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Thursday, October 06, 2005

Shootin’ Craps

Voros returns to BTF with a look at probability and the playoffs.

You often hear members of baseball’s underground intelligentsia (otherwise known as ‘stat drunk computer nerds’) describe baseball’s playoffs as a ‘crapshoot.’ Now despite the fact most of us subterranean baseball thinkers would likely soil ourselves if we ever found ourselves in the midst of a real back-alley craps game, in general we seem pretty damn confident we know what we are talking about when we use the term.

Not one likely to take these sorts of things on faith, I decided to take a cursory (please remember that word before someone starts chiming in with stuff you need a PHD just to get the introductory textbook to)…

…um, where was I—oh yes, I decided to take a cursory look at the issue and see if the statistical geekerati know what the hell they are talking about.

The experiment is simple. Estimate the winning chances in a game of two teams with given winning percentages and adjust for home field advantage. Then take those numbers and come up with the chances of winning a 5 or 7 game series.

The following tables list the chances of winning 5 or 7 game series for teams with differing everyday win percentages. The win percentages aligned vertically on the left side are the win percentages of the team with home field advantage, the winning percentages across the top are for the team with fewer home games in the series. The given resulting percentages are the chances of winning the series for the team with home field.

Home field advantage is set so that a .500 team would win at a .600 clip at home and a .400 clip on the road. Or, for our purposes, a series between two evenly matched teams would have the home team win on average 60.0% of the games. Why is that so much different than we see in the regular season?
(around .540) Well since the war, the home team has won roughly (very roughly but there are side issues at work that I don’t want to get into) about 60% of
the games in World Series play. Since there’s no inherent reason why a home team should be the better overall team in the World Series (until recently home field simply alternated leagues), this suggests that home field advantage is stronger in the postseason than in the regular season. I’ve decided to base the above on that assumption, since it’s quite reasonable to come up with reasons why that might be the case. (Insert gratuitous swipe at Eric Gregg here).

To come up with the winning percentage of a single game, the following formula was used:

A = Team A’s Win% (home team)

B = Team B’s Win%

((A*(1-B))/.5)/(((A*(1-B))/.5)+(((1-A)*B)/.5)) = Team A’s chance of winning

Batter-Pitcher Matchup

Then I raised that number by .737 to adjust for home field advantage in that game (an exponent works well here because you can’t go above 1 or below 0 with it). From there it’s easy to come up with full series winning percentages based on those numbers.

Anyway, what the table shows is that the geeks are, to an extent, correct. Any individual series can be a bit of a crapshoot. For example, if we assume the Cardinals face the Padres and their ‘true’ win percentages are .625 and .500 respectively, the Cardinals, even with home field advantage, expect to win the series only about 73.77% of the time. While that may seem like a lot, in actuality the Padres chances would be a little below the chances of rolling a ‘9’or higher in craps. In other words while the Padres are indeed underdogs, they certainly have a shooters chance.

Still, just like in craps, while any outcome can easily happen, some outcomes are more likely than others and the Cardinals do rank as clear favorites to win the series if we assume those win percentages are correct. Of course this is without adjusting for different starting pitchers and so forth, but remember this is just a cursory look to give us an idea of what level of crapshoot things are. Please do not use this info for wagering purposes, unless of course you win, in which case I’ll set up a pay pal site for you to send me my cut.

It’s also worth noting that even a favored team whose chances of winning each series it participates in is 70%, would still only win all three series about a third of the time.

So we geeks are essentially right. (And don’t we just love to announce it to the world when we are). The playoffs are, to a certain extent, a crapshoot. Baseball’s current playoff format ensures that even the very best teams are likely underdogs to win the World Series once they make the playoffs. There’s just not enough games against too strong of opposition to swing the balance too heavily in their favor. I’ll leave it to others to argue whether this be good or whether this be bad.

And while it’s unlikely the Padres will wind up winning World Series rings (or watches), their chances are not probably not too far from the chances of rolling snake eyes.

Which can happen, something we geeks know from many years of playing cutthroat games of

~~Risk~~

“Craps.”

Voros McCracken Posted: October 06, 2005 at 12:54 AM | 314 comment(s) Login to Bookmark
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301. Mister High Standards Posted: October 10, 2005 at 07:25 PM (#1674753)

Having said all of that I have had streaks of 12-15 of these tournaments out of the money, and have gone over 20 without winning one.

Then your not maximizing your return. Either playing at a level too high for max returns or playing suboptimal strategy.

Baseball is not flipping a coin. I coin flip doesn’t even reasonably simulate a playoff series or series of games. Its far more complex than that.

sufficiently large number of hands you will be a winner if you are a better player.

Who cares? These situations aren’t reality in baseball. There are no 10,000 game sample sizes.

302. Jasper109 Posted: October 10, 2005 at 07:27 PM (#1674764)

My final thoughts on the Braves streak and “underachieving” in the playoffs.

I guess it just annoys me a bit that very few people realize how amazing an accomplishment it is to win 14 consecutive division titles and have a team ERA in the top 3 in the league in virtually every one of those years. They have overcome injuries, retooled, and within a reasonable payroll have achieved something truly amazing.

