State of the League

[Albert]

14 odd matches to play and we're exactly we're in an amazing position. Whilst it obviously doesn't take a detailed statistical analysis to say that we're in for a red hot chance at promotion, it is worth having a look at the table as a whole, with a particular eye on who we're going to face and what they can realistically try and achieve in these final months. 

 

First up, I'm currently fiddling with a new method of calculating chances of various league places. I was ultimately unsatisfied with the messy nature of using past tables and interpolating positions (i.e. position 2.25 and such) and decided to try a more `natural' way of calculating the chances of a team finishing in a certain position. Using little more than the current league table and some previous data on the standard deviations teams have from their average points per game over the first 3/4s of the season I'll thrown together a slightly new method (although it comes to pretty much the same answers as before, but that's another point all together. 

 

The system basically works by using teams average PPG and from them calculating a standard points curve. That is, a probability density of a team finishing on a certain number of points. The average of course is that simply played out to the end of the season. This uses a basic normal distribution for simplicity sake, and the standard deviation is calculated based on the performances of Championship teams from many seasons worth of data. This is roughly the method used before, but now there is a new system to determine the chance that a particular points score will receive a certain position. Basically the new method calculates position from these probabilities densities by likelihood of a certain points score beating `n' number of other teams based on their standard points curves. Whilst that sounds simple enough in practice, it's a fairly serious calculation. Long story short though it should give a nicer method of calculating position. 

 

Keep in mind there may be small errors (<1% odd) due to an approximation method to allow the method to actual be calculated in a reasonable amount of time. 

 

Starting with our own situation now, in terms of probability of finishing in various positions:

 

Derby

1st: 7.61%

2nd: 26.7%

3rd: 29.4%

4th: 18.9%

5th: 9.57%

6th: 4.22%

7th: 1.93%

8th: 0.89%
9th: 0.41%

10th: 0.17%

~Below 0.1%

 

Another way of looking at that would be:

 

Derby

Automatic: 34.3%

Playoffs: 62.1%

Other: 3.8%

 

For comparison sake, the old method gives:

 

Derby

Automatic: 36.6%

Playoffs: 60.6%

Other: 2.7%

 

As for automatic promotion battle, the real contenders are now down to:

 

1st

Leicester: 74.4%

Burnley: 13.9%

Derby: 7.6%

QPR: 2.8%

Forest: 0.6%

<0.1%

 

2nd

Leicester: 16.4%

Burnley: 37.5%

Derby: 26.6%

QPR: 13.1%

Forest: 4.8%

Wigan: 0.7%

Reading: 0.3%

<1%

 

Automatic

Leicester: 90.8%

Burnley: 51.4%

Derby: 34.2%

QPR: 15.9%

Forest: 5.4%

Wigan: 0.7%

Reading: 0.3%

 

So at this point it really is down to a race between Burnley, ourselves and QPR for that second automatic promotion spot, with Forest less likely to make it than Leicester to not. 

 

The next obvious question becomes the playoffs, which is a interesting battle in and of itself. 

 

Playoffs

Forest: 73.7%

QPR: 73.1%

Derby: 62.1%

Burnley: 46.6%

Wigan: 43.9%

Reading: 38.4%

Brighton: 19.6%

Blackburn: 19.6%

Leicester: 8.9%

Ipswich: 6.3%

Leeds: 5.5%

<1%

 

For clarity sake, Leicester are bolded to denote that they are in 1st, whilst QPR, Derby and Burnley are italic to denote that they are also serious contenders for the top 2. In any case, it's clear that the table will almost certainly end up something like:

 

1st: Leicester

2nd-4th: Burnley/Derby/QPR

 

Keep in mind that:

 

Top 6

Leicester: 99.7%

Burnley: 98.0%

Derby: 96.4%

QPR: 89.0%

Forest: 79.1%

 

Leicester, Burnley and Derby are all almost certainties at this point for at least the playoffs, with QPR very close too. Forest is the only one of those mentioned with a realistic chance of missing out, but 4/5 is pretty much there too. 

 

Anyhow, the real question are spots 5 and 6 (keep Forest as an open question). For that it basically becomes:

 

Playoffs

Forest: 73.7%

Wigan: 43.9%

Reading: 38.4%

Brighton: 19.6%

Blackburn: 19.6%

Ipswich: 6.3%

Leeds: 5.5%

<1%

 

From that Forest is likely, but still not definite and Wigan would be the pick of the remaining but Reading, Brighton and Blackburn all are in with a serious shout. Of course, of those teams we've played:

 

Derby 1 - 1 Blackburn

Brighton 1 - 2 Derby

Derby 1 - 3 Reading

Derby 1 - 0 Brighton

Blackburn 1 - 1 Derby

 

We still have another match against Reading to play. It's an odd one, beating Reading could be vital to us going up automatically, but losing to them would be losing the double over a potential playoffs opponent. That said, in the form we're in, we should be confident regardless of head to head records by this point. 

 

The next question of course is the relegation battle. 

