The Probability Thread 2009

Mackster

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So 76.16 is the mean average, however I'm sure it will be less this season

Projected mean based on current form is:

1st Brentford - 83.6
2nd Gillingham - 75.8
3rd Exeter - 75.2
4th Bury - 73.2
5th Rochdale - 72.2
6th Wycombe - 72.0
7th Chesterfield - 71.6
8th Shrewsbury - 66.00
9th Bradford - 63.80
 

Mr Jinx

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got to agree with the Mackster here an look at current form. Wycombe are droping like a stone whereas Chesterfield are flying and should easily sneak a playoff spot. The way we're going with Fleetwood still to shine I'd say the last auto spot is very much a distinct possibility.
 

Chalicefc3

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Good work Poundstretcher-I think that you'd be hard pushed to find a single person who'd contest the legitimacy of your findings.

Makes for sound reading but it certainly does not account for Tisdale's team tactics. Any chance of formulating a graph or two to analyse his team choices each week?

Thank you for the Maths - very mind boggling yet awesome!!

City for 3rd - happy days.
 

mammooman

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What is 'current form' ? Just curious like. Is it the last 3/5/7/83 games?

There are so many factors to put into the equation such as weather, playing surface, '12th man', oppositions aims...... I look at the stats and graphs produced as very interesting and could be used to provide a logical estimation on our and other teams finishing position, something similar to what bookies would use. But as a fan I still prefer the 'support the team all the way and lets just wait and see' method.
 

Mackster

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What is 'current form' ? Just curious like. Is it the last 3/5/7/83 games?

There are so many factors to put into the equation such as weather, playing surface, '12th man', oppositions aims...... I look at the stats and graphs produced as very interesting and could be used to provide a logical estimation on our and other teams finishing position, something similar to what bookies would use. But as a fan I still prefer the 'support the team all the way and lets just wait and see' method.
The current form used is 8 games. But I have to agree any statistical analysis is based on historical data and doesn't take into account not only the things you mentioned, but admin point deductions, new manager syndrome, star player injured.

I know it's something the bookies use to help compile odds and they factor in these things in for Premier League or maybe Championship, but they rely more heaviliy on statiscal analysis for lower league football, and it is here you can sometimes get some real value based on your knowledge of the game.

Last year I won £300 betting against Stevenage at the end of the season because I could see they were gone. Obviously it wasn't guaranteed, but the odds were totally skewed for about 3 weeks. This year it was fairly obvious to many that Chesterfield were well capable of making a play-off charge and the bookies odds were so skewed towards Shrewsbury, Bradford & Wycombe that Chesterfield were excellent value (Shame my Paddypower account was empty and didn't bother).

Statistics would also tell you that Weymouth would comfortably stay up in the BSP, but we all know otherwise. Interestingly after the bookies got stung, they refused to take any bets on any of the Weymouth games because Probability in their case had been replaced by Chaos Theory.
 

Gozzer

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So, it's that time of the season again. The time when we start to get our calculators out and we begin to wonder about chance, probability and stochastic independence (well, that last one might just be me). I figured that it wouldn't be long before Lammie started nagging me about numbers - and in fairness, the "how many points..." threads have been dying for a definitive contribution for some time - so I settled down to figure out the best way of approaching things.

We've got an unbelievably tight division this year - with 78 games to play, every last fixture impacts on something: form and fortune interplay so closely that we could conceivably finish almost anywhere in the top half, and the playoff candidates could form up from any of many. So the logical way was to run a Monte Carlo experiment: simulate every match from here until the first weekend of May and sum the league table up to that point, before taking into account its implications for future fixtures. There are, in fact, 16,423,203,268,260,658,146,231,467,800,709,255,289 different result combinations from here to the end of the season (that's 16 billion billion billion billion) - even without thinking of goal difference...

I calculated probabilities in the Bayesian manner, looking to use home and away records separately, and averaging out the win/loss percentages to find the chance of particular outcomes. I then used a random process to simulate the result, randomly selecting the scoreline using a proportional representation of the season's league two results to date, and then updated the league table (e.g. 24% of home wins are 1-0, 16% are 2-0, etc).

For example, the next game of the season is Accrington v Lincoln. Stanley at home have an 8-5-7 record (40%-25%-35%), while the Imps are 7-3-9 on the road (37%-16%-47%). Averaging these out gets you a 44% chance of a home win, 20% on the draw and 36% on the away win. With the scoreline, this data was added to the league table, and used for the subsequent matches.

I then ran the entire league programme through 500 times (that's 39,000 simulated matches), to find out: (a) the average number of points gained by the third-placed side, (b) the average number of points gained by the seventh-placed side, (c) City's finishing position, and (d) the identity of the Champions.

Points for Promotion
This graph seems to bear out much of what's been discussed - 78 points is pretty certain to get you there, but if you don't get that many, then you've still got a chance. Four wins from our last six could well see us up. Mean: 76.16


Points for the Playoffs
It's conceivable that one more point could make the playoffs... conceivable, but really not likely. 72 points will get you there beyond reasonable doubt - two wins from six should mean we make the playoffs: should be no last-day worries here... in theory. Mean: 70.06



City's finishing position
Saying that, there's still a 15% chance we'll miss the playoffs altogether... and finishing so poorly we end up 12th isn't out the question. Still, at the other end, we have better than a 1 in 4 chance of making the top three - and one year in every 45, we'll be Champions from here. Mean: 5.13



Who else could win it?
The numbers point very, very convincingly towards Brentford. Don't rule the others out - anything can happen, after all, but three times in four the title goes back to West London.



Oh, and MikeB, if you're reading this, feel free to stick this in the programme. Everyone should have the chance to read mathematics this interesting.
I'm not going to argue with that!

Except...

Have you made any allowance for which games the City v PV ref will be officiating? He could blow any statistics out of the water!

What if City are sidetracked by pursuing glory in the Devon Bowl? ;)
 

finetime

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What would be interesting is to run it at the half way stage and then compare it to the odds at the bookies and see if you would actually make any money.

A lot more work, I have to admit.
Bookies employ hoardes of maths and programming experts to develop prediction programmes so I doubt you can catch out the system so easily.

Betfair on the other hand is a different matter...
 

STURTZ

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Fascinating statistics.

Who would have thought that four teams wear blue whilst only us and Brentford wear red and white!?
 
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Like Poundstretcher I’ve been working on a final table model using Monte Carlo / Bayesian methods (…. blah blah blah). I guess the main difference is the percentage assigned to win/draw/loss for each game is based on a ranking for each team, e.g. all games between promotion contenders are assigned 50%/25%/25% (Home/Draw/Away), promotion contenders v “low” performing teams 70%/20%/10% or when away 20%/30%/50% - but the final outcome will not be to different.

So first pretty picture (graph) with City’s predicted points – showing 90% 50% and 10% percentile and the model’s result for Auto promotion and Play-off place shown with 90/50/10 percentiles. So currently the model suggest Auto Promotion will most likely be gain with between 74-78 point (76 as an mid-point), Playoff 68-72 (70 average), Exeter’s range 70-78 (74 mid-point).
Over time since 14/3 the graph shows City’s likely points tally has gone down a bit but the Auto Promotion points have gone down more, therefore our chance of promotion will have gone up (a bit).



My finial two pictures (a little easier to understand) Percentage chance for promotion.



Percentage chance for gaining at least Playoff place



(note: the two entries for 28/3 are because I made some changes to some teams “rankings” – inc. moving Gillingham & Chestefield into the same group as other promotion/playoff contenders.)
 
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