## Recreational Math – How To Measure A Batter’s Performance

As I’ve mentioned before, I’m a pretty big baseball fan. In my youth the accepted measure for evaluation hitters was batting average. Today there are multiple measures to evaluate a hitter’s performance. I will compare and contrast three of these measures: batting average (BA), on base percentage (OBP), on base plus slugging (OPS).

### The Standard – Batting Average

A players batting average is calculated as the number of hits divided by the number of at bats.  An “at bat (AB)” is a place appearance that does not include walks, hit by pitch, or sacrifice fly. It simply measures how effective a hitter is at getting a hit.

### A Better Measure – On Base Percentage

On base percentage measures the percentage of time a player reaches base, including plate appearances that result in walks and hit batters. Here’s the official MLB formula:

OBP = (H + BB + HBP) / (AB + BB + HBP + SF)

To many teams this is a more efficient measure as it values getting on base, and an increase in base runners can produce an increase in runs scored. Players with plate discipline not only reach base by seeking to draw a walk, they tire out the opposing pitcher by causing the pitcher to throw more pitches.

At one time OBP was a undervalued attribute, one that Billy Beane of the Oakland A’s was able to use to assemble a highly competitive team on a meager budget. (I recommend reading Michael Lewis’s Moneyball for a complete understanding of Beane’s strategy.)

### Even Better – On Base Plus Slugging

On base plus slugging, or OPS, adds a player’s on base percentage to his slugging percentage. It is a great way to measure a player’s proficiency for reaching base (more times on base = more runs scored) and power (more power = more runs drive in).

### An Example – Barry Bonds

OK, I know that my choice of Bonds is questionable, but using OPS rather than batting average really demonstrates how outstanding Barry Bonds was. (I have nothing to add to the performance enhancing discussion.)

In 2001, Barry Bonds had 156 hits in 476 at bats, which resulted in a batting average of .328, which is good but not legendary.

In the same year he reached base 342 times when you add in his 177 (!) walks and the 9 times he was hit by a pitch. That was an on base percentage of 342/664 or .515. Bonds reached base more than half of the time. (In 2004 his OBP was .609, more than 3 out of 5 times he reached base.)

Finally, his OBP was .515 + .863 or 1.379 (rounding).  His best OPS (actually anybody’s best OPS) was 1.422 in 2004, when he was 39.

### Conclusion

I’m not sure that we’ll see OPS on the back of any baseball card, but if you want to build a competitive team or dominate your fantasy league, be sure to check this stat out.

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. Each Friday my blog contains an article on recreational mathematics. Let me know if there are other topics you’d like me to address. You can reach me hrough the contact page on my website – http://georgewoodbury.com.