State of the League and our chances

[Albert]

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.

[Srg]

Good job football ain't played on paper...

[RLACML]

The analysis doesn't quite work does it

[Gypsy Ram]

I'm lost for words.

[K-Ram]

Well, I'm glad Albert's analysis corner is back, even if I don't fully comprehend all of it.

[Albert]

Good job football ain't played on paper...

The Football isn't, but the league is.

The analysis doesn't quite work does it

How so?

[cosmic]

"uses fairly standard normal distributions based on Points Per Game"

 

So a bit like the ACTUAL league table?

[Inverurie Ram]

So which one's the breakfast pie?....,.... and who's go is it, to get the ale in?

[dave126]

I cant decide whether to be impressed by you Albert.......or feel really sorry for you 

[RLACML]

How so?

With the analysis about whether we would rather have lost to Ipswich or Forest, surely the impact on Ipswich chances should also have an effect on the statistic that you produce for us. But it doesn't seem to.

 

I'm not sure it takes into account who we were playing which is of course the most vital part of comparing the results. We've won 53.8% of our games, and lost 23%. Of course a defeat will have a larger impact. 

[Curtains]

We will finish top of the League.

[Mostyn6]

I appreciate this way of looking at things. Well presented and interesting.

[eddie]

Lies

[unclej]

I'm impressed...very. Thank you.

[Antonedcfc]

Someone needs a life..

[Thierry Ennui]

Someone needs a life..

 

Oh shut up.

[Duracell]

Albert thank you for the write up, it's interesting to see how past tables in this league have formed and it goes to show that we're still in a position to go up automatically based on what previous teams have done. But I'm not sure these figures actually say anything for our chances. All these figures reflect is the percentage of teams to get into the autos/playoffs from similar positions in past seasons, rather than actually taking this season into account and all the unique variables that come with that.

 

Our chances are to do with how many points we gain between now and the end of the season in comparison to our rivals. Data from what Hull or Swansea did a few seasons ago is meaningless.

[Albert]

With the analysis about whether we would rather have lost to Ipswich or Forest, surely the impact on Ipswich chances should also have an effect on the statistic that you produce for us. But it doesn't seem to.

 

I'm not sure it takes into account who we were playing which is of course the most vital part of comparing the results. We've won 53.8% of our games, and lost 23%. Of course a defeat will have a larger impact.

This was a very simple analysis (all other factors left, simply removed singular games to keep it consistent):

For us:

Current: 32.5%

Without Ipswich: 25.0% (-7.5%)

Without Forest: 43.3% (+10.8%)

Without either: 35.5% (+3%)

For Ipswich:

Current: 45.7%

Without us: 57.3% (+11.6%)

We made a much bigger dent in them than we gained ourselves, though the victory was absolutely vital for us. The point is though that, as you say, being so high up the league a loss does more damage to us than a win can help us, even when damaging a promotion rival. If you're wondering how much of an impact the damage to Ipswich did, you can compare these two sets of changes:

Without Ipswich: 25.0%

Current: 32.5% (+7.5%)

Replace Ipswich with a midtable side: 30.4% (+5.4%)

As you can see from that, us beating Ipswich (taking points off promotion rivals) did have an effect, the issue though is that the table is so dense there that beating Ipswich is only hurting one of those rivals.It wasn't a case of who you'd rather beat.

If you want to know which would be better for us directly, beating Ipswich or Forest:

Without either: 35.5%

Beating Ipswich (losing to Forest): 32.5% (-3%)

Beating Forest (losing to Ipswich): 29.4% (-6.1%)

It's obvious that beating Ipswich was worth more to us than beating Forest, and that is something obvious in those figures.

There is a version I can run which takes into account opponents, but the results are almost exactly the same with anything more than 5 odd games left (even then the difference isn't enough to really justify it). That's the beauty of long term averages though. The quality of opposition evens out over time.

"uses fairly standard normal distributions based on Points Per Game"

 

So a bit like the ACTUAL league table?

It quantifies the chances of a team being capable of being able to rise or drop down the table, unlike the actual table. When people look at the current table, there are still teams like Forest who might argue they have a realistic chance of the playoffs, despite being in no position to make it. It's not a matter for predicting, but rather just quantifying odds. Just a tool for putting context to the table.

[Albert]

Albert thank you for the write up, it's interesting to see how past tables in this league have formed and it goes to show that we're still in a position to go up automatically based on what previous teams have done. But I'm not sure these figures actually say anything for our chances. All these figures reflect is the percentage of teams to get into the autos/playoffs from similar positions in past seasons, rather than actually taking this season into account and all the unique variables that come with that.

 

Our chances are to do with how many points we gain between now and the end of the season in comparison to our rivals. Data from what Hull or Swansea did a few seasons ago is meaningless.

That's exactly the point though. A team in our position who have performed as we have will have those chances. That was done and calibrated off years of data. By definition there will be teams that have shock seasons and get top 2 from a "3%" position here, just very rarely (~1 in 33 years). It's not about predicting what will happen, rather just giving context to our position.

My own personal take is that if we click, we'll go up. Again, just a case of making sure that our position isn't over stated in any direction. Showing that we really are in a good position and are doing well in a very tight league.

[G STAR RAM]

I don't mean to be rude because obviously you have put a lot of though and effort into this but, have you not spent hours basically coming up with a complicated way of presenting the league table?

 

If everyone has played the same amount of matches and everyone has played each other once then surely the higher up the league table, the higher the probability of finishing higher up the league?!