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

I have been working on this and the best I could come up with is:

R=((T*1.25)+3)-RP

Where R= number of games required
T= number of teams in the league
RP= number of relegation places in the league

Unfortunately, it won't work for League One.

I think I've got it:

R=(([T*1.25])+3)-(]0.5RP+1[)

Where R = number of games required
T = Number of teams in the league
RP = number of relegation places in the league
[] = Floor function
][ = ceiling function

It is to work out the points required at the start of the season, not in the middle.

You can say that a club with 0 points will finish in the relegation zone - but may not actually get relegated if there are enough other clubs with 0 to fill the abyss to the top of the playoff area. There are many scenarios possible down at the bottom, all based around the performance of different clubs - and other factors like goal difference, even. No formula can take that into account. Think of snooker - someone may have the play but not have enough points left on the table to win without snookers. You can safely say a club will be relegated if there are not enough points left in the season for them to overtake others to get to a safe position. No number will be a safe number to obtain without taking relative positions into account. Also, three points taken from the club next up from you is worth far more than three taken from the league leader - in terms of safety. (The other will increase your crowds, though, and boost flagging morale...) It's 3 to you - and 3 they can't have. (Beating a club just below is also good for the same reason.) Beating a high club is 3 to you - and no effect on the club just above. Where's gmackematix when you need him?

From the season the Premier League was reduced to 20 teams, no team scoring 43 pts or more has been relegated:

------  --------  --------  -------
season Champions. 4th last. 3rd last
------  --------  --------  -------
1995-96 : 82 pts : 38 pts : 38 pts
1996-97 : 75 pts : 41 pts : 40 pts
1997-98 : 78 pts : 40 pts : 40 pts
1998-99 : 79 pts : 41 pts : 36 pts
1999-00 : 91 pts : 36 pts : 33 pts
2000-01 : 80 pts : 42 pts : 34 pts
2001-02 : 87 pts : 40 pts : 36 pts
2002-03 : 83 pts : 44 pts : 42 pts
2003-04 : 90 pts : 39 pts : 33 pts
2004-05 : 95 pts : 34 pts : 33 pts
2005-06 : 91 pts : 38 pts : 34 pts
2006-07 : 89 pts : 38 pts : 38 pts
2007-08 : 87 pts : 36 pts : 36 pts
2008-09 : 90 pts : 35 pts : 34 pts

To put that in a formula is probably impossible, as there would be too many IF variables .. if the champions finish with X pts and the runners up with Y pts, and last place finishes with A pts and 2nd last with B pts, how many pts would 4th last need to avoid relegation? It'd be a never ending (actually it'd be finite, but very very long) list of variables, as it depends on what everyone else does.

arsenal-mad.co.uk/footydb/loadlgt.asp?divno=3&ssnno=138 no longer exists

There are 38 rounds of 10 games = 1140 pts on offer to the 20 teams. If one team won all 38 of its games they'll have 114 pts at the end of the season and everyone else is already looking at a max of 108 pts (as they lost home and away to the champions). If the 2nd placed team won all their games except for those two, they'll have 108 pts but the other 18 teams would now be looking at a max of 102 pts and so on ... and then throw in draws where one point disappears ...

OK, I meant if the team in 17th scores as highly as possible and the team in 20th scores 0 points, to work out the theoretical earliest point in the season a team can be relegated, counting from the start.

You are over thinking this question. The only way to be confirmed to be relegated is to not have enough points left in your remaining matches to move up to 17th place. So all you'd have to do is take a team's point total, games remaining x 3, add it to the current point total. If new total is greater than the total of 17th place then you are not confirmed relegated.

Then you'd just have to compare tie breaker stats for when the new total equals the total of 17th place.