.00 and one at 2.50 you get ERA+’s of 122, 133 and one at 144 (one is 22% better than the league, one is 33%, and one is 44% better). It seems to me the numbers make a little more sense this way.”

I’d like to see this expanded to FIP. It shouldn’t be hard to create FIP+, and I do wonder sometimes why it’s not a readily available stat. Probably because FIP stands fine by its own, since it’s not really based on the same value scale as ERA. Still, I do like the concept of adding context by scaling to 100. It gives us a one-glance idea of how a player performs compared to his peers.

Next up

There will be one or two more posts in this series, touching on some other offensive and pitching measures. The ones in the series so far, though, are the ones we’ll primarily use.

2010 Season Preview: The Four Benchmen

Photo credit: Kathy Willens/AP

The days of the 11-man pitching staff seem behind us. Bullpen specialization, combined with managers employing a slightly quicker hook for starters, makes teams more comfortable with seven available bullpen arms rather than six. This becomes a big deal when creating a 25-man roster. In the AL it means a shallow bench. Eight position players plus a DH leaves just four sports for reserve players, one of which must be a backup catcher. Teams must be cautious, then, when choosing their bench players.

Thankfully, the Yankees have the personnel to make the bench work. While both Nick Swisher and Nick Johnson start at other positions, they can fill in for Mark Teixeira at first if needed. They also have a number of players in the system who can play the other three infield positions, making only one of them necessary for the 25-man roster. That leaves one spot for a reserve outfielder and one spot for a pinch hitter. The bench need not necessarily work that way when the team breaks camp, but it should end up that way soon enough.

Photo credit: Charlie Riedel/AP

Last season the Yankees started the year with a heavy bench, even with A-Rod sidelined with his hip injury. The only consequence was a downgrade from Cody Ransom to Ramiro Pena, not a huge one at all even considering Pena’s rookie status. In the outfield they had Melky Cabrera and Nick Swisher, both starters the previous year. It’s tough, actually, to build a better bench than that. It was probably the Yankees’ best in five or more years. Xavier Nady‘s injury thinned it out in April, though, and the team had to react. They later traded for Eric Hinske for pinch hitting purposes. The bench, again, seemed strong.

Photo Credit: Steve Senne/AP

This season the Yankees’ bench doesn’t appear as strong as 2009, but it still provides the Yankees with what they need. Ramiro Pena or Kevin Russo will serve as the all-purpose utility man, Brett Gardner or Randy Winn will serve as a reserve outfielder and possibly half of a platoon, Francisco Cervelli will back up Jorge Posada, and Marcus Thames will get at-bats late in games mixed with the occasional start against a lefty. That doesn’t seem too bad at all. Perhaps the Yankees will seek a better pinch hitter than Thames come mid-season, but he’s a serviceable option to start the season.

Even though solid, the bench doesn’t come into play a lot, especially the utility infielder. Robinson Cano played 161 games, Derek Jeter played 153, and Alex Rodriguez, a year removed from his surgery, likely won’t take as many days off. This should limit the utility infielder to 100 plate appearances or so through August (there’s no telling what happens in September when rosters expand). If the winner of Pena/Russo doesn’t hit, or has problems in the field, the Yanks can swap them. The actual difference it makes, though, will be marginal. There will be chances in the outfield, as the left field situation doesn’t seem quite settled. Also, since neither Brett Gardner nor Randy Winn carries a heavy bat, a pinch hitter could get late-game opportunities.

Photo credit: Kathy Willens/AP

Just how do the projection systems view the Yanks’ four bench players? Mike already covered Winn in his left field preview, so here are the remaining three.


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The average projections seem fairly reasonable. Thames, as we know, is all power and not much else. That could make for a good bench player, at least to start the season. If he doesn’t prove effective, the Yankees can go shopping in June. That yielded Eric Hinske last year and could easily net them a similar player this year should the need arise. Pena and Cervelli appear perfectly reasonable for their roles. Cervelli could see more playing time, depending on Jorge’s situation.

