Statistics and Mathematical Modelling...and Promotion

Banana · 22 Feb 2015

After all the talk about Statistics and Mathematical Modelling being the new direction of the club over the past week or so; we've decided to take the same direction to predictions at GPG Towers. Some of you will remember we tried this before towards the end of the 2009 Promotion Season where we successfully predicted that Brentford would be promoted with time to spare.

So how does the (non-upgraded) model come out this season? We ran 1,000,000 simulations of all the remaining Championship fixtures. From this we predict that we have a 10.65% chance of finishing in the Top 2 places, and a 57% chance of ending up in a play-off spot (places 3-6 inclusive). However the most likely place we believe we will finish is 7th with an 18.1% chance. Full results in this table:

and the same in a chart...

How many points will be required to get promotion? Well the same set of 1,000,000 simulations suggest that 89 points will get promotion over 96% of the time. We are currently sitting on 55 points so this would suggest we need 34 points from our remaining 14 matches - or an average of a rather heady 2.43 points per match. However if you are more optimistic 84 points will give us half a chance of automatic promotion which is a 2.07 points per match - 2 wins every 3 matches.

Here's are the points required for automatic promotion and the same info in a chart

Finally, the play-offs. 79 points would give us a 95% chance of promotion (give or take) requiring 24 points from our remaining matches at a rate of 1.71 per match. Below 79 points and the probability of making the play-offs drops-off rapidly - only three points (or one loss) and our chances of making 6th place are down to roughly 60%.

Here's the stats for the play-off positions.

N.B. Horizontal Axis is incorrect

Of course nothing is played-out on the computer, and a few changes in results and the end-state predictions change too. We'll publish updates accordingly.

belvederebee · 22 Feb 2015

My brain hurts.

chizbee · 22 Feb 2015

Whooooosh!!

Ace Face · 22 Feb 2015

This will upset the GPG group.

N16QPR · 22 Feb 2015

We have 33,65% chance of finishing 5th or 6th, as oppose to 28,31% chance of finishing 7th or 8th.

badgerbee · 22 Feb 2015

We have a 68% chance of either going up automatically or being in the Play-Offs.......

EarleyBee · 22 Feb 2015

N16Bee said:
We have 33,65% chance of finishing 5th or 6th, as oppose to 28,31% chance of finishing 7th or 8th.

I liked the one from last season, that over time accumulated the teams that could no longer mathematically catch us, hopefully we are not too many weeks away from being able to start that one

seanrs · 22 Feb 2015

The main thing I know and care about is we have 0% chance of getting relegated and you don't need to be Carole Vorderman to work that one out !!

JTofBFC · 22 Feb 2015

There is a 100% chance of me not visiting this thread again..........

opinions5u · 22 Feb 2015

Do you have time to run it for League One? Pretend you give a monkeys!

I'm going Oldham 12% chance of play-offs!

BYOBee · 22 Feb 2015

Can we ask MB for his statistical analysis? Then we can all relax for the rest of the season.

Banana · 22 Feb 2015

EarleyBee said:
I liked the one from last season, that over time accumulated the teams that could no longer mathematically catch us, hopefully we are not too many weeks away from being able to start that one

We can't finish lower than 18th, and that's less than a one-in-a-million chance.

opinions5u · 22 Feb 2015

badgerbee said:
We have a 68% chance of either going up automatically or being in the Play-Offs.......

It's yours to throw away!

ade211 · 22 Feb 2015

Banana said:
After all the talk about Statistics and Mathematical Modelling being the new direction of the club over the past week or so; we've decided to take the same direction to predictions at GPG Towers. Some of you will remember we tried this before towards the end of the 2009 Promotion Season where we successfully predicted that Brentford would be promoted with time to spare.

So how does the (non-upgraded) model come out this season? We ran 1,000,000 simulations of all the remaining Championship fixtures. From this we predict that we have a 10.65% chance of finishing in the Top 2 places, and a 57% chance of ending up in a play-off spot (places 3-6 inclusive). However the most likely place we believe we will finish is 7th with an 18.1% chance. Full results in this table:

View attachment 15826

and the same in a chart...
View attachment 15823

How many points will be required to get promotion? Well the same set of 1,000,000 simulations suggest that 89 points will get promotion over 96% of the time. We are currently sitting on 55 points so this would suggest we need 34 points from our remaining 14 matches - or an average of a rather heady 2.43 points per match. However if you are more optimistic 84 points will give us half a chance of automatic promotion which is a 2.07 points per match - 2 wins every 3 matches.

