State of the League and our chances

[cheron85]

Newcomers may not know that the creature called"Albert" is an alien who lives in a distant

galaxy,where football isn't played on grass with a ball.It's played on computer using,graphs.stats

and spreadsheets.

 

He has been banished for constant Trolling,don't reply to his posts it only encourages him.Also

he did the same thing a couple of years ago,and got everything totally wrong.Teams just wouldn't

perform like they were supposed to.

 

Leave Albert alone! He's a protected species like B4...

[Albert]

Being an actuary by profession, there's nothing I like better than a well constructed probability model(which is what this is - note for all similar pedants, the stats part is the historic analysis that has created the parameters for Albert to use in calibrating his forward looking model).

The assumption of normality can be questioned in the curves but that's unlikely to be material given Albert is working with a pdf over a finite domain (maths ****** for the only possible outcomes from each match are 0,1 or 3 points hence the possible outcome for the season is "bounded").

Well done to the posters who quite correctly point out that statisticians (and actuaries) are defined amongst other things as "highly remunerated experts who can tell you today, with micrometric precision, why what they said yesterday would happen tomorrow did not come to pass".

Have a like Albert and please give us updates from time to time.

The data when collected fit a normal distribution remarkably well, but it was hard to calibrate perfectly, which leads to a few problems for the most exceptional results (i.e the 1 in 100+ season level stuff).

The hardest part was actually going from a series of Cumulative Distributions to "League Placing". I'd previously tried doing so by creating standard league tables, but ultimately they change enough from season to season, that even when calibrated couldn't be done to a standard I was happy with. The behaviour of two normal distributions is fairly trivial, and can in the end be boiled down to a success-fail (in this case) defined by a probability, but the issue was being able to compare this across a league. As the probabilities aren't equal I wasn't able to use a binomial distribution, and ended up needing to use a Poisson Binomial Distribution with a Discrete Fourier Transform. Not exactly that much work in the end, but it takes a while to output if I want to calculate across the entire league. For the output posted, I basically set it running and went for a stroll.

I would probably try and optimise it a bit more, but it's not exactly a high priority, it was just something to test out a program I was trying to get a bit more familiar with.

[StaffsRam]

2 from 4 for the autos and I'd wager that the 2 that end up 3rd and 4th will be at Wembley.

[Albert]

2 from 4 for the autos and I'd wager that the 2 that end up 3rd and 4th will be at Wembley.

The reason I like this kind of analysis is that it gives some kind of direction to this kind of discussion. At this time, that top 8 are on:

1. Bournemouth: 41.5%

2. Ipswich: 34.7%

3. Middlesbrough: 34.7%

4. Derby: 34.5%

5. Brentford: 22.1%

6. Watford: 12.6%

7. Norwich: 9.0%

8. Wolves: 9.0%

Whilst these are the 4 most likely, at this time it is still significant chance that someone outside the top 4 will finish top 2. That's not that surprising when you consider that there is still Watford, Norwich, Brentford and Wolves all still in the battle.

[Van der MoodHoover]

The data when collected fit a normal distribution remarkably well, but it was hard to calibrate perfectly, which leads to a few problems for the most exceptional results (i.e the 1 in 100+ season level stuff).

The hardest part was actually going from a series of Cumulative Distributions to "League Placing". I'd previously tried doing so by creating standard league tables, but ultimately they change enough from season to season, that even when calibrated couldn't be done to a standard I was happy with. The behaviour of two normal distributions is fairly trivial, and can in the end be boiled down to a success-fail (in this case) defined by a probability, but the issue was being able to compare this across a league. As the probabilities aren't equal I wasn't able to use a binomial distribution, and ended up needing to use a Poisson Binomial Distribution with a Discrete Fourier Transform. Not exactly that much work in the end, but it takes a while to output if I want to calculate across the entire league. For the output posted, I basically set it running and went for a stroll.

I would probably try and optimise it a bit more, but it's not exactly a high priority, it was just something to test out a program I was trying to get a bit more familiar with.

Tail events is what usually messes up my models and the usual challenge is that Normal (Gaussian) curves have thin tails when compared to eg Students-t. But for the body of the stats if the fit works (Least Squares method?) then I fall back on them as the mathematics is more tractable.

The one thing you have not quite captured in your model is that based on N seasons (where N is more or less any natural number you can think of) Mostyn is more than 50% likely to be disagreeable over the course of a season.

[Albert]

Tail events is what usually messes up my models and the usual challenge is that Normal (Gaussian) curves have thin tails when compared to eg Students-t. But for the body of the stats if the fit works (Least Squares method?) then I fall back on them as the mathematics is more tractable.

I'd probably need a dedicated computer running the calculations to use any other distribution sadly, hence using a normal distribution.

The one thing you have not quite captured in your model is that based on N seasons (where N is more or less any natural number you can think of) Mostyn is more than 50% likely to be disagreeable over the course of a season.

When Nigel was here that value was far higher than 50%.

[DEL]

To this point I felt that our chances were pretty self explanatory, we are one of the favourites to go up, but due to the compact nature of the top of the table there are many who could claim that. With the loss to Forest though it's worth asking the question of exactly where we are at chances wise, how many are in with such chances, how the rest of the league is shaping up, and ultimately how much damage was truly done on the weekend.

To start with, rather than go back in depth through the methodology, essentially the code used to generate probabilities from the league table uses fairly standard normal distributions based on Points Per Game (PPG) to this point in the season, which is then used to generate a probability distribution for PPG for the rest of the season, and hence create a probability distribution of points. That is, you can get a percent chance of a team getting P points. This is then doing for the entire league, and used to then generate the chance of finishing above N teams, hence finding the probability of finishing in a particular position. For example, Derby's results for this season so far:

Top 2: 33%

Playoffs: 49%

Midtable: 19%

Relegation: 0%

So basically, in 10 seasons you'd expect us to up 3 times, end up in the playoffs 5 times and midtable twice (well, upper midtable) and not relegated in any of them.

