# Magma diver!

January 15, 2009 20 Comments

Let’s talk about expansion.

First, an aside. As you may or may not have judged, I spend an awful lot of time thinking about things like replacement-level baselines. Sky from over at Beyond the Boxscore certainly contributed – he and I have been having an e-mail exchange on replacement level pitching that spilled over into this post. I’m still working on organizing my thoughts into a whole article – y’all should be seeing that in a few days – and in the interim I wanted a sanity check on the idea that pitching should come with a higher replacement-level baseline than hitting.

I find the best way to double-check a set of results is to look at the problem from a different light, and see if the results are still similar. When studying individual players, the best sanity check (I find) for a model is to see if the notion holds at the team level.

So there lay the rub – where was I going to find a set of replacement-level teams?

We can’t simply use a team’s win-loss record; the ’03 Tigers were one of the worst teams in baseball history, but they were highly compensated for their troubles, and so it’s hard to call them replacement level. We can’t really use team salary, either; there are teams like the A’s and Twins who thrive on low payroll, as well as teams like the Marlins who constantly restock with top prospects with fire sales.

Ideally we find a set of teams that is:

- Bad
- Cheap
- Prospect-free

And so where do we find these teams in the wild? Expansion teams. There have been four in the free agency era – the Rockies, Marlins, Rays and Diamondbacks. And in their debut seasons, they’re about as close to pure replacement-level teams as you’re likely to find.

These teams are strictly speaking not replacement level – they have a win percentage of .400, well above pretty much anyone’s replacement level. They were salted with some real talent by the MLB expansion draft. But they seem to represent the ideal we’re talking about – a useful proxy, if you will.

So, again, a little thumbnail sketch. I took their RS and RA out of the Baseball Databank, and then park-adjusted using the included park factors (which aren’t fantastic but are better than nothing; if it wasn’t for the Rockies being a quarter of our sample I might not have even bothered with park adjustments – again, thumbnail.)

On average, our expansion teams’ RA was -11; their RS was -132. Or put another way – these four teams were, on average, 16 wins below average. If you gave all of them an average defense/pitching, they win 2 more games. If you have them all average hitting, they win 14 more games.

The suggestion – a strong one, I might add – is that hitting is harder to replace than defense. We’ve done nothing here to try and separate pitching from fielding at this point, however.

Taking a quick look at BABIP – all except the Rockies seem to be very close to the league averages, within about .014. We know that Coors inflates BABIP as well, so we’re not terribly worried by the results there.

Again, I’m just spitballing here. If you think I’ve done something wrong here, please feel free to let me know.

That’s a huge discrepancy. Very interesting. We usually see HR increase from expansion don’t we? I guess thanks to expansion, EVERYONE is giving up the home runs, not just the expansions.

This may suggest that, obviously, replacement level is lowered by expansion. Because the teams are able to pick from MLB talent first, given the previous replacement level, their pitching level would not be as low as the new replacement level would suggest. What do you think? Maybe taking pitchers from other teams just has a larger effect on them, rather than a smaller effect on the expansion team? I’m just throwing things out there, too.

Yeah, the rep level shifts whenever you have an expansion.

Going by BABIP, it seems like our expansion teams are average on defense. That makes a good deal of sense to me – most studies have shown that rep-level players are close to average defensively. I think that limits the amount of damage that can be done by having poor pitchers.

I don’t know that we see HR increase after expansion; Tom Tango wrote an interesting article a while back where he concluded changes to the ball probably were to blame.

A possible alternate theory: the talent distribution for pitchers contains a very few elite pitchers, and a lot of interchangeable parts (more than MLB really needs). At that point, the expansion teams really just picked up a bunch of the extra flotsam, which in reality is what most teams are staffed with to begin with, so we wouldn’t see much difference. Hitters, on the other hand, might have a more gradual talent distribution, so that the guys who got snagged by the expansion teams were the bottom of the barrel.

I’m spitballing too. I suppose that can be checked by looking at the standard deviations (maybe some sort of SD/mean ratio) on some of the better pitching and hitting stats.

I’ve been wondering about that, PC. I think the answer is just to draw the same talent curve I did for hitters, using the CHONE projections. The trick is just to figure out what metric to use to get hitters and pitchers on the same scale so that the graphs line up.

Here’s a question, though – is SD the best tool to measure a distribution with a right tail but no left tail? I’m not exactly a pinball wizard here when it comes to that sort of thing.

Actually, there are measures of skew (how not-normal a curve is) out there. That would actually give you an idea of the shape of the curve…

The only one I’ve found so far is taking the difference of the mean and the mode. Would that work, or is there something else I should be looking at?

