On Twitter, pals and co-authors Tom Tango and Mitchel Lichtman had a fun little argument about two interesting baseball statistics, OPS (On Base Plus Slugging Percentage) and wOBA (Weighted On Base Average).

Tango made the solid argument that OPS is a mathematical crime -- you are adding together fractions that do not have the same denominator (which, you might remember from middle school math, you aren't supposed to do). OBP is built on plate appearances. Slugging is built on at-bats. The deeper you go into the math, the hairier it gets.

Lichtman, meanwhile, makes the compelling counterpoint that OPS makes up in ease what it lacks in mathematical integrity -- it's super easy to add up on-base percentage and slugging percentage.

And Tango respond by pointing out that, sure, it's easy to add up OBP and SLG but that's only because someone ALREADY FIGURED THOSE OUT.

As for wOBA, which involves multiplying each baseball event by its weighted value, both agree that it is a more perfect statistic with numerous mathematical and analytical advantages over OPS. But Lichtman points out that it is impossible to figure in your head and all-but-impossible to figure at all unless you are one of those people who loves working spreadsheets.

Tango (who invented wOBA) comes back and says that wOBA is plenty easy to figure because it already has been figured FOR YOU on Fangraphs and other places.

I like this discussion a lot because I think it gets at something fascinating about baseball statistics, something that I don't think we talk about enough: Does it matter if statistics are simple?

***

One of the most touching things I ever heard about baseball involved my childhood baseball radio announcer, Cleveland's Herb Score. Herb was, if we're being picky and judgmental, not exactly Vin Scully behind the microphone. Storytelling wasn't really his thing. People in Cleveland would sometimes call him "Herb No Score," because he could go innings, hours, days, weeks, years without giving the score of the game.

We loved him just the same because he was sturdy, and he was there every night, and anyway I don't want to hang out with the person who dislikes the baseball announcer they grew up listening to.

In any case, Terry Pluto once asked Herb Score why he didn't explain the baseball strategies of the game. For instance, he would never say, "This is a bunt situation," or "You've gotta believe they'll bring in a pinch hitter here."

And Herb said: "That's not for me to do. That's for a father to explain to his son."

That one gets to me every time -- baseball is a game for a father to explain to his daughter, a mother to explain to her son, a grandparent to explain to a grandchild, I love that so much. It was my father who would explain such things to me when we listened and watched games, and I know that's a big reason why I feel such a soulful connection to baseball. It is a game that is meant to be passed down, to be shared, to be taught.

Meanwhile, Mom taught me how to figure batting average. She didn't know a thing about baseball then, but in 1976 she helped me collect the entire Topps baseball card set. One of the enduring memories of my entire childhood was the day she came home with a plastic baseball card pack, the see-through kind with three panels, remember those?

She handed me the pack and there, in the front, was the last card I needed, the Boog Powell card, one I had simply come to believe didn't exist.*

I so love that in the 1970s, Topps simply didn't care what the photo looked like. Could you have a worse photo than this one? I mean, he's looking away, he's looking awkward, and there's a shadow covering his whole face.

My mother is, as I have written before, a fairly obsessive person, a trait I inherited, and so in addition to helping me collect the whole set, she helped me keep a notebook listing every single card I got along with that player's team, position, and key statistic. For everyday players, that key statistic was obviously batting average. So from the backs of those cards, she naturally learned how to figure out batting average and, then, taught me.

Ah, batting average is such a simple formula, isn't it?

H / AB = Batting Average

I didn't know -- and didn't know for many years -- that the simplicity of the batting average formula is actually an illusion. The reason figuring batting average is so simple is because people went out of their way to make it so. It's like saying playing Words for Friends on your phone is simple -- sure it is but that's only because of about 12 trillion technological breakthroughs that you never have to think about.

In batting average, there is nothing necessarily simple about figuring out what a hit is, and it's even harder figuring out what an at-bat is. What do you do with walks? With errors? With sacrifice hits and flies?

Baseball people did that work for us so that batting average APPEARED like the simplest thing in the world. They pounded the concept of hits into us until that seemed like the most obvious thing around. They pounded the concept of at-bats into us so convincingly that later, when trying to figure out on-base percentage, we had to do mathematical loop-de-loops ...