Again, the Yankees’ advantage is that they don’t need the bench for very much. Pena will give the infielders a day off, while Winn will spell the outfielders. Thames will come up when the team needs a long fly and Gardner or Winn is due up. Those all seem like very limited roles. Cervelli is the only one who figures to play regularly, though we hope not too regularly. He’s fine as a backup. Hopefully that’s the only role he fills this season.

Yanks tab Hughes as fifth starter

Yankees manager Joe Girardi has officially announced Phil Hughes as the team’s fifth starter. While the team will say that Hughes earned the job with his confident and solid Spring Training pitching, the truth is that the job was Hughes’ to lose. For some reason or another — and I’m sure it will be discussed ad nauseum over the next few days — Joba Chamberlain had pitched himself out of contention by the end of last season.

For now, this leaves Joba Chamberlain twisting in the wind. After the Yanks kept him tethered to a strict set of rules, innings and pitch limits throughout 2007, 2008 and 2009, the team has yet to determine his role in 2010. “I think Joba could do either job,” Girardi said to reporters this morning, “but right now we feel Hughes is ahead as a starter.” Girardi’s comments, apparently, stem from the development of Hughes’ change-up.

When asked about the ever-important eighth inning, Joe Girardi said, “You have to earn your spot.” While Joel Sherman seems to think this makes Chamberlain destined to be Mariano Rivera‘s prime set-up man this year, I wonder if Girardi is referring to Joba’s spot on the team. As I speculated just this morning, the Yanks could opt to go with Boone Logan while sending Joba to AAA to keep his innings up.

Meanwhile, Phil Hughes, all of 23 years old, hasn’t been a starter over the course of a full season since his injury-free 2006 campaign. That year, he threw 146 innings but hasn’t reached that total as a professional at any level since. Last year, over the course of the Minor League season, his Major League campaign and the playoffs, he threw 111 innings, and I believe the Yankees will try to cap him somewhere within the 165-175 innings range. Based on the team’s schedule, they don’t need a fifth starter until April 24, and Hughes should, in other words, be able to last the season in the rotation.

Dave Eiland discussed the end of restrictions for Joba in February, and he did mention that Hughes would be on a limit. “You’ve got to remember,” Eiland said, “Joba had restrictions because he never had a full season in professional baseball as a starter. Phil Hughes has had several minor league seasons as a starter. So there’s going to be restrictions, but they’re not going to be as strenuous as Joba. And I’ll just leave it at that, right there. There’s restrictions, and we’re on the side of caution with all our guys.”

What all of this means for Joba, I have no idea. Girardi said that Joba would throw one inning on Saturday, and if that doesn’t sound like relief prep work to me, I don’t know what is. Yet, for now, a limitless Joba will be seemingly in a limited role. How this makes sense for the Yankees of 2010, the Yankees of 2011 or the Yankees of the future, I don’t know. Joba needs his innings; Phil needs his innings. The Yanks shouldn’t be giving up on Joba after three years of yoking his chain. The team, though, hasn’t made an announcement regarding Chamberlain’s future, and until then, I’ll hold my breath.

Photo Credit: Kathy Willens, AP

And then there was one

After last night’s victory over the Washington Nationals — a playoff preview if ever I saw one — the Yankees cut five more players from their ever-dwindling Spring Training roster. As the Yankees now have 26 guys for 25 spots left in camp, we’re quickly seeing how the team is operating this spring. Their next decision, one Joe Girardi says will be announced later today, will determine the Yanks’ pitching staff for the start of the season.

The cuts were, by and large, as expected. Jonathan Albaladejo and his 33.75 March ERA found themselves exiled to the Minors while Mark Melancon and his 10:1 Grapefruit League K:BB ratio were sent down as well. Melancon should be the first guy called up if the pen needs some right-handed relief. Greg Golson, a toolsy outfielder and former first-rounder, impressed during the spring but will start the year at AAA. Juan Miranda, potential trade bait or potential back-up DH, will as well.

