Tom Tango’s Triple-Slash Conundrum
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 SLGB.
.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:
| 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:
| 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.
Ben is a writer at FanGraphs. He can be found on Bluesky @benclemens.
This is an interesting thought experiment; it’s really hard to choose one just based on what’s given.
Without any further information, I’d likely take player B, as they’re more likely to drive themselves in or be in scoring position.
However, if player A has teammates who also get on base with frequency, the greater quantity of hits might lead to more runs driven in as well as frequently being in scoring position.
EDIT: I scrolled to comment before reading the meat of your article and realized belatedly that you made basically the same arguments, albeit without the teammate angle.
The value to the team does hinge on the rest of the team.
Oftentimes it’s not justhow good tbe best player is but how well the mix of skills balance out. A team with a lot of power but lousy defense or low OBP won’t get the full benefit of the bat. The total lineup matters.
Also defense, not addressed by the thought experiment.
What the bat gives, the glove throws away.
We’re seeing this in the depreciation of bat-only 1B/DH types.
Right, a real life choice between those two players would depend on the rest of the lineup and where the manager was going to choose to hit the chosen player. wOBA deliberately strips all context from every plate appearance, which is helpful in some ways, but is not necessarily ideal for lineup construction. As mentioned elsewhere, you’d also want to think about BABIP, HR/FB and other things that can indicate luck on batted balls. You could explore this question so many ways!
That’s why WAR is so prevalent. It tries to roll in more factors than the traditional rate stats.
A WAR-based thought experiment might be interesting. Two equal but drastically divergent 5 WAR types.
Given that these hitters will face the gamut of defenses from world-beating to atrocious over the course of the season, I didn’t feel that would be worth considering (for the purposes of this thought experiment), especially since the parameters of the question don’t include how well their teams do – just the value of the hitters themselves.
However, a team’s lineup remains fairly constant given good health, so felt that was worth considering.
What would player B’s wOBA look like if he had equal number of doubles and HRs and only a handful of triples (which is what I think of when seeing his BA, OB, and SLG) instead of twice as many doubles as HRs and a bunch of triples?
It’s kind of neat that it doesn’t actually matter that much. Pardon the sloppiness, but doing this on my phone while I wander around:
Metric Player A Player B
PA 1000 1000
Outs 635 635
Singles 201 115
Doubles 41 50
Triples 10 9
HR 40 49
Walks 73 142
BA 0.315 0.260
OBP 0.510 0.510
Slug 0.365 0.365
wOBA 0.3676 0.3673
Thanks – that’s interesting! I’m guessing that, if you kept player A’s numbers as originally stated and changed player B’s numbers to these, and placed them both in the same slot in the same lineup, player A would score more runs and player B would hit more RBIs.
Fangraphs… where authors love the content so much they respond to questions publicly while on their phone.
This reminds me of Craig Edwards’ suggestion to aspiring baseball writers(this was in his most recent chat). Basically, if you have a question about baseball that intrigues you, investigate it. Don’t do things that you think other people find intriguing, because your best work stems from things that you like. Ben found a tweet that piqued his interest and he investigated it. It’s not of huge import, but it challenged the status quo(most people preferred player A). It was entertaining and allowed me to fulfill my quest to learn something new today.
I think I’d still want the guy who has the higher batting average, simply because he’s more likely to knock in other runners or to take extra bases on errors. That might not amount to a lot over the course of the season but I bet it’d be something.
It’d be interesting to look at the question from the standpoint of WPA or RE24, rather than the all-in-one wOBA/wRC+ type numbers.
Are the extra bases that runners take on errors something that is factored into wOBA?
They are not, and that’s a good point. About 1% of batted balls turn into errors (something I learned in the process of researching something else yesterday), though, so the 70 extra balls in play player a gets are worth around one extra error. Probably not a huge game changer, but extra value nonetheless.
And, of course, some players (Derek Jeter) are better at forcing errors than others.
B-Ref has, annoyingly, removed RoE from its stats (and FG has never included them, to Tango’s chagrin as his version of wOBA includes them) – I don’t subscribe to Play Index, so I’ve no way of accessing the career RoE leaders to find out if RoE/PA correlates to BABIP (Player A’s would almost certainly be higher, considering the lower power numbers and higher average).
I’d also like to dick around with SPSS to figure out if any stat correlates to outperforming your wRAA in RE24, but that’s another question entirely.
also more likely to hit into double plays
Even GDP’s can drive in runs. All of this could be debated to death.
I can’t think of a situation where it would be better to GIDP (or FIDP I guess) and score a run than most any other outcome of the batted ball. Maybe some whacky play where the defense was attempting a triple play, but only got 2, and the play somehow didn’t involve the runner coming home and that was the walk-off winning run?