Here's are the points required for automatic promotion and the same info in a chart

View attachment 15825

View attachment 15822

Finally, the play-offs. 79 points would give us a 95% chance of promotion (give or take) requiring 24 points from our remaining matches at a rate of 1.71 per match. Below 79 points and the probability of making the play-offs drops-off rapidly - only three points (or one loss) and our chances of making 6th place are down to roughly 60%.

Here's the stats for the play-off positions.

View attachment 15824

View attachment 15821

Of course nothing is played-out on the computer, and a few changes in results and the end-state predictions change too. We'll publish updates accordingly.

As you may know I love this sort of stuff. See stats thread. At present we are predicted to finish about seventh but very near sixth place. Read somewhere that for the Premiership the points range at the end of the season is plus/minus seven. No idea what it is for championship but assume the same so if Lady Luck smiles on us could easily get in the playoffs. Statto predicts 76 total so range would be 83 to 69.

http://www.statto.com/football/stats/england/league-championship

badgerbee · 22 Feb 2015

EarleyBee said:
I liked the one from last season, that over time accumulated the teams that could no longer mathematically catch us, hopefully we are not too many weeks away from being able to start that one

Beat Blackpool on Tuesday and we'll only need another 3 points to make it impossible for them to overtake us........

jmsljj · 22 Feb 2015

Statistics are useful thanks banana. We have to play two of the top eight teams Ipswitch have to play six of the top eight teams, statistically do we have a better chance of finishing above Ipswish?

Babbelfish · 22 Feb 2015

What data did you put in to get these probabilities ???

Banana · 22 Feb 2015

jmsljj said:
Statistics are useful thanks banana. We have to play two of the top eight teams Ipswitch have to play six of the top eight teams, statistically do we have a better chance of finishing above Ipswish?

In this (probably unprofitable) model, we finish below Ipswich 58% of the time.

Banana · 22 Feb 2015

Babbelfish said:
What data did you put in to get these probabilities ???

Current league table (with home/away, wins, draws, losses)
Remaining Fixtures
Dressing room harmony

Note: One of above three may not appear in the model

Babbelfish · 22 Feb 2015

Banana said:
Current league table (with home/away, wins, draws, losses)

Remaining Fixtures

Dressing room harmony

Note: One of above three may not appear in the model

And how did you work out the range of possible results of the remaining fixtures? Genuinely interested!

Banana · 22 Feb 2015

Babbelfish said:
And how did you work out the range of possible results of the remaining fixtures? Genuinely interested!

It's on the thread linked to in the first post https://griffinpark.org/forums/showthread.php?t=71097

reheat104 · 22 Feb 2015

Just to add a fact............In the 11 years of the Championship, 76 points would have got you a Play Off spot without having to worry about goal difference.
Be interesting to see how many pts will actually get one this season.

Nottsbee · 22 Feb 2015

If you make the assumption that the play-offs are a lottery (I know, I know), then we can add a 25% chance to the 10.65% chance of automatic promotion.

That gives us a more than one in three chance of playing Premier League football next season. I'll settle for that.

Banana · 22 Feb 2015

Nottsbee said:
If you make the assumption that the play-offs are a lottery (I know, I know), then we can add a 25% chance to the 10.65% chance of automatic promotion.

Er...no

You can take the sum of 3-6th place (57%) and take 25% of that (14.25%) to get chances of going up via the play-offs. So total promotion "chances" are 14.25% + 10.65% = 24.9%

bees66 · 22 Feb 2015

I like this thread.. Warburton to the rescue..

Nottsbee · 22 Feb 2015

Banana said:
Er...no

You can take the sum of 3-6th place (57%) and take 25% of that (14.25%) to get chances of going up via the play-offs. So total promotion "chances" are 14.25% + 10.65% = 24.9%

Ah yes you're quite right, of course. I thought it seemed a bit optimistic.

So we have almost a one in four chance of playing Premier League football next season. I'll still settle for that.

Beat Blackpool on Tuesday and it should edge up to more than 25%!

Babbelfish · 22 Feb 2015

Banana said:
It's on the thread linked to in the first post https://griffinpark.org/forums/showthread.php?t=71097

Thanks. I see the Bayesian model is used.

ade211 · 22 Feb 2015

Babbelfish said:
Thanks. I see the Bayesian model is used.

