erathirea

Not posted much in a while, but I do love some good stats.
Systematic approach.
Our maximum possible points is 58. So currently, Norwich, Watford, Swansea, Brentford, Bournemouth, Barnsley, Reading, Cardiff are "safe". Our worst case scenario is therefore them all to lose ALL their remaining games (except when playing each other, because those results don't matter for the purpose of this).
If you do that, then that pushes some more teams about 58 points. Millwall, QPR, and Luton, to be exact. So, then we assume they lose ALL of their remaining games (apart from the ones where they beat the current top 8).
Now 3 more teams are "safe" - Middlesbrough, Bristol City and Stoke. So repeat the process...
(remember, this is *literally* the worst case scenario for Derby - teams below 58 points are picking up points against teams above 58 points only) 
Once you repeat the process, no more teams *automatically* go above Derby.
So now we look for other "worst case scenarios". 
If you put the results in as I've described, the bottom of the championship looks like this:
15 Derby County 46 58
16 Rotherham United 43 54 (max theoretically 63)
17 Preston North End 44  54 (max theoretically 60)
18 Nottingham Forest 42 52 (max theoretically 64)
19 Coventry City 43 51 (max theoretically 60)
20 Huddersfield Town 43 50 (max theoretically 59)
21 Birmingham City 43 48 (max theoretically 57)
22 Wycombe Wanderers 46 48 (max 48)
23 Blackburn Rovers 42 47 (max theoretically 59)
24 Sheffield Wednesday 44 41 (max theoretically 47)
So there's 3 teams that, in this situation, we *guarantee* finish below us   (because we beat Birmingham).
 
I wanted to take it a step further, though. It's almost impossible in this scenario for Wednesday to catch us - even if we lose *to* them, we'd need to lose at least 2 other games). 
So our worst case scenario therefore should assume they have gone. So if they lose their other 2 games, that benefits other teams in the bottom few. Wycombe have also gone, despite wins against some good teams.
 
We already know Derby are safe if they win all their remaining games. Let's put Birmingham to one side, and talk about 2 other teams- Huddersfield and Birmingham. For them to finish above us in this scenario, they BOTH need to win *all* their remaining games. They *can't*, because they have to play each other.
Coventry would need at least 7 points, but they have to play Huddersfield too. In fact, there is no combination of results that leaves many of these teams ahead of us - Preston need 4 points from 2 games, but need to take points off Coventry to do it..
 
So let's adjust our view - what if we lose the worst possible game- to Birmingham?
This scenario immediately makes things more dicey, and puts Forest safe (55 points in this playthrough). So they lose their other 3 games, putting Preston safe in the process, who subsequently lose their other remaining game. Bottom of the table now looks like this:
17 Derby County 46 55
18 Rotherham United 43 54
19 Coventry City 44 54
20 Birmingham City 44 54
21 Huddersfield Town 44 53
22 Blackburn Rovers 43 50
With 6 games to decide it:
Rotherham v Coventry, Rotherham v Birmingham, Blackburn v Hudd, Hudd v Coventry, Rotherham v Blackburn, Blackburn v Birmingham.
Rotherham v Coventry v Huddersfield v Blackburn v Birmingham v Rotherham again, allows all 5 of those to win a game, with Blackburn having a spare game against Rotherham to pick up the win they need. - very contrived, but possible (any draw, by the way, guarantees at least one team to finish level on points with us.
 
SO- Don't Lose to Birmingham!
But what if we draw with BIrmingham?
In this scenario, Birmingham need 7 points to draw level with us - given their inferior GD (and that they aren't making it up by thrashing us), they realistically need 3 wins, against Rotherham, Blackburn and Forest. Blackburn then need to win their last 2 games to draw level with us, against Rotherham and Huddersfield. 
This combination of results would put Blackburn level with us, Birmingham ahead of us... but this leaves Rotherham needing 1 win from 1 and Huddersfield winning 2 from 2... meaning Coventry lose 2 of theirs and they can then NOT catch us.
 
SO- Drawing with Birmingham means we're safe.
 
Final scenario - what if we beat Birmingham, but lose to Blackburn (losing to Blackburn being *slightly* worse than losing to Preston.
This immediately makes Forest and Preston safe (as discussed previously).
17 Derby County 46 55
18 Rotherham United 43 54
19 Coventry City 44 54
20 Blackburn Rovers 43 53
21 Huddersfield Town 44 53
22 Birmingham City 44 51
Birmingham need 4 points from 2 games to draw level. Let's start by going with 2 wins, against  Blackburn and Rotherham. 
All 4 remaining teams need a win, which is, unfortunately, possible, as they are playing each other in such a combination that a round robin of wins is possible, albeit convoluted.
 
So, in summary. If we win all remaining games, we're safe. If we win 4 and draw with Brum, we're safe. If we do anything else, we're not mathematically safe.
 
 
 
 
 

I agree with at least one other person on this topic.
 
Can't be bothered to read 53 pages, but I can safely assume that's true.