Your argument that the wOBA and wRC+ are pretty much the same for both hitters is interesting, but aren’t those stats context neutral? With men on base (which is dependent on team mates but will happen reasonably often even with the worst team) a single is better than a walk since it is pretty rare for a runner to go from first to third or score from second on a walk. I don’t think that will be captured by wOBA or wRC+.
Either way, it isn’t a big difference.
Context neutral can be a little deceiving. It means that the value of each event is averaged across its value in each base/out state, weighted by how often that base/out state occurs. That’s why a single has a higher wOBA value than a walk- there are plenty of times where a walk and a single are the same, plenty of times where a single is much more valuable than a walk, and you basically just take a weighted average of those.
If your team gets into each base/out state at the same rate as the league as a whole (an average offense), wOBA will capture what you’re talking about, the fact that runners on base juice the value of the singles some. That said, BaseRuns and RE24 are even better for that, since they adjust for the outcome distribution specific to your team, just a pain to calculate and less useful in a vacuum (since you need so much specific detail about the situation in question).
Thanks for clearing that up for me. Appreciated.
Player B will have more doubles, triples, and homers though. And just like there are plenty of cases where a single is much better than a walk, there are also cases where an extra base hit is much better than a single. If that key tying or winning run is at first rather than second, then suddenly you need at least a double to score him, and player B is probably your better bet.
This same question was discussed on the baseball fever forum about two weeks ago:
A: .250/.297/.350
B: .211/.297/.350
A
40 BB x .681 = 27.2
120 1B x .908 = 109.0
15 2B x 1.346 = 20.2
15 HR x 2.337 = 35.1
191.5 (wOBA .299)
B
70 BB x .681 = 47.7
80 1B x .908 = 72.6
20 2B x 1.346 = 26.9
20 HR x 2.337 = 46.7
193.9 (wOBA .303)
I actually carried out my calculations using the linear weights from three years: 1930 (the highest offensive era since the beginning of the 20th century); 1968 (the lowest offensive era); and 2019 (which is high, but not as high as 1930). These three seasons should cover any effect due to changes in LW.
In all three cases, there was a slight edge to player A, with the higher BA:
1930 254.4 vs. 249.596 RAA
1968 261.266 vs. 255.121 RAA
2019 242.918 vs. 237.998 RAA
This generally seems to be the case. In Tango’s example, while the two players have essentially identical wOBAs, even then there is a very slight edge for A (not seen due to rounding):
1930 384.362 vs. 383.652
1968 398.205 vs. 397.21
2019 367.525 vs. 366.892
Maybe the triples matter? I didn’t use them in my example. There is less increased value in going from a double to a triple than from a single to double, or double to HR. Player A has fewer of every kind of XBH,but having fewer 3B may lower his total RAA relative to B, as opposed to the case where neither player has them.
OK, I changed player B so he had more triples: 59 2B, 51 3B, 18 HR. Singles and BB and all the rate stats remained the same. As a result, his total RAA is now lower than it was before, significantly below player A. For 1930, it’s 382.158, for 1968, it’s 394.008.
I think player A’s having some 3B, even if less than B, hurts hims worse than the case where neither player has them.
This may give new meaning to the title, “Triple Slash Conundrum”.
I suppose this could go down an endless rabbit hole. What are their babips? If they seem to have been a bit lucky on balls in play then you favor the guy with more walks…etc…What would they each cost in arbitration? Just kidding. Fun experiment.
Easily the best new wave FanGraphs writer
How about a lineup of 9 Player A’s and 9 Player B’s? or a mix of the two?
Here’s two questions:
1. What player in MLB history closest resembles player A?
2. What player in MLB history closest resembles player B?
From a very messy RMS of the rates of all hitters with at least 5000 PA, I got:
1. Player A = Joe Medwick (.324/.362/.505); Honorable mentions Magglio Ordonez, Jim Bottomley, Nomar Garciaparra
2. Player B = Darryl Strawberry (.259/.357/.505); Honorable mentions Mark Teixeira, Harmon Killebrew, Jose Canseco
Very neat sets of names.
Thanks! I’ll take Player B, thank you very much.
Running the numbers out with 1000 PA gave me a headache.
I think Player A is definitely the more valuable player because–and this is based purely on feel and a lifetime of observation, I have no numbers to back this up–I believe average-heavy OBP scales much better against pitcher talent level than walk-heavy OBP does.
Interesting hypothesis on that part, and if it were same OBP, same ISO I think everyone would agree, on base via hits is better than on base via walks.
But it’s also an average-heavy SLG, more singles and fewer XBH, you have to account for.
I guess what I’m saying is that my hypothesis is Player B tends to overperform against bad pitchers, because he’s patient enough to wait for a really juicy pitch or for the pitcher to walk him, but will underperform against good pitchers because those juicy pitches and walks might never come. Conversely, Player A would underperform against bad pitchers because they aren’t always patient enough to wait for the pitcher to mess up, but would overperform against good pitchers since he has the contact skills to hit his way on base, even on hard pitches to hit.
