Context

[Albert]

After some comments by Ramblur it became obvious that my previous posts tended to pave over the current Championship table in favour of the general Championship table constructed from averages over the last 15 seasons. This is all well and good early in the season, or as a rough guide, but at the end of the day, 19th in 2008-09 isn't the same as 19th in 2009-10, 2010-11, etc. I have previously used in discussions a system using the results a team has had during the season to find the probability of getting to a certain position within the table, this however used the general Championship table, rather than the current season's table, which can be rather different. With the difference between the important positions such as the playoffs, promotion and relegation can vary by as much as 12 or more points from season to season, it is of course important, especially in a situation where every point may matter to be a bit more precise in this area. As such I've decided to redo some of what I originally did, especially with these odd mentions of relegation creeping into the forum.

Now, I realise that a lot of people don't like walls of text, in fact the above may well have been a bit much for some people, so I'll do things a little differently this time. If this is all a bit much, skip to the bold sections for key points, and look under the figures for a quick description.

Now, having gone through a lot of past data, it's hard to get across the key points at times, especially with things like the shape of the table. One way to show what is meant by shape is to plot the points or points per game of teams in various positions against the league place. For the sake of consistency throughout, teams will be sorted only by points per game as the teams can be left nameless, the key is how the league shapes up by points per game in order to take games in hand out of the equation for the time being. Below is a plot of the general league table (the red line) and the current league table (blue diamonds) as league position against points per game.

"dkvhoL3" alt="dkvhoL3">

Figure 1: A plot of league position against points per game, with the red line being the 'general league table', that is, the average league table from the last 15 seasons, whilst the blue diamonds are this season at this point

As can be seen in the above the lower part of the table is quite flat, however, midtable, whilst flat, is around it's average level. Compare this to last season:

"In5pv1P" alt="In5pv1P">

Figure 2: As with figure 1, this is a plot of league position against points per game. As before, the red line is the 'general league table', whilst the blue diamonds are now the final league table for the 2011-12 season

Carefully note how the midtable is quite compact, whilst there is a layering effect towards the end, with a break between the mid table and the relegation battlers, before another break between them and the teams that were relegated. Also note that points deductions are included within this table.

The question after this of course becomes how the general league table relates to the final league table. This is quite difficult to really show, but the league tables don't change a huge amount after the middle of the season, the teams in various position may change, but the overall shape stays roughly the same. The real question for now though is whether or not the table will change, shape wise at least, from what it roughly is now. Rather than offer piles of previous seasons tables comparing them, below is a plot showing points per game at around the end of the 3rd quarter of the season (so, around ~35-36 odd games in) as compared to the points per game at the end of the season. The bottom axis is the points per game for the end of the 3rd quarter, whilst the other is the points per game at the end of the season. This is using data for 5 seasons from 2007-08 to 2011-12. The red diagonal line represents 1:1 correspondence, that is, if they stayed identical:

"ABsPus6" alt="ABsPus6">

Figure 3: A plot of points per game after ~35-36 games against points per game at the end of the season. Here the red line represents a 1:1 relation

What is clear from this is that whilst there is a small amount of movement off the 1:1 line, any movement is very small indeed. In fact, the average change is only ±0.0423 points per game (~2 points over a season), with a standard deviation of ±0.0335 points per game (~1.5 points over a season). From this you can say that within 95% confidence that the change to the final table won't be more than ±0.109 (~5 points) from what was found from the quarter 3 table. That's still a fair bit to vary, but that is either way and taking into account 95% of cases. There seems to be a slight bias towards the bottom 6 moving up slightly. Taking into account only the bottom six over the 5 years of the analysis shows that they on average move up around 0.0164 (~0.75 points). This however is small enough to ignore for the most part, although some further investigation into this may be interesting.

So, what does this all mean then?

• There can be significant change in the shape of the Championship table from season to season
• This change can be quite large, particularly the relegation places, where the last relegated team's points total can vary as much as 12 points (in the last 15 seasons)
• The table after 35-36 games is very similar to the final table, with changes very unlikely (less than ~5%) to be more than ±5 points from what would be expected, and most likely to fall within ±2 of what would be expected
• The bottom six appear to move up on average between the 35-36 game mark and the end of the season, but less than a point, and not enough to be considered particularly major

So, what does this mean then? Well, it means that a interpolating table created from the current table should be a good approximation of the final table. That is, getting the table by points per game should be a good guide of the final table, as such it can be used to replace the general table in calculations such as the one used to calculate the probability of our finish as done earlier this season for the playoffs, and recently to show how unlikely a true relegation battle is. Below is that a plot of the results, done as a probability density, that is, the left hand axis represents the likelihood of finishing in a position, whilst the bottom axis represents the position. The green region is automatic promotion, the blue is the playoffs whilst the red is the relegation places:

"k2wAHQw" alt="k2wAHQw">

Figure 4: A plot of the final position against probability of getting that position at the end of the season

In order to find the probability here, a range has to be selected, as the probability is the sum of the area under the curve. For example, the chances of us finishing 12th or above here are 6.17% (76-5), whilst relegation is 1.77% (388-7). Even losing the next 3 games will only increase this probability of relegation to 20.71% (23-6). As things stand though, the chances of a finishing in the bottom 6 are now 18.71% (13-3). Overall, even using this corrected form, relegation is still extremely unlikely.

