[Archived] The math's behind survival

[Glenn]

Reposted from Facebook, with permission (it's by a former regular of this parish) because I love geeky math stuff like this

 

The maths behind survival

Here is a list of the teams we can possibly finish above and the statistical probability of achieving that outcome.

This is based on the four events each head to head involves.
For each head to head there are 81 permutations of possible results. Three possible outcomes in each event (win, lose, draw) across four events gives 3 to the power of 4 possible outcomes equals 81.

Form is not taken into account. This is based on each outcome having equal probability.

Bristol City 1 chance in 81 (1.23%) provided we overhaul a 9 goal difference.

Burton Albion 1 chance in 81 (1.23%). We win both ... they lose both.

QPR 3 chances in 81 (3.70%) provided in the two cases where QPR draw a game we win at least one of our two wins by more than 1 goal or the QPR drawn game involves them scoring less than 2. If it is a 2-2 draw and we win both our games 1-0 then goal diff and goals scored will be equal. If it then goes to the head to head results we win!

Nottingham Forest. 6 chances in 81 (7.40%) or if we make up the three goals difference in the cases when final points are equal then 13 in 81 (16.05 %).

Birmingham City. 22 chances in 81 (27.16%). Unless in the cases where final points are equal City overturn a 7 goal difference it becomes 13 in 81 (16.05%).

Hope that's made everything clear!

[47er]

That's excellent! We really are up against it statistically eh? Let's hope the players don't read that!

[jim mk2]

The Grammar Vigilante from Bristol is eyeing up your thread title, Glenn!

 

[jim mk2]

So we have about a 1 in 4 chance of catching Birmingham ? 

[Mike E]

Re: The title, the 'math' certainly is not behind survival!

[superniko]

This only takes into account all things being equal. I.e every team being rated exactly the same. 

This isn't the case and Huddersfields win tonight alone proves that.

The probability of Birmingham winning on Saturday has gone from 37.5% this morning to 41.7% now, on the back of Huddersfield motivation / resting players. 

You'd have to give each team in the league a rating, then model and simulate the remaining matches over 100,000+ times to see real probability of each outcome. 

Some bookmakers may have done this (others copy). 4/9 Rovers v 2/1 Birmingham v 25/1 Forest is your best guide. I.e we've got a ~69% chance of relegation, Brum ~33%, Forest ~4% and QPR ~2% obviously that adds up to 108% but the 8% is the bookmakers margin. 

E.g suggesting Bristol have 1.23% chance of relegation suggests they should be priced at ~80/1. Wouldn't back that with a gun at my head. 

[RevidgeBlue]

Was about to post similar. That guide is completely meaningless and inaccurate because it assumes each outcome is equally probable which they aren't due to form and variables such as injuries and things like Huddersfield already being in the playoffs and fielding a weakened side etc.

[Mike E]

Guys, the post itself states that it is based on all things being equal. It's meant to be for interest, not realism.

Obviously, you know how to come up with a 'realistic' analysis using the same principles but I don't see you sharing it.

[RevidgeBlue]

59 minutes ago, Mike E said:

Guys, the post itself states that it is based on all things being equal. It's meant to be for interest, not realism.

Obviously, you know how to come up with a 'realistic' analysis using the same principles but I don't see you sharing it.

It's not correct though. Its a bit like saying that x, y and z are the case but its basef on the assumption the world is flat.

I'd say the actual maths are as follows. (Might be stating the bleeding obvious but here goes)

The easiest route to survival is to finish above Birmingham.

We need a minimum of two points to have any mathematical chance of survival. That assumes BIRMINGHAM lose their last two games.

If they get one point we need 3.

If they get two points we need 4

If they get 3 or 4 we need 2 wins.

If they win their last two we have to as well and hope we finish above one of the other sides.

There's no way you can predict how Brum will do or put an actual probability on any of the above therefore we have to assume the worst and target six points. You would hope two wins would be enough to see us stay up at Brum's expense. Trouble is I can't see us getting one win let alone two.

[McClarky]

Ruined by the flagrant misuse of an apostrophe.

[Wing Wizard Windy Miller]

To be fair, if I was Huddersfield manager, I would be trying to gain a winning momentum going in to the play offs as they've been on a shocking run recently.

