MLB Senior Data Architect Tom Tango posed an interesting question on Twitter today:

Which is the more productive hitter A.

.315 batting average

.365 OBP

.510 SLG B.

.260 batting average

.365 OBP

.510 SLG — Tangotiger (@tangotiger) August 14, 2019

The best questions are usually simple, and this one is perfect. What does average matter? What does slugging percentage mean in the context of two different batting averages? If your OBP and slugging are the same, does it even matter how you get to them?

The first-level answer is “give me the average.” If I’m going to get the same OBP and slug, I’ll do it with extra hits, because hits advance more runners. As you can see, that was the most common answer on the poll.

Go a level up, and you might end up where I was at first. With a lower batting average but the same slugging percentage, Player B is hitting for a ton of power. An easy way to think about the trade-off is that Player B is getting the same number of bases per at-bat (slugging percentage) and reaching base as often (on-base percentage), which means there’s an exchange where Player B adds a base to a hit (stretching a single into a double or a double into a triple) and converts a single to a walk.

Since the increase in wOBA value from adding a base to a hit is higher in every instance than the loss from changing a single to a walk, option B looks like it should be better. But wait! Slugging percentage and on-base percentage don’t look at the same population of plate appearances. Slugging percentage only cares about at-bats, while OBP cares about all plate appearances.

Player A slugs a ton (the league average slugging percentage is .436), and does so on more plate appearances than Player B. Put another way, both players are above average at getting on base over the exact same number of plate appearances. Both players also generate an above-average number of bases per at-bat — but Player A gets to do so over more at-bats. It’s not a clean tradeoff, not exactly exchanging a hit for a walk and an extra base, because the two ratios have different denominators.

In fact, the question was carefully calibrated — take a look at these two players with 1000 PA each:

Player Comparison Metric Player A Player B PA 1000 1000 Outs 635 635 Singles 186 95 Doubles 63 77 Triples 11 15 HR 32 36 Walks 73 142 BA 0.315 0.260 OBP 0.365 0.365 Slug 0.510 0.510 wOBA 0.367 0.367

The lines are so close that which player has more value changes based on whether you use 2019 weights or pre-rabbit-ball weights for wOBA.

The general concept holds true for other weights as well. Take a look at two worse hitters with the same trade-off:

Player Comparison (but worse) Metric Player A Player B PA 1000 1000 Outs 680 680 Singles 171 117 Doubles 35 40 Triples 8 10 HR 33 38 Walks 73 115 BA 0.266 0.232 OBP 0.320 0.320 Slug 0.428 0.428 wOBA 0.318 0.318

If you want to know how good a hitter is, wOBA is great, and wRC+ is even better if you want to adjust for park and league. If you can’t have wOBA, though, you don’t even need batting average — two hitters with identical OBP and SLG are probably going to be very similar, regardless of whether they get there mostly with walks and extra bases, or mostly with singles. That’s a neat little fact.