Are we about to sign him? Not many Reverends play in the league. Just the new thinking we need to propel ourselves forward.

Babbelfish · 22 Feb 2015

ade211 said:
Are we about to sign him? Not many Reverends play in the league. Just the new thinking we need to propel ourselves forward.

Ha ha! Had a look at what this model entailed and quickly got lost
https://math.uc.edu/~siva/mdbayes/chap2p.pdf

Babbelfish · 22 Feb 2015

All of this made me think: unless you are a very proficient mathematician, you have no way of judging the merit of any of these statistical models. Not just Banana's model, but the whole approach we will be embracing next season. MB obviously knows what he is doing - his company has been hugely successful. But almost all of the rest of us have to take this on trust. We haven't the knowledge to argue with statistical modelling. We might argue with the philosophical approach but such arguments will be based on instinct. Ultimately of course results count. But even results just tell you about a period of time, not whether a model works in the long term. Will be interesting.

grepo · 22 Feb 2015

How on earth do you quantify dressing room harmony. We do appear to still have bucket loads (what's that in mls) of that. What about creativity, moral, perceptive advantage, mood on the day, the support and mood of the supporters, Mr Strouds of the world, lady luck and all the wonderful cocktail of non-mathematically measurable influences that thank goodness make football such an unpredictable and exciting game.

Stanley · 22 Feb 2015

Wing Commander Charles Reep would be loving all this and telling us to told us so over 65 years ago.....

Aussie Bee · 23 Feb 2015

Banana

Can you post what the modelling predicts as the final top 7 spots please?

teesbee · 23 Feb 2015

grepo said:
How on earth do you quantify dressing room harmony. We do appear to still have bucket loads (what's that in mls) of that. What about creativity, moral, perceptive advantage, mood on the day, the support and mood of the supporters, Mr Strouds of the world, lady luck and all the wonderful cocktail of non-mathematically measurable influences that thank goodness make football such an unpredictable and exciting game.

You missed out marital equilibrium, underpant comfort level, and hangnail incidence. As you say - alchemy.

hobbsy · 23 Feb 2015

Stanley said:
Wing Commander Charles Reep would be loving all this and telling us to told us so over 65 years ago.....

Quite, although we'd have a lot of midfielders standing around not doing much.

Aussie Bee · 23 Feb 2015

Never heard of Charles Reep - very interesting

http://en.wikipedia.org/wiki/Charles_Reep

hobbsy · 23 Feb 2015

Aussie Bee said:
Never heard of Charles Reep - very interesting

http://en.wikipedia.org/wiki/Charles_Reep

You should read The Numbers Game, it's well covered in there amongst many other things.

vcmazz · 23 Feb 2015

Banana said:
Finally, the play-offs. 79 points would give us a 95% chance of promotion (give or take) requiring 24 points from our remaining matches at a rate of 1.71 per match. Below 79 points and the probability of making the play-offs drops-off rapidly - only three points (or one loss) and our chances of making 6th place are down to roughly 60%.

Utter tummy rubbish. :thetruth:

I said 4 games ago that a 50% win rate (9 out of 18) would be enough to make the play-offs. 2 out of 4 so far so right on track. 7 out of the last 14 gives us 76 points. The pointage achieved by the team finishing 6th in the 2nd tier over the past 15 years is as follows:

68 (x 1)
70 (x 2)
73 (x 2)
74 (x 3)
75 (x 5)
76 (x 2)

No team has required more than 76 points for at least 15 years to make the play-offs and even then, just twice. So where do you get 60%ish for 76 points? Eh? Eh? :suspect:

AB · 23 Feb 2015

vcmazz said:
Utter tummy rubbish. :thetruth:

I said 4 games ago that a 50% win rate (9 out of 18) would be enough to make the play-offs. 2 out of 4 so far so right on track. 7 out of the last 14 gives us 76 points. The pointage achieved by the team finishing 6th in the 2nd tier over the past 15 years is as follows:

68 (x 1)
70 (x 2)
73 (x 2)
74 (x 3)
75 (x 5)
76 (x 2)

No team has required more than 76 points for at least 15 years to make the play-offs and even then, just twice. So where do you get 60%ish for 76 points? Eh? Eh? :suspect:

Interesting and encouraging that 76 has been enough in last 15 years. However, despite internally being new brentford, the outside world is still "brentford innit?" so need to factor in the need for an unprecedented number of points just because it is us. Also, given that the top 8 all seem to be on similarly strong runs, 8 wins from the remaining 14 sounds about right intuitively.