Come playoff time, when there aren’t really any 4th and 5th starters for Player B to tee off on, I would trust Player A far more to perform, thus making him more valuable.
Again, just a hypothesis based on seeing way too many low-average/high-walk-and-power guys suddenly become completely useless against pitchers who can actually hit their spots. I’d be interested to see someone do an analysis on it.
This reminds me of something that I saw on the Sons of Sam Horn forums way back during the 2004 or 2007 WS. One of the members had invented a stat he called “slope,” which was basically a measure of whether a hitter got his numbers by feasting on poor pitching or performing consistently. I’ve always wanted to see that expanded on – is it predictive at all, do certain profiles do better, that sort of thing.
I would think that player A would lead to a more balanced distribution of runs across games than Player B as Player A has more (by number) positive run scoring events.
Of course the next question, is a balanced distribution of runs a good thing?
If AVG and SLG were calculated per PA rather than AB, would Player A be better (not saying that he does the same thing but you just calculate the stats differently, but rather that he gets a hit in 31% of PAs and gets 51 bases per 100 PAs) ?
It’s fascinating to me, reading the comments, that the answer can depend on the interpretation of “is the more productive”.
Ben makes the point that these sets of stats are essentially equivalent – meaning that the batters have been equally productive.
Some commenters, however, are interpreting this as which batter is better – meaning that they are looking at future performance. Who will hit into more double plays? Who will induce more errors? Who will produce better against better pitching? Who has more sustainable stats?
These are two very different analyses but both are great points.
Who had more RBI’s?
More RBI’s? Who let Joe Morgan in here?
Anecdotally, Player B will be able to take good swings against high-velocity pitching better than Player A will due to a likely higher bat-speed. Player A slapping a 95 mph fastball on the outer half at one of the middle infielders is as useful as Player B striking out.
Player A has a .195 ISO – until this year’s bullshit ball, that was a solid 55 power, to go with 75 hitting.
He almost certainly has more than enough “bat speed” to send an outside 95 mph fastball into the gap in left field.
It’s “Would you rather” between Max Muncy and Justin Turner – or Starling Marte and Joc Pederson – from a hitting perspective.
I think the fundamental answer must be decided by moving beyond linear models. wOBA and its ingredients are fundamentally linear models: if you add two runs worth of hit-bases, you’ll get 2 “actual” runs of results. That’s the fundamental model for nearly all baseball stats.
But of course “actual” run production is *not* linear, which is easily observed, for example, in the correlation between overall team-season offense by some linear metric (for example, wRC+) and team-season PAs. Better offensive lineups will make fewer outs, which means they will in turn get *more* PAs over which to accrue the benefit of the better hitting. If you compare two lineups, say one with an overall wRC+ of 100 and one with 110, we’d expect the better lineup to score *more than 10% extra runs* because in addition to the 10% extra runs there’s some percentage more PAs as well, so you get super-linear run production as a function of wRC+ improvement.
Such can also be examined even on a more granular level. If you imagine three lineups with a .250 OBP, a .300 OBP, and a .350 OBP (call em A B and C), we note that the gap between them is an equal .050; on the other hand, if you compare runs scored by such lineups *even over the same quantity of PAs*, you’ll find that B’s runs minus A’s runs is *less* than C’s runs minus B’s runs. In other words, improving OBP by .050 has *different impacts on actual run production depending on where your OBP started*. This exactly means that run production is a *non*-linear function of OBP (or of any other linear metric you want). Put another way, *context matters* when converting linear PA outcomes to actual run production (which is exactly why we frown on RBIs as a measure of individual batter skill).
The catch of course is that, on a large scale, the league is very homogeneous — very little stuff, only very small sample sizes, ever deviate by more than a few percentage points from the mean, so on the whole, the linear-model metrics are still extremely powerful and capture almost everything measurable about individual, context-free baseball performance. But if we expand the view from trying to argue about “which player is better, outside of context” to “which player, in the context of an actual lineup, will lead to greater overall run production”, I believe I would take the guy with the higher average for the exponential effects. It would only be a few percentage points difference in run production — possibly not noticeable in less-than-a-season sample size — but more of a difference than their wOBAs, for example.
It’s also going to depend on the run environment and more specifically the batted ball event environment. In a low-scoring environment heavy with singles and walks, hitter B will do relatively better by bringing some “lumpy” production instead of needing to string together enough single-base events. But as discussed above, if runners are often on base, A will advance them by some baserunning above his own TB.
I think it would be relatively easy to find an answer by using Monte Carlo Simulation, but it likely depends on the hitter’s teammates and their respective OPS(s, es?).
I do think that this exercise illustrates precisely why team OPS is still a better predictor of team offensive production than any of the more advanced metrics.