Based on the playoff stucture and the quality of opposition winning 3 titles would probably be about “par” So if things had gone a bit better in 2 of the other 13 years we wouldn’t be having this discussion.

The Cards had better win this year or they will soon also be called chokers and LaRussa will be called an overated manager again.

303. Mister High Standards Posted: October 10, 2005 at 07:34 PM (#1674787)

Having said all of that I have had streaks of 12-15 of these tournaments out of the money, and have gone over 20 without winning one.

Then your not maximizing your return. Either playing at a level too high for max returns or playing suboptimal strategy.

Baseball is not flipping a coin. I coin flip doesn’t even reasonably simulate a playoff series or series of games. Its far more complex than that.

sufficiently large number of hands you will be a winner if you are a better player.

Who cares? These situations aren’t reality in baseball. There are no 10,000 game sample sizes.

304. Jasper109 Posted: October 10, 2005 at 07:37 PM (#1674797)

My final thoughts on the Braves streak and “underachieving” in the playoffs.

The Cards had better win this year or they will soon also be called chokers and LaRussa will be called an overated manager again.

305. ERROR---Jolly Old St. Nick

Posted: October 10, 2005 at 08:53 PM (#1675043)

My final thoughts on the Braves streak and “underachieving” in the playoffs.

But again, nobody’s denigrating what the Braves have done.

We’re just not confusing it with what they haven’t done.

And a few of us heretics still don’t consider it comparable to winning the whole thing 4 times in 6 years, and getting to the playoffs 11 straight years as well. That’s open to debate, I know, but it’s not exactly an unarguable point that division titles are the be-all and end-all of a definition of “dynasty.” It’s a curious “dynasty” when your every year seems to end with being some other team’s stepping stone.

306. Mister High Standards Posted: October 10, 2005 at 08:59 PM (#1675071)

Daniel Negreannu is one of the best tournament poker players in the world. In this years WSOP

WSOP is very different than a 10 person sit and go style event.

Online like forums have never had a reasonable discussion on correct strategy for these events. Likely because the incentives to discussing it costs you money.

For example any time anyone talks of pot odds in re: to a sit and go has no concept of correct play. Its also more often correct to fold a hand likely best in a sit and go, when it is rarely correct in ring.

Anyway I don’t give out free poker advice to people I don’t know. But the Braves result has nothing to do with poker.

Sample size is an overrated term used in baseball analysis. You have a defined time frame which you must succeed in. Which makes comparisons to events with unlimited horizons futile.

307. Mike Emeigh

Posted: October 10, 2005 at 09:00 PM (#1675073)

Was Boyer even on the postseason roster?

Boyer was injured; that’s how Devine was able to be put on the roster in the first place (the infamous KRod exception).

—MWE

308. Mike Emeigh

Posted: October 10, 2005 at 09:12 PM (#1675105)

The only available pitchers for the Braves after the 16th were Devine, McBride, Smoltz, Sosa, and Horacio Ramirez (who would have started game 5). Houston had, at that point, an all RH-hitting lineup except for the switch-hitting Vizcaino (who is a better RH-hitter). It was logical for Cox to use Devine there.

—MWE

309. Mike Emeigh

Posted: October 10, 2005 at 09:13 PM (#1675113)

—MWE

310. Jasper109 Posted: October 10, 2005 at 09:15 PM (#1675117)

So you are saying that you have played a minimum of 2000 SNGs and have never had bad streaks like the ones I have described?

311. Mister High Standards Posted: October 10, 2005 at 09:44 PM (#1675194)

S+G only - roughly:
20 per week for 2 years.
15 per week for 2 years.
10 per week for 1 year.
5 per week for 1 year.

I did not money in 18 in a row once, in my first year, playing a format that paradise poker doesn’t support any more if I recall. With a very no understanding of game adjustments, re differences between tourney play with cash game play. In other words I was playing my ring game style in tourney which is a big money loser for even the best players (which i wasn’t, though I have been a winning player for 7 of the last 8 years), and never a losing 6 month period online.

I had similar steaks to what you described when playing prior to gaining a fundamental understanding I didn’t have prior.

I did not money 10 in a row about 2.5 years ago. I shut down for 2 weeks and completely reviewed my game, and realized the poker beliefs I held through classic poker study: TTH simularion, DS &MM;, RGP, Super System ect… were completely misapplied in sit and goes with typical online opponents. Since then in roughly 1,600 S+G I have not lost in 14 consectutive events. I do believe I might, but i don’t believe it would be as common as you referred to.

312. Jasper109 Posted: October 10, 2005 at 10:04 PM (#1675248)

I f you haven’t yet, I would recommend reading Harrington. I’ve only read vol.1, but even though it’s written mostly for multi table tournaments, it helped my SNG game quite a bit.
Also, if you haven’t checked it out I would highly recommend the message board on internettexasholdem.com. Lots of good advice there.

313. Red Menace Posted: October 13, 2005 at 07:57 AM (#1681011)

Oh, good Lord! I read and read and thought and comprehended and explored the further reading cited… and then I got to the end of the first page! There are four pages?! I give up. You’ve all beaten me.

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Shootin’ Craps

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