[1864roverite]

HTAFC will not want to finish lower than 3rd to ensure they are home in the second leg of the play offs. So IMO they will go for the win at Brum

[bazza]

Will we go for the win against Villa? I doubt it.

Too many rubber dingy men in the squad.

[Stuart]

Have to laugh at those slating the OP.

Of course it's ok to set some baseline assumptions, however wild, and hypothesise on that premise.

To say otherwise is to dismiss the entire basis of Science!

[blueboy3333]

7 minutes ago, bazza said:

Will we go for the win against Villa? I doubt it.

Too many rubber dingy men in the squad.

Rovers fans line streets in huge show of support as players arrive early for Villa game.

[Earlydoors]

21 hours ago, Glenn said:

Reposted from Facebook, with permission (it's by a former regular of this parish) because I love geeky math stuff like this

 

The maths behind survival

Here is a list of the teams we can possibly finish above and the statistical probability of achieving that outcome.

This is based on the four events each head to head involves.
For each head to head there are 81 permutations of possible results. Three possible outcomes in each event (win, lose, draw) across four events gives 3 to the power of 4 possible outcomes equals 81.

Form is not taken into account. This is based on each outcome having equal probability.

Bristol City 1 chance in 81 (1.23%) provided we overhaul a 9 goal difference.

Burton Albion 1 chance in 81 (1.23%). We win both ... they lose both.

QPR 3 chances in 81 (3.70%) provided in the two cases where QPR draw a game we win at least one of our two wins by more than 1 goal or the QPR drawn game involves them scoring less than 2. If it is a 2-2 draw and we win both our games 1-0 then goal diff and goals scored will be equal. If it then goes to the head to head results we win!

Nottingham Forest. 6 chances in 81 (7.40%) or if we make up the three goals difference in the cases when final points are equal then 13 in 81 (16.05 %).

Birmingham City. 22 chances in 81 (27.16%). Unless in the cases where final points are equal City overturn a 7 goal difference it becomes 13 in 81 (16.05%).

Hope that's made everything clear!

So does that mean there is a 40% chance we stop up and 60% chance we go Down? 

The sum of all those is about 40%

Is that how it Works? 

[Irishrover213]

Four points is the minimum needed but are relying on other results. 

If we get point on Saturday and Birmingham win were down 

On Saturday we must match(if they win we must also) or better Birminghams result. 

If we lose and birmingham draw it's a stay of execution IMO

One thing is for sure we can't get stage fright. They need to perform for 180 mines over the next two games and get results. Hopefully we can. One thing is for sure it's going to a nervy 90 mines 

 

[Paul]

Anything but relegation will be a surprise to me. I accepted that about 5.00 in the car park after the Barnsley defeat.

[DE.]

I accepted it on the day Owen Coyle was appointed.

[lraC]

Birmingham were 9/4 to beat Huddersfield before the the Wolves V Huddersfield game had taken place, but they are now 6/4. The only thing I can suggest is either a double on Birmingham to win and Villa to win with a one goal start which is 3.17/1  or add Forest in to that as well with a goal start, as that boosts the odds to 5.25/1.

That way, you either blow your money, or it goes to the final game, or we are relegated on Saturday and you go out and drown your sorrows on the profit.

[Earlydoors]

What is the maths now, Glenn's mate?

[Stuart]

If ROVERS WIN (51 pts):

Birmingham must only draw (51 pts, -7 GD worse off) or lose (50 pts).

Or, Forest must lose (48 pts) or draw (49 pts). If Forest win (51 pts), Rovers must win (51 pts) by a margin 2 goals better. E.g. 1-0 = 3-0.

 

If ROVERS DRAW (49 pts):

Birmingham can't be caught (50 pts)

Forest must lose (48 pts) - a draw sees Rovers relegated by -1 GD.

[Guest]

I've knocked up a Google Spreadsheet that anyone can download and use.

Just put the scores in the "Fixtures" worksheet, and it will simulate the league standings in the "League Table" worksheet.

Note: The link is read-only, so go to File -> Download as, and you should be able to save yourself a copy and pop your scores in.

[Claytons Left Boot]

If ROVERS LOSE

It's between us and Forest but Forest would have to lose by two more goals than we do, for us to stay up :-(

[Stuart]

The way this season has panned out, it would probably take 3 Ipswich goals to save Rovers from the drop!