That is indeed excellent. I realise this is a theoretical thread, and I’m cool with that. But as the question has been asked and answered, I’ll just comment that in a normal season, very few teams get 64 points, and by the time anyone does, they are already mathematically safe from relegation anyway, by virtue of being ahead of the third from bottom team by more than 3 x the number of games remaining. As such, I wonder what the typical cut-off point is, i.e. at what point in the season does, say, 60 points tend to absolutely guarantee you safety.
To illustrate what I mean, let’s look at last season (2013/14). I have just discovered the official Premier League website has a really useful historic tables feature where you can look at any point in the season: here, just change the year. Anyway, after every team had played at least 27 games (Chelsea had played 30), Chelsea had 66 points. Third bottom Sunderland had 25 points from 27 games, with 11 to play they could ‘only’ get to 58 and so Chelsea were safe already at that point, as were Man City, Liverpool, and Arsenal on 60, 59, and 59 respectively. So the latter did not need to get to 64 to guarantee their safety that year. And that was with over a quarter of the season left.
For info, as it turned out, that season 33 points could have kept you up if your GD was better than Norwich, a pretty low total. I believe the highest ever points total that resulted in relegation was 43 by West Brom. In fact:
13/14: 33
12/13: 36
11/12: 36
10/11: 39
09/10: 30
08/09: 34
07/08: 36
06/07: 38
05/06: 34
04/05: 33
03/04: 33
02/03: 42
01/02: 36
00/01: 34
99/00: 33
98/99: 36
97/98: 40
96/97: 40
95/96: 38
The above shows the points total at the end of the season of the third from bottom team (i.e. the highest points total to get relegated, which is the same as the lowest points total at which it was possible to not be relegated). Seems I misremembered about West Brom - it is actually West Ham that holds the unwanted record of 42 in 02/03. The data only go back to the 95/96 season as prior to that the league was 22 teams with a 42-game programme.
The mean of the above is 35.84, the mode is 36, and the median is 36. The standard deviation is just under 3, so the classic number of 40 puts you just above one SD away from the mean. That’s where my meagre stats knowledge runs out; perhaps someone can say if this tells us anything about the likelihood of a team with 40 points or more being relegated in any given season? Based on the figures we have it’s happened 15% of the time so far, which sounds about right. It’s probably wrong to say this gives us an 85% confidence that 40 points is safe but that seems about right to me. I wonder what number gives you 99% confidence - suspect it’s around 44.