With those cuts in hand, the Yanks picked a back-up infielder as well. The final battle came down to a deathmatch between Ramiro Peña and Kevin Russo. While Peña enjoyed the luxuries of incumbency as the back-up middle infielder, Russo offered up a better bat. He hit .333/.393/.458 during the spring, but his glove isn’t on par with Peña’s. And so the Yankees have chosen to go with Ramiro for now. Russo could see some time in the Majors later this year.

But what of the players who are left? That’s where things get interesting. Of those signed to Major League deals, the outfielders will be Brett Gardner, Curtis Granderson, Randy Winn and Nick Swisher. Marcus Thames is expected to make the team as well. Mark Teixeira, Robinson Cano, Derek Jeter, Alex Rodriguez, Ramiro Peña and Nick Johnson will be the infield crew with Jorge Posada and Francisco Cervelli behind the dish. That’s 13.

The pitchers left in camp also number 13 as Chad Gaudin was released and will not be coming north with the team, obviously. Who will be cut? The likely 26th man is Boone Logan. A lefty who came over in the Javier Vazquez trade from the Braves, Logan has thrown seven pretty good innings this year. He has allowed two runs on three hits and a walk while striking out five, and the team would feel comfortable about using him as a second lefty in the pen.

Yet, there is also this looming matter of the fifth starter. If, as we suspect, Phil Hughes is announced as the fifth starter later today, the Yankees will have a choice. In fact, even if Joba Chamberlain, and not Hughes, is announced as the fifth starter, the Yankees will have the same choice. Do they start the season with the loser of the fifth starter race in the bullpen as a potential set-up man or in AAA as the team’s sixth starter? Sending the odd man out down to AAA would allow the Yanks to keep Logan on the team as a second southpaw, and it would allow the Yanks to stretch out Hughes or Chamberlain to keep them on track to meet their innings goals.

I’m holding out hope, perversely, for a minor league assignment for the sixth starter. The future of the team will benefit greatly if neither pitcher is encumbered with an innings limit. Joe Girardi says this final announcement will be made later today, and only then will we finally see what developmental course the Yankees have charted for their young arms. Boone Logan might just be the beneficiary of a team looking not only to 2010 but also beyond.

Chad Gaudin Released

According to The Star Ledger’s Marc Carig, Chad Gaudin has been released. He had been placed on waivers earlier this week. The Yanks only have to pay him 45 days of termination pay (approximately $737,500), so this absolves them of the bulk of Gaudin’s $2.95 million salary for 2010. They could always re-sign him to a minor league contract to keep him in the organization, but I don’t think it’ll be hard for him to find a big league job elsewhere. After all, there are teams out there seriously interested in Jarrod Washburn.

I’m really not sure I get this, Gaudin is a damn useful piece. I guess the team must really have faith in Sergio Mitre now that he’s further away from Tommy John surgery.

The best value player for the Yankees

The Yankees do not cheap out when they have the opportunity to land a superstar player. Whether it’s locking up Jeter, trading for A-Rod, or signing CC Sabathia, we all know that the Yankees will spend money. They’ve spent so much, in fact, that they currently have $144 million committed to just nine players in 2011. With such a top-heavy group of players, the team still needs young, cost controlled talent to fill out its roster. Thankfully for them, there can be plenty of value in those players.

To examine how much the Yankees paid their best players for their contributions, I’ll put their Wins Above Replacement (WAR) up against their salary for the season. We can take this all the way back to 2005, just because it’s easy and the data is so readily available. I’m going to leave out players who the Yankees traded for mid-season, just to make everything a little easier. Also, I’m clearly only going with position players, at least in this post.

2005: Alex Rodriguez

Photo credit: Gregory Bull/AP

Yes, the Yankees got more value out of Alex Rodriguez than any other player in 2005. With his salary that might not have seemed possible. Remember, though, that Texas was still paying a chunk of that salary, at least until 2008. According to Cot’s, the Yanks paid $16 million for a $25 million player. That covers 2005 and 2006. In 2007 his salary escalated to $27 million, so we’ll add another $2 million to the Yankees’ contribution (even though they might have still paid him $16 million). The team also got quality values from Jorge Posada, Jason Giambi, and Hideki Matsui, for whom they paid less than $2.6 million per win above replacement.