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

... rather than the much simpler and more obvious:

TOB (Times on Base) / PA (Plate Appearances) - SH (Sacrifice Hits) = OBP

See, we didn't grow up with Times on Base or Plate Appearances as a concept. We grew up in a world of hits and at-bats, that was it. We didn't consider the complexities because we were shown no complexities.

And batting average was as simple as could be, simple enough that my mother -- who had come to America just two years before I was born and cared nothing about baseball -- sat down at our dining room table, figured out how to do it, and then showed me.

Was that apparent simplicity part of batting average's magic? There is no doubt about it.

Learning how to figure batting average, learning how to keep score, learning how to calculate ERA (a bit trickier with that multiplying runs by nine), learning what a pitcher needed to do to get a win, these were the secret knocks of baseball, the little bits of wisdom you picked up that made you a REAL baseball fan. And, as far as I could tell, such things were ONLY true of baseball. You could watch and love football without knowing about any statistics. You could watch and love basketball without caring a thing about anything other than maybe points. There was no division or multiplication involved.

But baseball, with just a little bit of math, you could make the game sing. A .400 batting average was like going two-for-five every day. Incredible! George Brett was incredible! Rod Carew was incredible! Tony Gwynn was incredible!

And, if you were lucky, someone you loved taught you how to do the math of batting averages -- and you would forever connect the two.

And this brings us to our moment. Batting average, well, we know what it is. It's a statistic you can't take too seriously. We know too much about baseball now to spend all that much time worrying about a statistic that treats singles, doubles, triples and home runs the same, that entirely ignores walks, that unpredictably and inconsistently separates hits and errors, etc.

And yet, at the same time, batting average can still fils the heart. Why? You see that Cody Bellinger is hitting .376 and ... wow. That number is so fulfilling, so powerful, so satisfying; with a hot streak he might get back up around .400, how incredible would that be?

It tells you so much more that his wOBA is an almost impossible-to-believe .481. It tells you so much more that his OPS is an almost-impossible-to-believe 1.195.

And yet, do those things clutch at the heart the way that .376 batting average does? I fear they do not. Because we -- and by "we" I mean those of us of a certain age -- did not grow up with wOBA and we did not grow up with OPS and we did not spend time with our mothers and fathers and aunts and uncles and grandfathers and grandmothers and neighbors learning how to calculate wOBA and OPS.

In this way, yes, I do think simplicity matters. I do think we, many of us, long for it, long for statistics that we can figure out with a pencil and a piece of scratch paper. I think we still long for the feeling that we KNOW baseball in a deeper way. We learned it when we were young.

In my opinion, this is the part of advanced baseball statistics that those of us who love too easily miss. It's easy enough to say -- and entirely accurate to say -- that wOBA gives you a deeper view of a players offensive contribution than just about anything else and don't worry about figuring it out because they've figured it out for us. I mean, it's not like people were out there figuring out batting averages. Those were being figured out for us too.

And that's true ... but deep down we always knew that we COULD figure out batting average if necessary. We could take out a calculator or piece of paper and get up to the minute batting averages during a game because we knew exactly how to do it.

The same is true of slugging percentage, by the way. That's just total bases divided by at-bats.

The same is SORT OF true of on-base percentage, if you just give us times on base and plate appearances (the sacrifice hits adjustment comes into play less and less because there are fewer and fewer sacrifice hits).

But wOBA? No. This is what the stat looks like via Fangraphs:

And, even if you CAN figure it out, well, it changes slightly year to year based on run environment.

This is not to downplay how great a statistic wOBA is -- it's absolutely a mathematical miracle when you dig deep into it. But you do have to dig deep into it to understand it. Same with bWAR and fWAR and FIP and Win Shares and Defensive Runs Saved and so many of the other great advanced statistics that have opened up entirely new ways of looking at baseball. We might understand what the final number means. We might know some, most or even all of what's in it. But we don't KNOW it, in and out, the way we do batting average or slugging percentage or on-base percentage.

And the more we shift toward these stats that none of us can figure out on a simple sheet of scratch paper, the more I fear that we move away from something that was always wonderful and powerful about baseball.

