Subject: Nationals Predictions (Scientific!)

From: price@carla.lbl.gov (Phillip N Price)

Date: 1995/11/01

Newsgroups: rec.sport.disc

Here's the story.

Jim Parinella of reigning champs "Death or Glory" (DoG)

sent me a list of what he feels are the odds for each team

at Nationals to beat any other team.

Using his odds, the pools (which are known) and the method

used for breaking ties, I generated 500 possible outcomes

of pool and semifinal play. I had to fudge on the tiebreaks,

since it's possible for the decision for three-way ties to

rely on point differential, and I don't really have a statistical

model for that. Pretty rare case, though.

Anyway, based on Parinella's odds estimates, here are the

probabilities of various outcomes:

Prob.

NY makes it to finals: 0.68

DoG makes it to finals: 0.55

DH makes it to finals: 0.52 ("DH" = Double Happiness)

PCS makes it to finals: 0.14 ("PCS"=Port City Slickers)

Ring makes it to finals: 0.05 ("Ring"=Ring of Fire)

Other makes it to finals: 0.06 ("Other"=any other team)

(Most likely other teams

Seattle, San Diego, and Z)

Those aren't independent, though, mostly because of the

pool structure. Most likely finals matchups:

Prob.

NY/DoG 0.29

NY/DH 0.26

DoG/DH 0.22

PCS/NY 0.09

PCS/DH 0.03

all others very unlikely

All of this suggests a tossup between NY, DoG, and DH

for the championship, with long odds (9:1 or so) on PCS

and very long odds on any other team.

However, it also suggests that there's almost a 25% chance

that a team other than the Big Three will make it to

finals.

All of these odds are based on the assumption that Parinella's

odds are the "true" odds. What does that mean? Well, this

is a technical question that requires a technical answer.

Suppose this were an episode of Star Trek, and that we discovered

millions of "parallel universes" that are similar to ours,

but not exactly identical. We visit a few thousand of them,

and see how many of them feature a game between, say,

Ring of Fire and Double Happiness, and in what fraction

Ring beats Double. If this fraction is equal to JP's estimate

(which, by the way, is 0.3) then JP's estimate is "correct".

Now, JP was a little sloppy when he made up his odds matrix---for

example, he has some games being won or lost with probability 1,

which is obviously incorrect. If the odds really are very high

or very low, then the errors won't really affect the likely outcomes

much. But what about, say, NY's chance of beating DoG? (JP

estimates it to be 0.65). A NY/DoG semifinals matchup is

fairly likely, so if the true chance is 0.55 instead of 0.65,

it could make a difference in NY's odds of advancing to finals.

To include such uncertainty, I really ought to do many sets of

simulations, varying the odds slightly in each one, and then

summarizing the results. If I do that, almost certainly

the odds of "long-shot" teams making finals will increase u

slightly.

It's a pain, though, so I probably won't do it.

By the way, JP has made NY a sizeable favorite to beat every

other team (with only DH and DoG having good chances to

upset, at 0.4 and 0.35, respectively). But it's likely

that NY will have to play both DH _and_ DoG (one in semis,

one in finals) to win the championship, while DH and DoG

have easier roads since one of them should have a weaker

semifinal opponent. Basically, if there are only three very

strong teams, then a two-pool system hurts the favorite.

That's it for now.

--Phil Price