While WAR is a big picture value tool, it can’t see the nuances throughout a season. For instance, it has the Yankees paying Tino Martinez $4.58 million per win, since he produced only 0.6 WAR. His home run streak in May, though, did help the Yankees recover from a stagnant start.

2006: Robinson Cano

The Yankees got excellent value from Robinson Cano in his second season. At a league minimum salary he produced 3.5 WAR, finishing third in the AL batting average race. His buddy, Melky Cabrera, was also effective, producing 1.6 WAR at his paltry salary (which, during a partial season, I estimated at about $300K). Gary Sheffield’s and Hideki Matsui’s injuries skewed their value numbers, though that’s to be expected. The Yankees did seemingly pay a lot for Johnny Damon and Jason Giambi that season, over $4.5 million per win.

2007: Robinson Cano

Photo credit: Frank Franklin II/AP

While Cano did lead the Yankees in win value in 2006, he was outstanding in 2007. His 5 WAR at a $490,800 salary meant under $100,000 per win, easily the best mark on this list. His overall WAR mark is also impressive, as it ranked third on the team behind Alex Rodriguez and Jorge Posada.

Again, we see A-Rod come in under $2 million per WAR despite his enormous salary. Jorge Posada made a bit more in 2007 than he had in the past, but still came in at $1.7 million per win. He hasn’t gotten close to there since. Then again, he hasn’t come close to his 2007 production, either.

2008: Brett Gardner

I made something of an exception to the partial season idea by including Melky in 2006 and Gardner in 2008. There was good reason, though, as both produced more than 1 WAR. Gardner, in fact, produced somewhere around $200,000 per WAR, though that comes with a roughly estimated $200K salary. Adjust that all you want, he’s still way out in front of the rest.

Johnny Damon, at 3.7 WAR, was the next highest, followed by Alex Rodriguez, his full salary finally realized. Bobby Abreu, or at least Bobby Abreu’s defense, was the goat here, as he produced just 1.3 WAR for his $16 million. While a team certainly can win while paying a lot of money for its wins, it’s unsurprising that the Yankees didn’t have any players, other than Gardner, for whom they paid less than $3.5 million per WAR. That doesn’t sound like a winning formula.

2009: Brett Gardner

Photo credit: Jim Mone/AP

Clearly, if Gardner took home the prize in 2008 he did again in 2009. He produced 2 WAR while earning just $414K, or $207K per win. Melky Cabrera, with 1.7 WAR, was also a decent value. Count Cano and Swisher as others for whom the Yankees paid less than $2 million per WAR.

Alex Rodriguez falls to the cellar on this list, not only because of his $32 million salary, but because his shortened season hurt his value. Jeter’s 7.4 WAR season also played nicely with his $20 million salary, as he cost only $2.7 million per WAR. Damon and Matsui were trailers here, too, but it wasn’t as bad as the situation in 2008. Not by a long shot.

Here’s the spreadsheet, in case you wanted to take a look at the whole list:

Selig implements a better LCS format

Baseball will do away with the unnecessary off-day between Games 4 and 5 of the league championship series, Commissioner Bud Selig announced today. In responding to complaints by players, team managements and fans over the voluminous amount of October off-days, the Special Committee for On-Field Matters proposed eliminating the extra day off, and baseball has accepted the change. A seven-game LCS will now take place over nine days instead of ten. “The removal of the off-day,” Selig said, “during both League Championship Series marks the first step in a process that will ultimately result in an improved postseason format for our game.”

As for the Yankees, this news is obviously an interesting development because they used the extra off-day in 2009 to keep their three-man playoff rotation in tact. As much as I enjoyed that pitching advantage, the truth is that the Yanks played 15 games over 30 days in October, and that stop-and-start schedule disrupted the flow of the games. With weather always a fact in mid-fall, the games should be as close together as possible. Baseball might lose some money on this one, but the powers-that-be made the right decision.