The Probability Thread 2009

[SDRighton]

One bit I don't get - you said there were however many billion different possible result permutations till the end of the season, but surely mathematically speaking there are infinite result combination possibilities even in one game?

Or is your billions limit based on the more sensible approach that only a set number of goals can physically be scored in 90 minutes? If so, what is this number? Is it the record 36, for example?

 

[spodman]

One bit I don't get - you said there were however many billion different possible result permutations till the end of the season, but surely mathematically speaking there are infinite result combination possibilities even in one game?

Or is your billions limit based on the more sensible approach that only a set number of goals can physically be scored in 90 minutes? If so, what is this number? Is it the record 36, for example?

Think it's even simpler than that, each match as one of 3 outcomes, home win, away win or draw. If there are 78 odd matches left then the combinations of results for those matches is the 16 billion billion billion figure that was quoted (3 to the power 78 for the maths boffs!)

 

[older-codger]

why not 78 to the power of 3?

 

[spodman]

why not 78 to the power of 3?

Because that would be the calculation if there were 3 matches left, each with 78 outcomes!

 

[older-codger]

Modern maths (or is it statistics?)!!! What happened to the old 2+1 = 3? Seems to me that if you have 78 matches, each of which has 3 alternative results, the total options are 78 x 3. The larger figures only kick in if you take scores into account. But then - I'm a simple soul and to me it's far more relevant that Matt Taylor may be back to change the chances of City winning.

 

[SDRighton]

Thanks guys - all clear. Way too clever for me. Just shows why the bookies love laying accumulators.

 

[mfcrocker]

Modern maths (or is it statistics?)!!! What happened to the old 2+1 = 3? Seems to me that if you have 78 matches, each of which has 3 alternative results, the total options are 78 x 3. The larger figures only kick in if you take scores into account. But then - I'm a simple soul and to me it's far more relevant that Matt Taylor may be back to change the chances of City winning.

Your definition of options is wrong. By options, they mean each set of 78 games, so the first option is that all 78 are home wins, the next is that the last game is a draw, the next that the last game is an away win, etc etc etc.

Number of options = number of alternative results ^ number of matches
= 3^78
= that god awful number that was posted

 

[StroudGrecian]

Good to see Bayesian statistics being put to proper use!

I occasionally dabble at work, when building chronological models from radiocarbon dates. It seems to be a very long-winded way of telling you that something you think has a certain probability, does.

 

[haka]

Excellent work, Poundstretcher (and honourable mentions to Tyne and Pete).

So is this going to be updated after each set of games? (Answer: "Yes"). Thanks!

 

[Grecian-on-Tyne]

So is this going to be updated after each set of games? (Answer: "Yes"). Thanks!

since you ask - after a great round of result this afternoon - he's some updated graphs.....

Playoff now showing at 98.3% - Surly not even City can mess up from here.

Automatic Promotion now up to 45.8% - please note my model does not take current form into consideration - we are behind Bury because of our harder run-in & Wycombe due to their games in hand.

and finally - shows % change of getting auto-promotion / playoffs depending on number of points gained, and frequency (chance of getting that number of points) - example our most likely outcome is 75 points (eg 2W 1D 2L) 17% chance of this occurring - it will give a 38% chance of Auto Promotion.

Of course it's stating the obvious to say the next two results are going to have a BIG effect on our Promotion chances.