Calculating outright "fair" odds

[Squirrel]

Afternoon Guys.

There is something I have never really done that I would like to learn a little bit about. Say I have a random darts tournament (for argument sakes) thats in bracket style, similar to what you guys would see in the playoffs, and I have a method of obtaining a %chance of each outcome between every player. How would I go about calculating this into "fair" outright odds if I trusted my numbers enough.

IE, Round 1
(Match 1)Player A v Player B
(Match 2)Player C v Player D
(Match 3)Player E v Player F
(Match 4)Player G v Player H

Then winner of Match 1 plays 2, and 3 plays 4 - then obviously the final between the winners of that. Now I have a method of predicting percentage chance between any set of players, for EG I could say that A beats B 65% of the time, A beats C 33% of the time, C beats D 44% of the time etc etc

You all know what i'm on about i've just made a bad example of explaining - now what I want are methods to calculate outright prices based on those probabilities, and anything else that might help me with this. The ONLY important thing is any advice comes in the form of telling me what to look for and what to learn about, I dont actually want it done for me.

I know how to work out the fair odds of each matchup based on my percentages, of course, but what I dont really know is how to work out the chances of each team winning overall when you dont know exactly who they will face in the next round etc etc

Cheers if anyone can help <yup<

[Squirrel]

I would just like to add i'm intending to use this for euro sports (such as darts, snooker etc) so spreads aren't a factor, it's all about the ML and who will win.

[uva3021]

there are two ways of calculating, you could run a simulation, weighting the teams based on matchup and your given probabilities for each team

or do a straight combinatorial calculation

for each teams, find the odds of winning every possible sequence of games and add them all together

i.e.

Team A 65% vs Team B 35%

Team A 51% vs Team C 49%

so the chance of team A beating both B and C is 65% * 51%

and do that for each additional game

[Squirrel]

Thanks for the simple response fella, will probably start with the latter method for now since i'm starting small whilst I get a grip on things. Down the line I will have to look into the simulator method since at some point I will be wanting to do it when I have 16 teams involved and not just 3 or 4.

Babysteps for now though and I appreciate the response.

[Romanowski]

welcome to cm squirrel

[Squirrel]

Thanks Roman :msh<

Just to clarify if I have the general idea correct, I *think* I do but I just want some clarification before I go steaming in and start using the method.

Semi Final 1 - Team A (54% prob) vs Team B (46%)
Semi Final 2 - Team C (50% prob) vs Team D (50%)

I know that A would have a 75% chance of beating C in the final, and a 32% chance of beating D in the final.

So to get Team A's outright odds I would go......

(.54 * .50 * .75) + (.54 * .50 * .32) = 28.89% chance (+246)

Does that seem to be correct? I've done it and redone it and it seems right to me.

Thanks fellas <yup<

[uva3021]

all your odds for every team invovled, if its a tournament, should equal 1

for Team A you should only have to multiply the sequence of possible matchups they player, regardless of the probabilities of the previous games

I may have misinterpreted but lets say you have

Team A vs Team B

Team C vs Team D

Team A's chances of winning the tournament are

AB% * AC% + AB% * AD%

[Squirrel]

Thanks for the responses fella, i've got this sorted now and pretty much know where I am at.

Another question, how would I do the same for the NFL playoffs? I'm struggling to get a grip on all the possible playoff permutations because of re-seeding after every round, I was hoping there would be a spreadsheet already out there but google hasn't helped me find what I am looking for.