Tunis Bee · 23 Feb 2015

Banana said:
Finally, the play-offs. 79 points would give us a 95% chance of promotion (give or take) requiring 24 points from our remaining matches at a rate of 1.71 per match. Here's the stats for the play-off positions.

Interestingly (or not, depending on your view), the 1.71 points per match which your model gives us for a play off place is exactly our ratio up until this point in the season. Just need to hold that form!

Banana · 23 Feb 2015

vcmazz said:
No team has required more than 76 points for at least 15 years to make the play-offs and even then, just twice. So where do you get 60%ish for 76 points? Eh? Eh? :suspect:

Fair point.

I mean that in 60% of simulations the 6th placed team gets 76 points or fewer, and in 40% of the cases the 6th place team had 77 or more.
I think you are saying that because in the last 15 years that the 6th place team hasn't required more than 76 points then 76 points has a (95%?) certainty of making the play-offs.

And I can see your point that that makes my model appear sh*t (and it probably is to be fair otherwise I'd be buying a few football clubs)

However, it would be interesting to see the points distribution after 32 matches in each of those seasons - this season is close between the top 8 teams and then has a drop-off. In other seasons the points distribution has been different (of course).

But right now I would say we need more than 76 points

Just saw this from a few seasons ago that makes an interesting visual http://www.footballforums.net/showthread.php/271690-Championship-Run-in-Ladder

Where are you getting the historical information from BTW?

Banana · 23 Feb 2015

One further point.....

After 32 matches the 6th place team had the following points:

2014-15:: 56 (Watford)
2013-14:: 50 (Reading)
2012-13: 50 (Middlesborough)
2011-12: 53 (Cardiff)
2010-11: 53 (Leeds)
2009-10: 49 (Cardiff)
2008-09: 51 (Sheff Utd)
2007-08: 48 (Ipswich)
2006-07: 53 (Cardiff and Sunderland)
2005-06: 54 (PNE)
2004-05: 51 (Derby)

or in a ladder

56: 2015
55:
54: 2006
53: 2012, 2011, 2007
52
51: 2009, 2005
50: 2014, 2013
49: 2010
48: 2008

Looks like more points are required for 6th place this season than in any of the previous 10 seasons....

kevalutonbee · 23 Feb 2015

ade211 said:
Are we about to sign him? Not many Reverends play in the league. Just the new thinking we need to propel ourselves forward.

If it is the Rev Ashley Bayes please God no

King Bee · 23 Feb 2015

What stats tool did you use Banana?

nick logan · 23 Feb 2015

seanrs said:
The main thing I know and care about is we have 0% chance of getting relegated and you don't need to be Carole Vorderman to work that one out !!

There was never any danger of that , and i am now going into the store room to do a massive scream

nick logan · 23 Feb 2015

King Bee said:
What stats tool did you use Banana?

No Coat

brooks · 23 Feb 2015

Lies, damned lies, and statistics

Banana · 23 Feb 2015

King Bee said:
What stats tool did you use Banana?

My code (and excel for the charts)

Banana · 23 Feb 2015

Here's something interesting for you.

Columns are:
1. Season
2. Points after 32 matches for the team in 6th place
3. Points after 46 matches for the team in 6th place
4. Difference between columns 2 and 3 (i.e. points gained by team in 6th place)
5. Column 3 divided by Column 2.

Code:

2015	56		23	1.458
2014	50	72	22	1.440
2013	50	68	18	1.360
2012	53	75	22	1.415
2011	53	75	22	1.415
2010	49	70	21	1.429
2009	51	74	23	1.451
2008	48	70	22	1.458
2007	53	75	22	1.415
2006	54	75	21	1.389
2005	51	73	22	1.431

The maximum points gained for 6th place between now and the end of the season is 23 (column 4) - that would predict 79 points required for the play-offs.
If we use the maximum ratio (1.458) and multiply 56 points by that then it predicts that 82 points are required to get into the play-offs

ade211 · 23 Feb 2015

kevalutonbee said:
If it is the Rev Ashley Bayes please God no

He is great at saving his team mates.

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