Nice NGE reference Colin – didn’t know you were a fan

Colin, I don’t think anyone’s saying that rep level is the same for hitters and pitchers. If anything it MIGHT be similar for starters and hitters.

Using Tango’s rep levels for pitcher and giving 2/3 time to starters, you get 1/3 * 4.80 + 2/3 + .370 = .407. Position players are at, uh, what? .350? .380?

.350 into Pythag using 1.92 exponent yields .266 rep level team, which is too low.

To produce a .300 team, I’m getting .380 for position players. Which is a touch higher than Tango’s starter rep level. That doesn’t seem quite right.

Huh.

Correcting myself (though it doesn’t make much of a difference)

Tango’s rep level for starters should be .380 and relievers should be .470.

Pitchers are much more ‘replaceable’ in season.

If your 11th, 12th or 13th man on the staff isn’t performing, down he goes, and someone else comes up. Repeat all season long.

You’ve got 24 guys at AAA and AA that can be promoted to piching, vs. about 4 at each of the 8 major positions. Now, in total that’s about the same number of Pitchers vs. Position players, but if it’s your 2B/SS backup isn’t performing, and your best AA/AAA position player guy is a 1st baseman, you can’t necessarily replace one with the other, while with pitchers you can always pick your best pitcher out of those 24 available guys to bring up.

There are better skew statistics. I have no idea how they are calculated, but I know that my software can calculate them…

I think Tom’s rep-level is a bit below .300. (Off the top of my head I think it’s .29_ or so.) I think it’s probably a bit too low.

(And am I the only one that finds that describing an offense or defense as a win percentage is unwieldy and confusing? I’m just asking here.)

I agree with you Colin about the win% thing. It’s extremely confusing to me, since I have no idea what a .520 player looks like. I’m not sure why he uses that instead of runs or wins. It’s the same words, but a slightly different language.

So I took all MLB players, 1998-2008, so a good 10 years of data. I’d love to have good MLE data to go with it, but you take what you can get.

Using Excel’s skew function, I get 5.58 for position players (based upon wOBA) and 11.79 for pitchers (based upon RA). If I’m reading this correctly, this is based on STDEV so the units are directly comparable.

Put in a playing time cutoff of 20 IP/20 PA (I know, I know) and I get a skew of 4.93 for RA and 0.32 for wOBA.

…I of course have only a vague idea of what this MEANS.

Colin, were those skew numbers positive or negative? It makes a huge difference.

Both positive. Remember that ERA runs high to low and wOBA runs low to high, so that a positive skew means different things. It seems that there are actually more above-average hitters than below-average, at least in MLB. There seems to be more below-average than above-average pitchers in MLB. (I did some quick graphs that seemed to bear this out, but I haven’t made them presentable yet and I won’t have a chance until tomorrow.)

OK, that makes more sense. I thought you were running RA from low to high. As to what it means, the usual cutoff for skewed/not skewed is 3.0. A skew of 0.32 is almost nothing, suggesting that batting talent/performance follows a mostly normal curve.

The pitching talent/performance curve looks more like a brontosaurus, with a long tail out to the “elite” end and a big fat hump down at the “not so good” end. Translation: there are a few elite pitchers and a lot of crappy ones. So, if an elite pitcher goes down, good luck in replacing him. If a crappy one goes down, there are probably five more where he came from.

Good pitching is a lot harder to find than good hitting. I’d be curious to see what that looks like broken down by primary position though.

I don’t believe this: “It seems that there are actually more above-average hitters than below-average, at least in MLB.”

I can MAYBE believe there are more PAs from above-average players than below-average players. But still probably not.

I mean, say league average is .335 wOBA. You have some players at a .400+ wOBA, which is .065 points above average. Do you have many .270 wOBA hitters? Uh, no. In order to balance the great players, you need lots of below-average players. Hitters have to be skewed right, no? (Where “right” means higher wOBA).

Mistakes were made.

In short, I was watching two kids and cooking lunch at the time, so I, ahem, ended up looking at the wrong column on the spreadsheet when it came to report results for the spreadsheet post-cutoff. (I didn’t notice this when I was clarifying for PC, because, well, I was posting from work. I should get a great blinking light to put on all posts made from work.)

For pitchers, actual skew numbers:

RA: 0.753

ERA: 0.754

FIP 0.457

For position players:

All : -0.473

C: -0.360

1B: -0.688

2B: -0.653

3B: -0.463

SS: -0.561

LF: -0.326

CF: -0.928

RF: -0.563

That’s with a 20 IP/20 PA cutoff.

I hope your were cooking something good.

I’m not really up on my skew measures. Is the distribution looking at number of players or plate appearances?