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Topic Originator: istvan kozma
Date: Fri 15 Nov 17:22
Tomorrow in the championship its 1v2 3v4 5v6 7v8 and 9v10.
Thought odds were 1 in 945 but is that correct?
KOZMA
Post Edited (Fri 15 Nov 17:24)
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Topic Originator: RhinoPars
Date: Fri 15 Nov 17:59
I stand to be corrected (and have put my working), but I make it approx 1/30,244 if you also specify this has to happen only on a specific matchday.
If you take 1st then the chances of playing 2nd is 1/9 and the chance of 1st being at home is 1/2 (combined prob of 0.05555)
For 3rd to draw 4th then is a 1/7 chance multiplied by 50:50 chance of 3rd being at home (combined prob of 0.07143)
For 5th to draw 6th is 1/5 * 0.5 for 5th to be at home (combined prob of 0.10000)
Similarly 7 and 8 = 1/3 * 1/2 (combined prob 0.16666)
and the only option left for 9 is to play 10 and for 9 to be at home that is 1 *.5 (combined prob of 0.50000)
For all of these to happen together you multiply the above five probabilities together. This gives you 0.000033064815 and the reciprocal of that is 1 chance of in 30,244 (rounded) of getting this combination this weekend.
However if it was a case of getting this once in a season ... The first game of the season starts with everyone on 0. Assuming that from game 2 onwards we do have a 1-10 ranking (and we may not have) then presumably there would be a maximum of thirty five chances to get this over a season. The probability then increases to 0.0011572686 and the reciprocal of this gives 1 in 864 which is in the same ball park as Istvan`s 1 in 945 but a little more likely.
The odds of this happening in 20 seasons are much greater - approx 1 in 42 and a lifetime of supporting the Pars for 60 years in a 10 team league is roughly 1 in 14. Thus it is not such a huge coincidence if it is just a question of it happening once in a lifetime in just one league.
Post Edited (Fri 15 Nov 18:07)
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Topic Originator: parsfan
Date: Fri 15 Nov 23:24
Quote:
RhinoPars, Fri 15 Nov 17:59
I stand to be corrected (and have put my working), but I make it approx 1/30,244 if you also specify this has to happen only on a specific matchday.
If you take 1st then the chances of playing 2nd is 1/9 and the chance of 1st being at home is 1/2 (combined prob of 0.05555)
For 3rd to draw 4th then is a 1/7 chance multiplied by 50:50 chance of 3rd being at home (combined prob of 0.07143)
For 5th to draw 6th is 1/5 * 0.5 for 5th to be at home (combined prob of 0.10000)
Similarly 7 and 8 = 1/3 * 1/2 (combined prob 0.16666)
and the only option left for 9 is to play 10 and for 9 to be at home that is 1 *.5 (combined prob of 0.50000)
For all of these to happen together you multiply the above five probabilities together. This gives you 0.000033064815 and the reciprocal of that is 1 chance of in 30,244 (rounded) of getting this combination this weekend.
However if it was a case of getting this once in a season ... The first game of the season starts with everyone on 0. Assuming that from game 2 onwards we do have a 1-10 ranking (and we may not have) then presumably there would be a maximum of thirty five chances to get this over a season. The probability then increases to 0.0011572686 and the reciprocal of this gives 1 in 864 which is in the same ball park as Istvan`s 1 in 945 but a little more likely.
The odds of this happening in 20 seasons are much greater - approx 1 in 42 and a lifetime of supporting the Pars for 60 years in a 10 team league is roughly 1 in 14. Thus it is not such a huge coincidence if it is just a question of it happening once in a lifetime in just one league.
Given Falkirk are away* can you not remove all the 50:50s as what we have is just the successive pairs playing each other, not necessarily the higher placed one being at home?
So is it not just 1/9 * 1/7 * 1/5 * 1/3? Which is 1/945, like Kozma said.
With three leagues of 10 and 36 match days** a year, there`s 360 opportunities where this could happen in the three lower senior leagues in Scotland alone. Other leagues of varying numbers here and elsewhere are available.
So better than a 1 in 3 chance of it happening in any season in Scotland.
In the world ever? Absolutely. (Other thread reference I think)
* Going by the other thread, can`t be be arsed looking it up.
** I know all the games won`t be played over exactly 36 days.
Edit: predictive text gibberish in first paragraph.
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The universe is ruled by chance and indifference
Post Edited (Fri 15 Nov 23:28)
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Topic Originator: istvan kozma
Date: Sat 16 Nov 07:27
Think it`s simply 1/945. Other factors like specific date or which team is home or away are not being considered
KOZMA
Post Edited (Sat 16 Nov 07:30)
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Topic Originator: RhinoPars
Date: Sat 16 Nov 11:34
Thanks, Parsfan. You and Istvan are right. I missed that Falkirk is away, which changes things. It then is just 1/9 * 1/7 * 1/5 * 1/3, which gives you Istvan`s 1 in 945 chance (ignoring who is playing at home and just looking at odds of it happening this weekend).
Post Edited (Sat 16 Nov 11:36)
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Topic Originator: istvan kozma
Date: Sun 17 Nov 09:39
After much consideration I put the odds of yesterday`s fixtures matching the league positions at 1/113400.
This is based out the 1/945 chance of the pairings multiplied by the 1/5! or 1/120 chance of those pairings being in the right place in the league.
KOZMA
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