Judgmental Stats: Batting Average

This might sound familiar to you: I learned math by learning how to figure out batting average. I don't know how old I was when I first grasped that classic formula:

Hits / AB = Batting Average.

Maybe I was 10? I never had any ability to grasp geometry when I was young -- a flaw I seem to have passed along to my daughters -- but algebra generally made sense to me because of the many hours I spent pouring over batting average. I didn't just figure out that formula; I turned it inside out. Let's say I only had batting average and at-bats. How would I know how many hits? I played around with it and came up to with an answer:

Batting Average * AB = Hits

OK, but what I I knew how many hits a hitter had and his batting average. How would I figure out how many at-bats? Trickier, but I figured that one out too.

Hits / batting average = AB.

So, for Rod Carew's classic 1977 season -- I was 10 years old.

239 hits / 616 at-bats = .388 average

.388 average * 616 at-bats = 239 hits

239 hits / .388 average = 616 at-bats

Once I figured those three things out, well, it was a blast. We all know the various analytical flaws of batting average -- it doesn't take walks or hit-by pitches into account and it doesn't describe the TYPES of hits, meaning homers and singles count the same -- but it's pretty good at what it does. And the formula seems simple. Anyway, it did for me when I was 10 years old.

Truth is, of course, the formula isn't simple at all. We were tricked into thinking that because we were given "at-bats" and "hits." Nobody told us then that the things that make up an "at-bat" AND the things that make up a "hit" are, once again, influenced by the sorts of morality judgments that this series is about.

And in our increasing effort to create actual counting stats, I give you what I would call the TRUE batting average. There are three rules.

-- Rule No. 1: Sacrifice hits and sacrifice flies count as outs. Right now, as you know, sacrifices are considered non-at bats. This is as judgmental as it gets -- and it's ludicrous on two very different levels. On the first level, it's ludicrous because other plays that accomplish PRECISELY the same thing do not get the same consideration. A ground ball that moves a runner from first to second is an out; a bunt that moves a runner from first to second is a sacrifice. Silly. A fly ball that scores a runner from third is a sacrifice. A ground ball that scores a runner from third is an out. Sillier.

They're ALL outs. There is no difference at all except for "intent." As I've said before, if someone banks in a long jumper, they still get the points.

Which leads to my second point: The very word we use for these kinds of plays is SACRIFICE. The player at bat is supposed to be sacrificing himself for the sake of the team. Good for him. That's the sort of teamwork we want around here!

And yet ... we don't want it to hurt his batting average. That's insane. If it doesn't hurt his batting average, what is he sacrificing? Why is everyone high-fiving him and treating him like he's a war-hero? You want to sacrifice to help the team? Fine. Knock a point or two off your batting average. That's a sacrifice.

In the end, we consider one simple question: Does a sacrifice make an out? Yes. Then it counts as an out.

-- Rule No. 2: When you reach on an error, it counts as a hit. You probably know that the error is the very essence of the judgmental baseball stat -- "I think that guy should have MADE that play so I'm not giving the hitter any credit at all!" -- and it's wildly inconsistent. An error in Cleveland might not be an error in Atlanta. An error on a Tuesday in San Diego might be a high that next Thursday.

But there's an even more basic reason why we're counting it as a hit, one so basic that I will put it in capital letters:

YOU CANNOT CHARGE A HITTER WITH AN OUT WHEN HE DID NOT MAKE AN OUT.

That seems pretty fundamental, no? There are times when a hockey player gets a cheap goal that he probably didn't deserve. To be honest, it probably happens 10 times a week to every team. Sometimes a receiver or shooting guard gets open because the other team had a busted defense and forgot to cover him. Sometimes a golfer hits a tree and the ball bounces onto the green, perhaps even into the cup. You could argue they don't DESERVE the outcome.

Deserve, Clint Eastwood said, has got nothing to do with it.

So an ROE (Reached on Error) is a hit in true batting average. Now, this rarely makes a HUGE different, but as you will see, when you put it over an entire career, it can make a marked difference.

-- Rule No. 3: Hitting into a double-play counts as ... one out, just like now. Ha, you thought I was going the other way with that, didn't you? It's tempting to count double plays as two outs since two outs were recorded. But that's exactly the sort of judgmental thing we're trying to eliminate here. It's only one at-bat ... you can't be charged with more than one out per one at-bat.

And that's it -- everything else is the same with regular batting average. Here then were your true average leaders for 2016:

1. D.J. LeMahieu .352 (BA .348)

2. Jose Altuve .345 (BA .338)

3. Daniel Murphy .343 (BA .347)

4. Jean Segura .333 (BA .319)

5. Mike Trout .330 (BA .315)

As you can see, there are definitely some adjustments here. Trout and Segura's averages skyrocketed because they both had double-digit ROEs in 2016, as fast players often will. The biggest difference between average and true average, by the way, involved Carlos Correa who reached on error an amazing 16 times in 2016, most in baseball. His batting average was .274. His true average was .300.true average was .300; his batting average .274.

Player hurt most by the True Average? Nobody was hurt too badly, but as you can see Daniel Murphy lost four points on his average -- he only reached on error once all year and he had eight sacrifice flies.

Over a whole career, the True Average can be quite striking. Roberto Clemente, because he reached on error 188 times in his whirlwind career, has his already striking batting average jump from .317 to .334. Ken Boyer, Willie McGee and, surprisingly, Harmon Killebrew all got big jumps as well.

This is a fair time to ask: Is getting on baseball by error a skill? Hard to say. You look at the four above, they're very different players. McGee could fly. Clemente ran hard. Boyer could run a bit as a younger player. Killer was famously slow. But Killer and Clemente hit the ball HARD. Other reached on error leaders include Pee Wee Reese (fast), Johnny Bench (slow but hit baseballs hard), Derek Jeter (fast), Pete Rose (not too fast but a hustler) and Henry Aaron (sort of fast, hit the ball hard).

In the end, I don't know if it's a skill or even a half-skill. And, for our purposes, it doesn't really matter. We are just counting. That's the whole point of this series -- to make judgmental stats into counting stats.

And how would the formula look? Well, right now it wouldn't look too simple:

(H + ROE) / (AB + SH + SF) = True Average.

But over time, I would hope it woudl be redued to this.

True Hits / True At-Bats = True Average.

It could be fun for a whole new generation.