Hulks vs. Walkers: Stupid Fun With Stupid Math

[RonCo]

We’ve recently had some good fun talking about the value of homers and doubles and all that—especially on Slack, which I’m almost sorry to say is pretty clearly now taking up a big chunk of stuff that used to go to the forum. Sigh. That’s life, though. Technology moves on.

Anyway, these kinds of conversations are always great fun. Do you want a team of Hulks like HGH, or Walkers like Dusty Rhodes? (Yeah, I know Rhodes isn’t a walker, just go with me, right? I said this was stupid fun). The arguments are far and wide, and in the end everyone gets to play their own danged game, right?

Anyway…

Part of the conversation got me to thinking along these lines:

1) How many runs would I score if I had a team of Hulks who hit nothing but homers—but who homered a whole lot?
2) Likewise, how many runs would I score if I had a team who did nothing but walk, but walked at such a rate as to get on base a lot?

Of course, these kinds of questions are like catnip to me. So you know what I did, right? I went into my script library and took a minute to adjust a few things, arriving at a script that simulated innings and counted plate appearances based on results. I then assigned homer and walk rates to my teams, choosing .050 HR/PA for my Hulks (the league rate is .038, so these guys thump them pretty good), and .350 OBP for my Walkers (the league OBP is .346, so these guys get on base just a little over average).

I used 1,458 innings to represent a season (9 * 162).

I then got to it, counting the number of innings with X plate appearance in both cases, and converted them each to runs. By this I mean that for my homer hitting team, every 4-plate appearance inning represented one run scored. Every 5-plate appearance inning represented 2 runs scored. Similarly, the walking team needed seven plate appearances to score a run, eight represented two runs, and so on.

I did three passes, then averaged them all

The results were interesting.

Who do you think scored more?

The answer was resounding: the Walkers scored just over 300 runs a season, the Hulks only 223. In other words a Walker who did nothing but walk at barely above the OBP threshold contributed considerably more to the offense than a Hulk who did nothing but thump at a considerably high rate. Here are the numbers:

Yes, this is a contrived experiment. Nobody plays in teams like this. But it’s an interesting contrived experiment. Note, for example, that the OBP team will bat around 35 times in a season, or about once every four to five games. Note also that that the walkers inflict about 50% more total plate appearances on opposing pitchers (a little over 2100 per season on average). That’s gotta be worth something in a real life situation, too, right?

Right?

Or not, I suppose.

I mean, this is just stupid fun with stupid numbers.

[CTBrewCrew]

How many of those HRs were solo shots?

[jleddy]

How many of those HRs were solo shots?

[jleddy]

I would have guessed HR would have out-paced walks.

Just thinking aloud here and poking some holes...if I'm wrong, don't hesitate to call me out.

THE ENVIROMENT

• Given that it's a simulation, what is the environment* for the Walkers? Are their outs like essentially strikeouts where there's no advancement of runners ever? Or can an out (ie ground out) move a Walker over a base? Can an out (ie fielder's choice or sacrifice fly) score a Walker from third? I'm just going to assume (in below) that an out is a dead ball so there are no additional variables. If that's not the case, it ups my perception of running scoring ability of the Walkers but still not enough to catch the Hulks as you'll see.

THE MATH

• A HR guarantees a run scored every time that event occurs. Even with the frequency being one run every 0.05 plate appearances, it's still a guaranteed run at some point. A team of just Walkers would have to have four events (ie walks) take place BEFORE committing three outs to score a run. If the league average OBP is .346 -- more on that below -- and you can only move one base at a time*, that means mathematically the Walkers would average just over two baserunners (just over three, if the leadoff batter is walked) per inning before a third out is committed. Yes, a simulation causes variances from probability/straight math, but I don't think it would vary that much.

THE FACTORS

• Wouldn't designating the Hulks home run rate by plate appearances be incorrect? Since they either hit a home run or commit an out, there are no sacrifices, walks, hit by pitches, errors, etc., therefore their plate appearances would equal their at-bats, so shouldn't their rate be based on the league's HR/AB, not HR/PA?

