# Sabermetrics For Beginners Part III: The Plus Sign

95, 129, and 136, baby.

For our newest installment of SFB, I’d like to introduce you to two of the most deceptively simple and useful statistics, Adjusted On-Base Plus Slugging (OPS+) and Adjusted Earned Run Average (ERA+).

These two stats are used to show a player’s performance, either in hitting or pitching, as compared to the league average in each stat and compensating for that player’s ballpark.

The following assumes a basic knowledge of statistical understanding, so if you don’t remember what OBP and SLG are, check outÂ SFB Part 1, or here is Wikipedia’s dissertation onÂ ERA.

Adjusted OPS (OPS+) is a tool for examining a player’s offensive production, adjusted for the ballpark he played in and the average statistics from the rest of the league.

Here is the formula for OPS+:

OPS+ = [OBP/(league OBP) + SLG/(league SLG) -1] * 100

This is actually not as complicated as it looks. The league-On-Base-Percentage and league-Slugging are exactly what they sound like, and are then both adjusted to the batter’s ballpark. This means that if a batter is playing in a stadium that is better for hitters, it slightly discounts their batting performance, and vice versa. Take AT&T Park, for example, which favors pitchers over hitters (a little bit) because of its big outfields and damp climate, a fact that Triples Alley (among others) has examined in detail. Given that it helps pitchers, a ballpark adjustment would help a batter’s stats, but hurt a pitcher’s.

So essentially you’re taking the two components that make up OPS and comparing them to the league average. Because there are two components, you subtract 1 after that to get it back to the original scale. Then you multiply by 100 to get rid of the decimals.

If you’ve followed this so far, we end up with a number in and around 100, which is the league average. Above 100 is good, and below 100 is bad, as compared to the league averages. Here are the OPS+ values from the 2010 Giants:

1 Aubrey Huff* .385 .506 .891 138
2 Pat Burrell .364 .509 .872 132
3 Buster Posey .357 .505 .862 129
4 Andres Torres# .343 .479 .823 119
5 Juan Uribe .310 .440 .749 99
6 Freddy Sanchez .342 .397 .739 98
7 Pablo Sandoval# .323 .409 .732 95
8 Aaron Rowand .281 .378 .659 75
Team Totals .321 .408 .729 95
Rank in 16 NL teams 9 6 8
Provided by Baseball-Reference.com: View Original Table
Generated 2/22/2011. (* denotes lefty, # denotes switch)

This is not particularly surprising, as we remember who was good and who wasn’t (and yes, Pat the Bat did have better OBP and SLG than Posey). It’s interesting to see that, after everything, Uribe and Freddy were basically league average hitters, and Panda was just a smidge below average.

Keep in mind, the OPS+ number again does not mean anything by itself, but is rather a descriptive number that you can compare with others. Let’s pretend that the league average (ballpark-adjusted) OBP is 300, and the league average SLG is 400. Then let’s pretend that Johnny McBaseball bats 15% better than average in each statistic.

OPS+ = [.345/.300 + .460/.400 – 1]*100

OPS+ = [1.15 + 1.15 – 1]*100

OPS+ = 1.3*100

OPS+ = 130

An OPS+ of 130 is not 30% better than league average, given that it comes from two statistics, but is rather 15% better than league average in each category. The top-3 single-season OPS+ scores are all held by Barry Bonds (268, 263, 259), which were all MVP years for the big man. Babe Ruth holds the career OPS+ record with 206, with Bonds at third with 181 and Albert Pujols tied with Mickey Mantle for sixth with 172 (kind of puts Pujols’ contract negotiations in context, eh?). It’s a useful tool, particularly because of the built-in historical context, as you can see just how good somebody was for his time. Again, not the be-all-end-all of offensive statistics, but just another useful metric.

Adjusted Earned Run Average (ERA+) works along the same lines, comparing a pitcher’s ERA to the park-adjusted league average ERA from the same year. Here is the formula:

ERA+ = [(league ERA)/ERA]*100

Again, we end up with a number roughly around 100, with above being good and below being bad. Note that this is the opposite of ERA, where you obviously value low numbers. Given that the formula is constructed this way, higher is better. Here are the Giants pitchers from 2010:

1 CL Brian Wilson 1.81 226
2 RP Santiago Casilla 1.95 210
3 RP Sergio Romo 2.18 188
4 SP Madison Bumgarner* 3.00 136
5 SP Jonathan Sanchez* 3.07 133
6 SP Matt Cain 3.14 130
7 SP Tim Lincecum 3.43 119
8 RP Jeremy Affeldt* 4.14 99
9 SP Barry Zito* 4.15 98
10 RP Guillermo Mota 4.33 94
11 SP Todd Wellemeyer 5.68 72
Team Totals 3.36 121
Rank in 16 NL teams 1
Provided by Baseball-Reference.com: View Original Table
Generated 2/22/2011.

Again, not particularly surprising. We know that Brian Wilson was good, and Todd Wellemeyer was not so good. Interesting to note again that, despite everything, Barry Zito was essentially a league-average pitcher, at least ERA-wise. Also, note that ERA+ (and OPS+) do not take into account anything involving playing time, so take all averages with a grain of salt, as with relief pitchers you’re dealing with a much smaller sample size than starters. Even though Santiago Casilla kicked some major ERA+ butt, other metrics (like WAR) would show that given his limited playing time, he may not have been as valuable as somebody like Matt Cain, who had a worse ERA+ but played a lot more.

Mariano Rivera, the Yankees’ future-Hall of Fame closer, has the best career ERA+ with 205, which means that he has had an ERA somewhere around half of the league average for his entire careerÂ (the next highest career ERA+, Pedro Martinez, is 154, which just shows you how amazing Rivera really is). The highest single-season ERA+ is from 1880, but Martinez again has the highest in the modern era, with a 291 ERA+ in the year 2000. He had an ERA of 1.74, won his third Cy Young in four years, and made a lot of Red Sox fans really happy.

I hope that these help explain a bit of which we’re talking about. I’ll keep writing things like this, so please let me know if there is something specific you’d like me to help explain.

So now, comment starter: what’s your favorite, most descriptive statistic? How do you feel ballparks really affect hitters? Who the hell is Tim Keefe?

Go Giants!