 

Relegation

Yeovil: 87.6%

Barnsley: 76.7%

Millwall: 60.6%

Charlton: 34.2%

Doncaster: 28.7%

Bolton: 6.4%

Blackpool: 2.0%

<1%

 

Here it seems that Yeovil and probably Barnsley for that matter are pretty much already down, but you never know. Millwall is then the most likely for that third spot, but Charlton and Doncaster are certainly in trouble too. Might make an interesting battle. 

 

Then there's of course, mid table, those teams that aren't in a shout at either end at this time:

 

Midtable

Watford

Middlesbrough

Huddersfield

Sheffield Wednesday

Birmingham

Bournemouth

 

All that said, it should be an exciting end to the season, except maybe for those teams. Who knows though. 

[Ramchope]

This excites me. In more ways than one.

[RodleyRam]

Half way through reading this all I could hear in my head was:

 

"The Rams are going up,

The Rams are going up,

And now you're going to believe us,

And now you're going to believe us,

etc."

 

I think it's a shame that statistically the 3rd best team in the league does not go up, I don't like the play offs. A team who is the 6th best side in the league can get promoted, doesn't seem right to me.

 

(Before people start bleeting on at me about this, I know exactly why the play offs exist and that they make things interesting come the end of the season, doesn't mean I have to agree with it though!)

[DCFC_17]

you said it yourself albert "it obviously doesn't take a detailed statistical analysis to say that we're in for a red hot chance at promotion" 

[Gritty]

Albert

 

You have taken our current points per game which has seen us in 3rd position, and then essentially calculated that if we perform at the same rate for the rest of the season, and every other team performs at their same rate, we will most likely finish 3rd and they will all most likely finish in their current positions.  I know you have applied a confidence interval around that but I'm not sure that is really much new information.  

 

Now if you did something that looked at the points we scored vs teams in each quartile, and then worked out how many teams we play in each quartile for remainder of season that might tell you something interesting about our final points position. And if you repeated for our promotion rivals you might come up with a different predicted league table?

[davenportram]

If Wigan beat Forest on Sunday I reckon they will finish above them at the end of the season. They'd be 3 points behind with a game in hand

[zippy]

Albert

 

You have taken our current points per game which has seen us in 3rd position, and then essentially calculated that if we perform at the same rate for the rest of the season, and every other team performs at their same rate, we will most likely finish 3rd and they will all most likely finish in their current positions.  I know you have applied a confidence interval around that but I'm not sure that is really much new information.  

 

Now if you did something that looked at the points we scored vs teams in each quartile, and then worked out how many teams we play in each quartile for remainder of season that might tell you something interesting about our final points position. And if you repeated for our promotion rivals you might come up with a different predicted league table?

 

Scrap, scrap, ....................in the library Miss, it started with them just started swapping statistics, then someone threw a slide-rule and it all went bonkers 

[robglosta]

Delicious effort with the stats there, well played.

[Leicester Ram]

Out of interest Albert, what change could the result on Saturday to the stats?

 

Cracking post.

[CheltenhamRam]

Nice. How does this compare to the bookmakers?

[Albert]

Albert

 

You have taken our current points per game which has seen us in 3rd position, and then essentially calculated that if we perform at the same rate for the rest of the season, and every other team performs at their same rate, we will most likely finish 3rd and they will all most likely finish in their current positions.  I know you have applied a confidence interval around that but I'm not sure that is really much new information.  

 

Now if you did something that looked at the points we scored vs teams in each quartile, and then worked out how many teams we play in each quartile for remainder of season that might tell you something interesting about our final points position. And if you repeated for our promotion rivals you might come up with a different predicted league table?

Such things should even themselves out quite quickly, but on short enough scales such measures may well be useful (closer to the last 6 odd games for example).

As for measure just being a confidence interval, the key thing about this was as a show of what is reasonably attainable for various teams, not as a crystal ball. It's more a case of determining exactly who is and isn't a threat to various positions from here on out (i.e. Forest being effectively out of the automatic promotion race).

As from a purely mathematical perspective, the overall analysis was significantly more complex than simply applying points per game averages and confidence intervals. Producing a method of points per game to a league table is one of the harder parts of such analysis, but in this instance the method is now general enough that any new system to determine the points per game can actually be done quite readily, so we'll see what can be done from here with this method.

Out of interest Albert, what change could the result on Saturday to the stats?

 

Cracking post.

For just our match with us against Burnley, here are the top 2 chances for each results:

Current

Burnley: 51.4%

Derby: 34.2%

Draw

Burnley: 48.9%

Derby: 31.2%

Derby Win

Derby: 46.0%

Burnley: 36.9%

Burnley Win

Burnley: 68.4%

Derby: 18.7%

Basically, if we win we'll basically replace Burnley in their position, draw stays about the same and a loss puts up down around QPR's chances currently. It is a massive game.

Speaking of codependency of results, I might have a look into a way to include that in the data.

[Gritty]

Albert

Does your method predict that the most likely position for each team is their current position? If so, I think you have just said with stats that if everyone performs in the future as in the past, they will end up at the same place in the future.

[Albert]

Albert

Does your method predict that the most likely position for each team is their current position? If so, I think you have just said with stats that if everyone performs in the future as in the past, they will end up at the same place in the future.