This can be done for the entire table. For the purposes of data presentation, anything under 0.001% is to be considered 0%, and anything over 99.999% is to be considered 100%. First off, for the automatic promotion places:

1. Ipswich - 46%

2. Bournemouth - 39%

3. Middlesbrough - 33%

4. Derby - 33%

5. Brentford - 21%

6. Watford - 12%

7. Norwich - 8%

8. Wolves - 8%

That's 8 teams with any kind of realistic chance of the autos at this time. At this point Ipswich are in the best position, but nobody is more likely than not. That is an important point, there are no teams over 50% chance, and there are 5 with over a 1 in 5 chance. It speaks volumes about how tight the battle for the Top 2 really is right now. Below is a pie chart of the data above:

Note: Other includes Sheffield Wednesday, Blackburn, Birmingham and Forest

As for the playoffs:

1. Brentford - 51%

2. Middlesbrough - 50%

3. Derby - 49%

4. Watford - 47%

5. Bournemouth - 47%

6. Norwich - 43%

7. Wolves - 43%

8. Ipswich - 42%

9. Sheff Wed - 11%

10. Blackburn - 7%

12. Birmingham - 4%

14. Forest - 3%

15. Bolton - 1%

16. Cardiff - 1%

From this you can see that at this time we are one of the favourites for the playoffs. You'll also notice that again there are a lot of teams in with a very good chance, thought not as tight as with the Top 2. Carefully note that the probabilities here don't reflect who is most likely to finish higher, as many are likely to be in the Top 2 (i.e. Us, Ipswich, Bournemouth, Middlesbrough). As before, here is the above data in terms of a Pie Chart:

Note: Other includes Charlton, Fulham, Huddersfield and Reading

Finally we can consider the relegation battle, though it's not that interesting this year:

1. Blackpool - 100%

2. Wigan - 83%

3. Millwall - 57%

4. Brighton - 19%

5. Rotherham - 19%

6. Leeds - 8%

7. Reading - 4%

8. Charlton - 2%

9. Fulham - 2%

10. Huddersfield - 2%

11. Bolton - 1%

12. Cardiff - 1%

13. Forest - 1%

For some clarification, Blackpool's chance is given as 99.994%. That's about a 1 in 15,870. They are almost certainly down. It would be a miracle if they survived. Beyond that, Wigan are in real trouble, as are Millwall. At this point I would be surprised if any of the three of them played in the Championship next season, but with that said, Millwall have a greater chance of staying up than we do to end up top 2. Here is the Pie Chart of this:

Note: Other includes Birmingham, Blackburn and Sheffield Wednesday

Long story short, the league is tight at the top, light at the bottom. It would seem that it's more a case of a strong league than a weak one on that basis, at least on the basis that there are more teams capable of beating eachother, rather than one or two strong teams stomping the league.

As an aside to all this, many might wonder how much damage the Forest defeat did, and how much good the Ipswich win did. Well, consider where we are now in terms of top 2 chances, and here are the changes in chances removing those matches:

Current: 32.5%

Without Ipswich: 25.0% (-7.5%)

Without Forest: 43.3% (+10.8%)

Without either: 35.5% (+3%)

So long story short, the Forest loss did more damage to our chances than the Ipswich win helped, but ultimately without the Ipswich match we'd be far worse off. We did however take a lot of wind out of Ipswich's sail of course:

Current: 45.7%

Without us: 57.3% (+11.6%)

Additionally it's worth putting into perspective what a run could do now, either way.

Winning:

1. 38.1% (+5.6%)

2. 43.9% (+5.8%)

3. 49.6% (+5.7%)

4. 55.3% (+5.7%)

Draws:

1. 27.2% (-5.3%)

2. 22.3% (-4.9%)

3. 17.9% (-4.4%)

4. 13.7% (-4.2%)

Losing:

1. 22.2% (-10.3%)

2. 13.7% (-8.5%)

3. 7.4% (-6.3%)

4. 3.4% (-4.0%)

These all are assuming our opponents move along at the same rate. Any slip up from them could see a different scenario.

Ultimately though we're doing well in a tight league which has shown anything can happen. Done right from here we have a very good chance of going up, whether that be by the Automatic spots or playoffs. The key is patience though, which at the moment there doesn't seem a lot of on here.

You need get a life...

[turdburgler]

If this is a model you've created to get your head round something at work, have you put it against a season past??

Find the half way point in say 2010. Apply your wizardry and see how well it weighed against the actual season end??

It seems this awesome bit of research needs its moment in the sun!!!

Or have I missed the point. I'm only a GCSE grade D merchant when it comes to da Math.

[Angry Ram]

Er... It's called any thread that Albert starts... C'mon Angry you've been around long enough to know that!

Im just palying with Uncle Albert, been bored lately we have not lost to Forest for a while.

Mind you if Carlsberg did boring posts... Albets yer man. Zzzzzzzzz.

[Albert]

If this is a model you've created to get your head round something at work, have you put it against a season past??

Find the half way point in say 2010. Apply your wizardry and see how well it weighed against the actual season end??

It seems this awesome bit of research needs its moment in the sun!!!

Or have I missed the point. I'm only a GCSE grade D merchant when it comes to da Math.

It was calibrated with many years worth of Championship data which compared team performance up to a point (analysis was done at several points of the seasons). At such a point as I have the time and actually feel like doing it I might recalibrate it a bit with more data just to make sure it's working best it can.