#### Poundstretcher

##### Active member

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.