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# What is the earliest point in the Premier League season that a team can be confirmed relegated, provided they start the season on 0 points and have no deductions throughout?

Question #105578. Asked by joefoxon. (May 15 09 2:15 AM)

Datsmeharse

I have no reference for this, but a Premier League club couldn't be confirmed relegated until after their 25th match.
For example, let say our pathetic club (we'll call them Liverpool since I'm a ManU fan) has gone 0-0-25. (Oh what a dream!)
After 25 matches, 17 clubs would have to have a minimum total average of 13-1-11 and 40 points to shut them out, since Liverpool can only get 39 points in their final 13 matches.

So can 17 teams all have a minimum 13-1-11 record after 25 matches?
25 matches x 20 teams equals 500 results of all kinds (wins/draws/losses)
A minimum of 9 matches, or 18 results, have to end in a draw in order for all 17 teams to draw once.
500 results minus 18 draw results leaves 482 results. Only half of those results, or 241, could possibly be wins, obviously since the other 241 would be losses.
17 teams winning a minimum of 13 matches equals a minimum of 221 wins needed, so we have more than enough. We can even give a few wins to the other two bottom-feeders, we'll call them Arsenal and Man City.

24 matches isn't enough because:
with 14 matches left, Liverpool could earn 42 points, meaning our 17 clubs have to have 43, or a minimum average 14-1-9 record over 24 games to shut them out.
20 teams playing 24 matches equals 480 results,
again a minimum of 18 results have to be draws leaving 462 results, half being winners leaves 231 wins max.
But 17 teams times a minimum of 14 wins each means we need 238 wins, so we're short. You could argue that Liverpool would be eliminated after their 24th match if seven other clubs played their 25th match before them and all either won or tied as needed.

I'm sure there's a better mathematical way to present this -- we'd need a Millwall fan for that...

 May 15 09, 5:40 PM

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 Is there any sort of formula to work out the earliest point at which a football team can be confirmed relegated?

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