## Ok, so he’s good, but how good? The PLUS metrics

Hi everybody, I'm the SABR guy over at Purple Row, and over the past year, I've done my best to bring the readership up to speed on most of the commonly used and cited metrics in player evaluation. This article on OPS+ and wRC+ is the first I've written this season, and I figure it'd help out the readership. Jeff Aberle (of Bill Simmons fame) encouraged me to repost this here. Now, I know that you all probably understand OPS+ and wRC+ more than I do, but I figure that a primer couldn't hurt too badly for those of you who feel they could use a brushup. Don't worry, I won't tell anybody you're reading this.

Over the 2009 season, between articles with spreadsheets you could wallpaper your garage with and more numbers than a federal budget report, we took some time out of our busy lives to head back to math class and learn about a whole pile of advanced statistical metrics that several of have been citing ever since.

Well, there's more to cover still, so let's dive in.

Now to lead this article off, I'm going to borrow an illustration from our friends formerly known as the guys at Fire Joe Morgan. Not directly, but they do a great job.

When we look at statistical metrics in a historical context, it's kind of hard to compare apples to apples as far as stuff like OPS and wOBA (and all the other offensive numbers as well), because as anybody who has been watching for more than 10 years will tell you, the game was simply not played back then the way it is played today. Not necessarily just citing styles of play (speed vs. power), but just looking at the numbers.

Here's an example. In 1968, Carl Yastrzemski hit 23 dingers, posted a .922 OPS,  and a .418 wOBA. In 2004, Jim Edmonds had an OPS of 1.061 while driving 38 homers and posted a wOBA of .436. In 1970, Frank Howard hoisted 44 balls over the fence, settled for a .962 OPS and a .413 wOBA.

So we have 3 very different hitters here, and it's pretty obvious how they rank against each other. Edmonds is clearly the best, with that 1.061 OPS, then Howard with his .962, and finally Yaz at .922. Or if we want to rate by wOBA, it'd be Edmonds, then Yaz, then Howard. You see, ranking people by stats is easy. Jim Edmonds is clearly better than Carl Yastrzemski.

Now, take a deep breath, because I can already hear keys clacking telling me about how Carl Yastrzemski was one of the absolute best hitters of his generation, etc etc etc. and how wrong I am for saying that a guy who probably juicing or something (because everybody who posted good offensive numbers in the early 2000s was on steroids, no matter what) could possibly be better than HoF Yaz.

Well, you're right.

This is where we introduce the concept of OPS+ and wRC+.Simply put, OPS+ and wRC+ is balancing a player's OPS or wOBA against the league average. Both metrics do the same thing by first park-adjusting a player's individual OPS or wOBA, then balancing against the league average and coming up with a weighting on the scale of 100.

Let me explain further.

The idea is that OPS, which stands for On-Base-Plus-Slugging, is comprised of, you guessed it, On-Base Percentage and Slugging Percentage. So what OPS+ does is weigh OBP versus the league OBP, SLG vs. the league SLG, adds them, subtracts 1, and then multiplied by 100. wRC+ is calculated in a similar way, but even more complicated, given that it's comprised of linear weights.

Still confused? Yeah, me too. Well, ok, I'm not, but I also do mathy things and spreadsheets for fun.

The basic idea behind OPS+ and wRC+ is that if you post a 100 in either, you're by definition a league-average player (as far as either metric would represent). In 2009, two players (who qualified for the batting title in terms of PA) hit that 100 OPS+, and they were Kevin Kouzmanoff and Yadier Molina. In terms of wRC+, I regret to say that I can't see wRC+ on a year-to-year basis for the entire league, but I CAN tell you that Jose Lopez posted a 100 wRC+ (you can check individual players).

So for those players out there who AREN'T at a 100 OPS/wRC+, you simply take the difference between their actual number and that 100 average, and you can infer that they are that many percentage points above or below the league average.

In 2009, the best player in terms of OPS+ was Albert Pujols, whose 1.101 OPS was good for a 188 OPS+. Pujols also led the majors with a .449 wOBA and a 184 wRC+. Albert Pujols is very very good at baseball. That's 88% and 84% better than the average player, depending on which metric you prefer.