All of which leads to the final point: I think OPS really could be the stat of our time. It was a pretty hot stat there for a while and I feel it fading away now with the addition of so many more extensive and thorough stats. I see people making fun of it a lot, and I know exactly what they're saying.

But I find myself agreeing with Mitchel about OPS. Oh, Tango is right: It's a logical mess. And it's not exactly a simple statistic to figure out from scratch. You would need to figure out OBP and then figure out SLG and then add them together.

But it has something that batting average had: It has the APPEARANCE of simplicity. Because on-base percentage and slugging percentage are so readily available (the way hits and at-bats were so readily available), all you have to do is add them up. And while it isn't perfect or anything close to perfect, OPS is a pretty good statistic for determining a player's quality.

You can look at it more or less like this:

1.000 and above: Awesome
.900 to 1.000: Great
.800 to .900: Good
.700-.800: Average to Above Average
.600-.700 Below average
.0 to .600: Not good

This isn't precise, but it's a good starting point. And it's easy enough to pass down to the next generation, whether it's your own kid or one you happen to be sitting next to at the ballpark.

And finally, let's just look at 10 random players and their OPS:

-- Arizona's Eduardo Escobar: .343 OBP, .567 SLG
You can add that up pretty quickly, it's a .910 OPS, Eduardo is having a great year.

-- Cincinnati's Joey Votto: .342 OBP, .369 SLG
That's a .711 OPS which is down in that barely average category, not a good season at all for Votto so far though it should be said that all his career he's been a second-half player. His three highest career OPS months are July, August and September -- he has a 1.003 OPS in August.

-- Milwaukee's Christian Yelich: .425 OBP, .719 SLG
Whew, that's a 1.144 OPS. Legendary stuff. If he could keep this up all year, he would have the highest OPS in Milwaukee Brewers history by more than 100 points. Only three Brewers have had a 1.000 OPS over a full season, and he's one of them last year (exactly 1.000). The other two are Paul Molitor and Prince Fielder.

-- Washington's Anthony Rendon: .436 OBP, .650 SLG
That's a 1.086 OPS, another insane season for an amazing player that hardly anybody outside of Washington ever thinks about.

-- Atlanta's Josh Donaldson: .369 OBP, .432 SLG
An .801 OPS puts him right on the line between above average and good; Donaldson's power numbers are down from his heyday. From 2015-2017, he slugged .559 with 111 home runs. He still gets on base, but those home runs are harder to come by.

-- Philadelphia's Rhys Hoskins: .402 OBP, .538 SLG
For my newest, dearest friend and Phillies' fan Ellen Adair, that's a .940 OPS, a terrific start for a thoroughly likable player coming into his own.

-- Seattle's Daniel Vogelbach: .371 OBP, .550 SLG
I know that everybody loves Texas' Joey Gallo -- and for good reason -- but I find myself partial to Vogelbach, listed at 6-foot even, 250 pounds, swinging for the fences, a .921 OPS.

-- Oakland's Matt Chapman: .355 OBP, .558 SLG
He was third in WAR last year, sixth in WAR this year, and people still don't know enough about him. He's a defensive dynamo with a .913 OPS.

-- Cleveland's Jose Ramirez: .308 OBP, .313 SLG
Whew, it's good. Over the last two seasons, Ramirez had a .948 OPS and was one of the best players in baseball. Nothing is working for him -- he's just not hitting the ball with any authority at all. That .621 OPS is disastrous.

-- Boston's Mookie Betts: .387 OBP, .458 SLG
Betts' .844 OPS is certainly good ... but it's more than 200 points down from last year's astonishing 1.078. Last year, the Red Sox -- for the third time in their history, had two players with 1.000 OPS over a full season:

1939 Red Sox: Jimmie Foxx and Ted Williams
2006 Red Sox: David Ortiz and Manny Ramirez
2018 Red Sox: Mookie Betts and J.D. Martinez

-- New York's Gary Sanchez: .341 OBP, .653 SLG
That's a .994 OPS for Sanchez -- he will try to become the sixth catcher in modern baseball history to have a 1.000 OPS. Mike Piazza did it three times. The others are Joe Mauer, Roy Campanella, Bill Dickey, Gabby Hartnett and, the one that will stump the trivia nuts, Chris Hoiles in 1993.