Reading back your method from the first post. You are saying let the bottom 2 lose everything. All other games result in a winner. Don't you have to make those games be won by the lower placed team to make it worse case? ie if you were in a relegation scrap you'd be wanting the teams below you (and the one/s feasibly catchable above) to lose.
You might have already adjusted your method, and I missed the post...
I'm sure there's still some error because of so many teams still being on 55. For example, we are on 55 rqd, Palace on 54 rqd, despite us currently having 7 points more already?
I’m trying to answer the question of how many points are required to guarantee finishing above 18th, which is basically an exercise in finding the highest possible total for the 18th placed team in the final table. It’s not looking for ‘worst case’ as that would need to be from the point of view of a particular club, but this is the highest possible for 18th as applied across the league.
If the bottom two teams take points off those 18th to (currently) 3rd, then there are fewer points in the pool for those in 3rd to 18th. Let’s say for instance that Norwich still have to play 3rd-10th and Watford still have to play 11th-18th. If they win all those games and get another 24 points each, Norwich would have 46, Watford 55, and the others would be reduced to 51-53, which suggests you would only have to beat 51 to guarantee survival. I’ve produced a set of results that would have 18th on 54 points, so leaving the bottom two behind (and having those already safe also lose their games) to maximise the points available to the rest results in the highest possible total for 18th.
55 and 54 points that you pick out aren't required, they are just the total on this version of the league table, but the results could be cut to have different teams in that 54-56 range. Everyone from 3rd to 18th currently needs 55 to be certain, based on the league table as it stands. For Watford it will also be 55 as we could just swap them out for West Ham.
Norwich are interesting. The most they can get is 51, however their target is probably lower as to reach it they’ll have to take points off everyone else. I haven’t worked it out, so whether it’s as low as 51 I don’t know. I might look at this next to track ‘safe’ from the top, and ‘out of their hands’ from the bottom.