Just to clarify something, the naming of wRC+ is a little strange. OPS+ is the adjusted version of OPS, and wRC+ is the adjusted version of wOBA - sort of. You see, wRC is a metric that is sort of like VORP, just based on wOBA rather than eQA (I'm pretty sure that's what BP uses). wRC stands for Weighted Runs Created, which uses the system of linear weights used in the calculation of wOBA and multiplies that by PA, thereby creating the number of runs a player has created thus far in that particular season. So to calculate wRC+, they take the number of wRC accumulated by that particular player, and compare it to the wRC that the league average would have created with the same number of plate apperances. Past that, it's all the same, you multiply by 100, etc etc etc. Quick and dirty, it's the same formulation as OPS+, just using wOBA. I'm still not 100% sure why the guys over at Fangraphs chose to use wRC to find the metric rather than just a straight wOBA, as it seems to just be adding an additional step, but I'm sure they have very good reasons. Bottom line, I trust the metric, whether it's named wOBA+, wRC+, or Frank.

So let's jump back to our original example, with Edmonds, Howard, and Yaz. Obviously, despite the .100+ OPS discrepancy between the three players, we know that they're clearly not equal hitters as far as skill goes. But to compare their individual seasons, all three batters posted a 170 OPS+, essentially saying that stacked against their peers and adjusting for the park they play in, all three batters were equally as proficient at their craft. The idea is: based on the era one is playing in, runs may be at more of a premium, so a .900 OPS in 1965 is FAR more valuable than a .900 OPS in 2002.

But it's also good for looking at today's players. Carlos Gonzalez and Martin Prado are both posting a .920 OPS. However, Gonzalez' 131 OPS+ is overshadowed by Prado's 145 OPS+. Similarly, Johnny Damon and Marlon Byrd are both posting a .391 wOBA, but Damon has the edge with a 141 wRC+ as compared to Byrd's 137 wRC+. When we look at OPS+ or wRC+ in a given season, you're essentially just making park (or league) adjustments.

So now for my favorite part of this article: looking at the all-time numbers.

The best single-season OPS+ belongs to Barry Bonds' 2002, at 268. Yes, you read that right. Barry Bonds was nearly worth triple an average player in 2002. Argue about the reasons if you must, but even stacked against other juicers, he was simply otherworldly. In fact, Bonds holds the top 3 seasons of all time (2002, 2004, and 2001). The next 3 are Babe Ruth (255 - 1920, 239 - 1923 and 1921). Following that is 2 Ted Williams seasons. In fact, you need to get to 12th to get away from Bonds, Ruth, and Williams, and that's Mickey Mantle.

For a career, Babe Ruth tops the list at 207. That's right, for his entire career, Babe Ruth was twice as good as any average player. Next is Ted Williams (190), followed by Barry Bonds (181), Lou Gehrig (179), and Rogers Hornsby (175).

If you prefer the more OBP-heavy wRC+, the leaderboard doesn't really change. Babe Ruth heads things up again at 204, then Williams (196), Gehrig (182), and then a 3-way tie between Barry Bonds, Ty Cobb, and Mickey Mantle, all at 177 wRC+.

To flip the coin over, we can see the WORST batters of all time as well, at least as far as wRC+ goes. For batters with a minimum of 5000PA, Neifi Perez was by a long shot the worst, posting a career 60 wRC+. That means he was 40% WORSE than an average player. Career .297 wOBA. Tied for next-to-worst are Alfredo Griffin and Leo Durocher, at 66 wRC+. None of these players ever had a season at the plate that met or exceeded that 100 Average mark. Ever.

As a side note, we should all just sit back and bask in the absolute absurdity that was Babe Ruth. For the longest time, I was just convinced that he was a legend as far as Americana goes, in the sense that nobody hit home runs at that point in time, so his grandeur was just a gimmick that coincided with the Roaring Twenties, and set a bar for everyone to attempt to reach. Everybody look at how wrong I was. What's even more mind-blowing is that Lou Gehrig, while not AS good as George Herman Ruth, is in the top-5 all time. That's just how good the Yankees were back then.

So let's sum this whole shebang up. OPS+ and wRC+ are statistical metrics that represent OPS and wOBA, scaled to 100 being average, park adjusted and tried by a jury of their peers. Both metrics are essentially telling the same story, it just depends on if you prefer OPS or wOBA for your player evaluation. Both numbers are useful for a number of things: Evaluating on a year-to-year basis who the best batters were, comparing batters from different eras, and I like to use it as a barometer of Hall of Fame worthiness. You can find OPS+ on Baseball Reference and wRC+ on Fangraphs.

That's all we have for today, friends, so I hope that you can use these tools presented to you to explore some of baseball's history, and some of the players who have made this game as great and storied as it is.

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