The point of the analysis isn't predictive, it's to show what is reasonable to expect. That is, it's not saying that we're going to finishing 2nd because we have an easy run in, it's saying that based on what we've done this season, our current points total and previous data on the league, then here are the possible outcomes of the season with best guess percent chances.

As for a more predictive analysis, I'm currently working on a method to do this, but we'll see how this goes. The key is that it needs to remain self consistent.

[WoollyJumper]

Half way through reading this all I could hear in my head was:

 

"The Rams are going up,

The Rams are going up,

And now you're going to believe us,

And now you're going to believe us,

etc."

 

I think it's a shame that statistically the 3rd best team in the league does not go up, I don't like the play offs. A team who is the 6th best side in the league can get promoted, doesn't seem right to me.

 

(Before people start bleeting on at me about this, I know exactly why the play offs exist and that they make things interesting come the end of the season, doesn't mean I have to agree with it though!)

Unless of course your team is 6th and ends up winning promotion through the play offs.

[RodleyRam]

Unless of course your team is 6th and ends up winning promotion through the play offs.

 

Yeh even then I'd say fair play to the side in 3rd, they deserved to go up over the whole season.

 

this season the team in 3rd could easily be 12-15 points ahead of the team in 6th, just a bit sill really IMO.

[Albert]

I've managed to integrate the fixtures into the analysis. As expected the difference is fairly minimal. Our `predicted points' has gone from 88 to 89, but overall it's fairly minimal. Things roughly even out over these kinds of lengths of time and the numbers seem to suggest that again. It will become more significant coming to the very end of the season, but as things stand it doesn't offer any particular insight.

[WoollyJumper]

Yeh even then I'd say fair play to the side in 3rd, they deserved to go up over the whole season.

 

this season the team in 3rd could easily be 12-15 points ahead of the team in 6th, just a bit sill really IMO.

I agree with you. If the relegation is based on the lowest 2 or 3 teams at the end of the season, then it should be the same the same format when it comes to promotion. That the highest 2 or 3 teams gains promotion.

[CumbrianRam]

Used to be relegation play-offs didn't there?

[WoollyJumper]

Used to be relegation play-offs didn't there?

Can't say, although anything's possible.

I just don't see that there is a logical reason that relegation and promotion should be treated differently..

[Albert]

Can't say, although anything's possible.

I just don't see that there is a logical reason that relegation and promotion should be treated differently..

££££££££££££££££££££££££

Playoffs at the top end make sense financially as you can take advantage of the feel good factor around clubs, as well as that intensity that surrounds a knockout race for promotion. You could get some interest for a "relegation playoff", but the cost to interest would be far lower than a promotion playoff. The only way it could really work is if the playoff was between a number of teams in the higher division (going down) and the lower diving (going up), because at least then you'd have that added feel good factor from the teams with a chance of promotion, but that would be at a cost of the current playoff system, which seems a real money generator. It's not the only thing that's just there to add that `excitement' factor.

Sorting the table by goal difference rather than results between teams is, from what I've seen, to keep the table alive on the last day, and to get media interest in games that would otherwise be dead rubbers. It also encourages attacking play, but leagues where they sort the league by results between league don't seem to have an issue in that department (La Liga has got around 2.88 goals per match to the Premier League's 2.68 and the Championship's 2.54).

Then of course there's 3 points for a win, another gimmicky little rule that has just become natural. From what I can tell it's a way of getting teams to push for wins more often, and again, this is down to making the game more exciting.

This all said, there's nothing wrong with doing these kinds of rules, as long as it's kept subtle. With the playoffs, the best team should win, and to be blunt, if 3rd can't beat the teams it's finished above in the league, it probably doesn't deserve the Premier League anyhow. The playoffs as they are give interest late in the season all the way down to teams that haven't even got a real chance anymore (and I assure you, supporters of teams that my analysis wrote off with less than a 1 in 100 chance of making the playoffs, the Watfords and Middlesbroughs of the world, will surely still fancy themselves with some kind of chance). Keep in mind that without the playoffs, teams that currently have something to really get excited about right now, would now be near no chance of a promotion spot. Consider the top 3 chances of current teams that are Top 6 hopefuls, but not a serious chance of the Top 2.

Playoffs

Forest: 73.7%

Wigan: 43.9%

Reading: 38.4%

Brighton: 19.6%

Blackburn: 19.6%

Ipswich: 6.3%

Leeds: 5.5%

<1%

This group by Top 3 chances

Forest: 16.6%

Wigan: 3.43%

Reading: 2.06%

Brighton: 0.6%

Blackburn: 0.6%

Ipswich: <0.1%

Leeds: <0.1%

Forest would be the only team with any kind of real hope of making it now, and whilst I don't doubt that even Leeds would hold out some hope of making it, none of them would have any serious chance. That is the nature of the issue. It would be nice to have the best 3 teams go up, instead of the best 2 and a playoff winner, but keeping it interesting helps keep the league interesting, and keep fans coming through the gates. At the end of the day even with this system in place 6th place promoted teams haven't exactly made fools of themselves, but 3rd placed promoted teams have been known to.