# [R] How to work out 3-way probabilities

Charles C. Berry cberry at tajo.ucsd.edu
Tue Apr 27 17:53:46 CEST 2010

```On Tue, 27 Apr 2010, Dimitrij Kudriavcev wrote:

> Hello.
>
> I have a quick question.
>
> I try to use logit regression, to work out probabilities in the sport event.
> I have work out probabilities for group of 2 players:
>
> p1 - probability, what player1 will beat player2
> p2 - probability, what player2 will beat player1
> pt - tie probability, p1 <- 1 - p1 - p2;
>
> Now i want to work out probabilities for group of 3 players, like:
>
> pg1 - probability, what player1 will beat player2 and player3
> pg2 - probability, what player2 will beat player1 and player3
> pg3 - probability, what player3 will beat player1 and player2
>
> I have probabilities for every pair of players in that group. Is there a
> function in R, what can simply convert this 2-way probabilities in to the
> 3-way (or more)? Or can some body suggest, how to do it manually? I have try
> to work it out, buy just multiply corresponding probabilities, but it seems

So each player gets a score and the highest wins?

And your two-way probabilities are just the probability that player1
scores higher than player2, etc? Or that player1 won over player2 given
that player3 did not win?

Or you have a bunch of one-on-one competitions and you want to predict
what will happen in a three way competition?

Have a Google at 'McFadden conditional logit'. There is a literature that
should point you in the right direction.

Once you have a sense of what goes in conditional logit models you may
find survival::clogit() to be of assistance.

HTH,

Chuck

>
> Cheers,
> Dmitrij.
>
> 	[[alternative HTML version deleted]]
>
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