# The math is emotionally correct

Years ago, I got into a spirited discussion with a colleague about a quality measurement he wanted each production unit to use within all of our manufacturing sites. He wanted a single performance measure that could be trended over time that showed a production unit’s ability to produce a quality product the very first time. He proposed that we would sum into a single value our already derived individual percentages of rejects, rework, and reallocation of our produced product. I adamantly argued, pacing outside of an office complex, that *you cannot add the percentages together to create this "RRR" equation*.

I positioned my argument that all three are individually important and adding them together could drive the wrong behavior. I argued that rejecting a product is more unfavorable than rework and was tremendously more unfavorable than reallocation. I remember standing my ground and stating that adding these three values together into a single key performance measurement is just plain wrong. His response was, “The math may not be right, but the math is emotionally correct.” I remember saying, “what the heck is emotional math?”

## Performance measurement for batting in baseball

Imagine it's Spring, flowers are starting to bloom and the smell of freshly cut grass is in the air from your first mowing of the year. This is the smell that tells me it’s baseball season. During the offseason, trades occurred, free agents get picked up, and minor leaguer call-ups get the first glimpse of their life-long dream. As teams build their offensive lineups, there is always a lot of talk about a batter’s OPS, or their *On-base plus slugging*. Created by __Pete Farmer __in the 1950s popularized by __Branch Rickey and Allan Roth____ __in the 1980s, it is arguably one of the most important batting key performance indicators.

There is just one problem from my perspective; it is adding averages. OPS is a single number that adds the individual performance measurements of OBP (On-base Percentage) and SLG (Slugging Percentage). It's an acronym that places its mathematical dysfunctionality of “plus” right in the middle. To get you even more fired up, OBP has a max value of 1.000 and SLG has 4.000 and now you want to add them together to give an indication of a batter’s value? How can a multi-billion industry be so obsessed with an offensive key performance indicator of added averages?

Or are flawed? Are we missing something to measure the performance of an operating unit more effectively? In manufacturing, I am unaware of any best practice or performance indicator similar OPS, so is there something that baseball is doing right that we should consider? There are always new manufacturing industry trends and measuring techniques, so is there something manufacturing leaders could learn from OPS?

## On-base Percentage

Let's recap. OPS is On-base Percentage (OBP) plus Slugging Percentage (SLG). OBP has hits, base-on-balls, and a hit-by-pitch in the numerator. In its denominator, it is at-bats, base-on-balls, sacrifice hits, and hits by pitch. Within the at-bat, it is generally when a batter reaches base on a fielder’s choice, a hit, an error (a catcher's interference doesn't count as an at-bat), or a batter is out on a non-sacrifice. This is not the same as plate appearances, because it is quick to see that strike-outs, ground-outs, or pop fly-outs, are not in the denominator. This performance indicator is specifically around how good a player is at getting on base. Intimidation alone as a threat of getting a hit to drive in runs is enough to raise your OBS because walks are in the numerator.

Batting average tells us only how good a hitter is at reaching first base on batted balls. It doesn’t tell how good he is at reaching base because it doesn’t include walks or hit-by-pitches. Higher OBP players not only reach base more, but they make fewer outs. - John Grochowski -Chicago Times

## Slugging Percentage

Now, SLG is the number of bases divided by at-bats. Giving credit for each base achieved, this statistic, more of an average than a percentage, is how close to home the batter gets with a single at-bat. Historically, this statistic generally guides batters to hit in the middle of the lineup and routinely get intentionally walked due to the threat of them getting an extra-base hit. Think of the likes of Babe Ruth or Barry Bonds. And by the way, Barry Bonds has the highest SLG of all time at .863.

## Reflection of OPS

There are not many articles better on OPS that I have read that are to the caliper of Bryan Grosnick's in 2015. As you read his embracing article, you create a bit of sympathy for OPS in a world that can be overanalyzed and overwhelmingly complex. Just imagine, before the likes of __Money Ball__, the abundance of statistical performances and capabilities in baseball were typically limited to a select few within the organization with limited computing powers. OPS was an attempt to become more statistically "cool" and communicate to the gut-managing baseball bureaucrats a simple measurement that they could understand. There is nothing easier and more convincing than a simple calculation that gets pretty close to the applicator's opinion.

There's one big thing wrong here first: OBP uses plate appearances as a denominator in fraction form, yet SLG uses AB. What we have here are two mixed fractions, and if we learned anything in middle-school math class, it's that you can't really add two fractions with different denominators. If slugging percentage used PA instead of AB, this problem would be solved. But it doesn't. - Bryan Grosnick -Beyondtheboxscore.com

Within manufacturing, there are definitely times to have the macro views and the micro views within an organization. There are times when averages can work, and there are times when the __flaw of averages__ can destroy an organization. However, maybe sometimes these OPS-like views are all that we need to make a decision, quickly make a selection, or get us directionally correct to indicate the sway of a production unit’s performance. Within manufacturing, we have many performance indicators and measurement schemes for complex calculations that are marginally more accurate than simplistic calculations. However, they often tend to be difficult to calculate or understand, which leads to low popularity. Maybe OPS is right and I should have embraced RRR. Maybe we need more emotionally correct math.

If you like OPS, that's fine too. It's not one of those statistics that is downright misleading (I'm looking at you, wins) ... its kind of like using ERA as a judge of a pitcher's talent level or effectiveness rather than RA9. You'll lose something in the calculation -- something important, perhaps -- but you'll probably get it 75% right, at least. Bryan Grosnick -Beyondtheboxscore.com