# Baseball’s balance in math

Joe Posnanski | Jun 6, 2017 |

Earlier today, I wrote a little piece about what I called the balance that baseball is finding with all the strikeouts and all the home runs. I will have an interesting follow (I think) tomorrow as Bill James weighs in.

But before doing that, I wanted to share a little cool math from Tom Tango.

In the piece, I point out that teams in 2017 are essentially scoring the same number of runs as teams did in 1993 … but in VERY different ways. In 1993, hitters did EVERYTHING better except hit home runs. They hit for a significantly higher average, walked more, stole more bases, struck out a ton less often and averaged 4.6 runs per game.

In 2017, with a bunch more home runs, teams are also averaging 4.6 runs per game.

Well, Tango can show us how it works in math. If you like math, I think you’ll get a kick out of this. If you don’t — yeah, you can pretty much stop here.

In 1993, hitters had .80 more singles per game. They had a few more triples, a couple less doubles, so essentially the difference comes down to .80 more singles per game.

Using linear weights, which gives a value to everything, a single is worth .46 runs.

So you simple multiply .80 x .45 and you get: 0.37 runs. THat’s how many runs per game hitters today have to make up because of their lack of singles. Remember that number.

Well, hitters today are hitting .34 more home runs per game, which is a lot. A home run’s linear weight is worth 1.40 runs so .34 * 1.40 = .48 runs. So that’s quite a bit more than the singles value.

So why aren’t teams scoring MORE runs than in 1993? Ah, that’s the cool part of this — because if one group of hitters is hitting .80 more hits per game and the other is hitting .34 more homers per game, well, that means the difference (.46) are outs. And outs are bad. People tend to forget that part.

An out is worth negative-.27 runs.

So, you have to take away .12 runs away from the 2017 hitters because of those outs (.27 * .46 = .12).

And now, like magic: .48 runs (for the homers) - .12 runs (for the outs) = .36 runs.

Now look back up at 1993 — right, those singles were worth .37 runs. It’s almost exactly the same.

That’s how it evens out. Kind of cool, right?

Linear weights is fun to use. People have very strong feelings about them, good and bad, but they give you a good feel for the game. For example: Is it worth more to go two for six with two home runs or four for four with all singles?

You probably have an immediate answer that came to your head. Let's do the math:

— 4 singles is worth (4 * .45) = 1.8 runs.

— 2 homers is worth 2.80 runs. Then you have to subtract the four outs (4 * -.27). So that means you have to subtract 1.08 runs.

That makes the two-homer day worth 1.72 runs or SLIGHTLY LESS than the four singles day.

You might disagree with that (and it’s so close that it’s almost no difference at all; plus it’s hard to entirely separate individual play from team play). But the thing linear weights does really well is give you a good feel for just how much an out costs a team. It’s so easy to forget: Not making outs is still the most important thing a hitter can do.

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