• OBP comprises of hits, hit-by-pitches and walks, so the league average OBP is way higher than walk percentage. The Walkers rate should only be the league-average walk rate, not league average walk+hit+hit-by-pitch rate.

Again, if I'm thinking about this wrong, let me know!

[RonCo]

In this simulation no runner moves unless forced. So, yes, a Walking team cannot score a run unless it sends seven hitters to the plate. For example, in Sim 1 of the Walkers, the Runs Scored = 89 + 2*33 + 3*20 + ...

The interesting thing here is how often teams in which every hitter merely gets on base at a .350 clip will bat around in a season. If you bat around, you score at least three runs in that inning--more if they aren't all walks.

I think that's the power of this little thought experiment.

And, yes, part of the issue for Hulks is that they do nothing but homer. The ultimate "what is Emilio Morales NEVER doubled or anything else" scenario. In this way, they NEVER interact with their teammates, whereas the Walkers cannot create runs at all without that interaction. Three guys walking (getting on base) in an inning scores zero runs.


Regarding the PA/AB thing...let me use another rock for that one, as it's ... interesting.

[RonCo]

THE FACTORS

• Wouldn't designating the Hulks home run rate by plate appearances be incorrect? Since they either hit a home run or commit an out, there are no sacrifices, walks, hit by pitches, errors, etc., therefore their plate appearances would equal their at-bats, so shouldn't their rate be based on the league's HR/AB, not HR/PA?

• OBP comprises of hits, hit-by-pitches and walks, so the league average OBP is way higher than walk percentage. The Walkers rate should only be the league-average walk rate, not league average walk+hit+hit-by-pitch rate.

Again, if I'm thinking about this wrong, let me know!

First, yes, I've built the scenario to be Power (HR) vs. OBP (the watered down OBP to be the weakest possible OBP cause). Ultimately I've taken away singles, doubles, triples, and walks from the Hulks and changed all hits to walks for the Walkers. It's stupid math, but fun math.

But let's talk about HR/PA vs. HR/AB. At the end of the day, if you remove everything from consideration but HR and outs (like this simulation does), then HR/PA = HR/AB. I can then fairly use the league's HR/AB rate. This is also valuable in a few other OOTP ways. I note, for example, that the game's "Historical" figures includes these items:

- BB/PA
- K/AB
- HR/AB

The game does not give you K/PA, nor does it give you HR/PA. There are, IMHO, reasons for this. If you play with the game's ratings editor, you'll also see that the game adjusts projected BB, and projected K and HR totals for different ratings in different ways. If you think about this a little, I think you can make some guess as to why it does it that way.

[RonCo]

Another relevant aside: the conversation point of "would you rather have a homer or a double?" in any particular situation is that of course you'd rather have a home run. But when you are building baseball teams, you know your players can only create home runs at whatever rate the player hits them. So you have to look at overall skillsets and weight relative values--prior to when you need them.

Doubles (and singles, and walks, and whatnot) allow your teammates (both upstream and down) to interact with your events to create runs with you. Home runs--while deeply valuable, allow only guys ahead of you to interact with you.

For example, one can say that a single that you hit right before a guy hits a double to drive you in is (in that very specific instance) worth the exact same weigh as if you hit a home run. Both events score exactly one run. If, in this simulation, you could replace EVERY OBP event with a home run, then, yes, you'd score a bunch more runs. But no hitter ever created by the powers that be has ever been able to hit home runs at that kid of rate. So therein begins the seeds of trade offs.

[RonCo]

I mean, if the question is "would you rather have a guy who hits home runs at a .350/PA clip, or a guy who gets on base at a .350/PA clip?" you go HR all the time, eh? But that's also just having silly fun with stupid math, because that's not a relevant question.

[jleddy]

If, in this simulation, you could replace EVERY OBP event with a home run, then, yes, you'd score a bunch more runs. But no hitter ever created by the powers that be has ever been able to hit home runs at that kid of rate.

I beg to differ. (Do kids even read Matt Christopher books any more?)

[Fat Nige]

Nice to see stuff like this back on the forums, this is where it belongs, Slack isn't permanent enough. I don't always understand this stuff (being a baseball deficient Brit) but I do like to read it, just in case something sticks lol