As one final aside, using what was mentioned before, the likely "safe" points total is 48-49 points based on the current league table, with 54 being safe to 95% confidence, whilst 45 could also be safe, but less than 5% probability.

So to summarise that, taking into account of the Championship table at this point in time, it is extremely unlikely that we will be dragged into the relegation battle proper, only around a 18.71%, whilst actually being relegated is current only around a 1.77% chance. In terms of actual points on the board, 49-50 should be safe, whilst 54 would almost certainly be safe.

[Albert]

Albert if statistics were the be all and end all I'd be a rich man. Get this statistic. By the time we kick off against the Foxes in the televised late kick off the chances are we will be a mere 3 points off the bottom 6 due to Wolves playing Bristol unless it ends in a draw. FACT.

Wouldn't that also require Barnsley getting points as well?

[midtableforever]

Boring.

[cheron85]

Albert if statistics were the be all and end all I'd be a rich man. Get this statistic. By the time we kick off against the Foxes in the televised late kick off the chances are we will be a mere 3 points off the bottom 6 due to Wolves playing Bristol unless it ends in a draw. FACT.

 

If 'ifs' and 'buts' were candy and nuts then... well, I don't know... Never understood that phrase... I guess you'd have a lot of candy and nuts, just not sure why you'd want them...

[TroyDyer]

Ok. I can't say that I care about graphs and charts. I do care that once again we're a laughing stock. 

[uttoxram75]

If 'ifs' and 'buts' were candy and nuts then... well, I don't know... Never understood that phrase... I guess you'd have a lot of candy and nuts, just not sure why you'd want them...

Interesting. I've never heard that phrase before.

 

If "ifs" and "buts" were candy and nuts, wouldn't it be a Merry Christmas.

 

and I never want to hear it again, its bollux.

[Hucknall Ram]

After some comments by Ramblur it became obvious that my previous posts tended to pave over the current Championship table in favour of the general Championship table constructed from averages over the last 15 seasons. This is all well and good early in the season, or as a rough guide, but at the end of the day, 19th in 2008-09 isn't the same as 19th in 2009-10, 2010-11, etc. I have previously used in discussions a system using the results a team has had during the season to find the probability of getting to a certain position within the table, this however used the general Championship table, rather than the current season's table, which can be rather different. With the difference between the important positions such as the playoffs, promotion and relegation can vary by as much as 12 or more points from season to season, it is of course important, especially in a situation where every point may matter to be a bit more precise in this area. As such I've decided to redo some of what I originally did, especially with these odd mentions of relegation creeping into the forum.

Now, I realise that a lot of people don't like walls of text, in fact the above may well have been a bit much for some people, so I'll do things a little differently this time. If this is all a bit much, skip to the bold sections for key points, and look under the figures for a quick description.

Now, having gone through a lot of past data, it's hard to get across the key points at times, especially with things like the shape of the table. One way to show what is meant by shape is to plot the points or points per game of teams in various positions against the league place. For the sake of consistency throughout, teams will be sorted only by points per game as the teams can be left nameless, the key is how the league shapes up by points per game in order to take games in hand out of the equation for the time being. Below is a plot of the general league table (the red line) and the current league table (blue diamonds) as league position against points per game.

"dkvhoL3" alt="dkvhoL3">

Figure 1: A plot of league position against points per game, with the red line being the 'general league table', that is, the average league table from the last 15 seasons, whilst the blue diamonds are this season at this point

As can be seen in the above the lower part of the table is quite flat, however, midtable, whilst flat, is around it's average level. Compare this to last season:

"In5pv1P" alt="In5pv1P">

Figure 2: As with figure 1, this is a plot of league position against points per game. As before, the red line is the 'general league table', whilst the blue diamonds are now the final league table for the 2011-12 season

Carefully note how the midtable is quite compact, whilst there is a layering effect towards the end, with a break between the mid table and the relegation battlers, before another break between them and the teams that were relegated. Also note that points deductions are included within this table.

The question after this of course becomes how the general league table relates to the final league table. This is quite difficult to really show, but the league tables don't change a huge amount after the middle of the season, the teams in various position may change, but the overall shape stays roughly the same. The real question for now though is whether or not the table will change, shape wise at least, from what it roughly is now. Rather than offer piles of previous seasons tables comparing them, below is a plot showing points per game at around the end of the 3rd quarter of the season (so, around ~35-36 odd games in) as compared to the points per game at the end of the season. The bottom axis is the points per game for the end of the 3rd quarter, whilst the other is the points per game at the end of the season. This is using data for 5 seasons from 2007-08 to 2011-12. The red diagonal line represents 1:1 correspondence, that is, if they stayed identical:

"ABsPus6" alt="ABsPus6">

Figure 3: A plot of points per game after ~35-36 games against points per game at the end of the season. Here the red line represents a 1:1 relation

What is clear from this is that whilst there is a small amount of movement off the 1:1 line, any movement is very small indeed. In fact, the average change is only ±0.0423 points per game (~2 points over a season), with a standard deviation of ±0.0335 points per game (~1.5 points over a season). From this you can say that within 95% confidence that the change to the final table won't be more than ±0.109 (~5 points) from what was found from the quarter 3 table. That's still a fair bit to vary, but that is either way and taking into account 95% of cases. There seems to be a slight bias towards the bottom 6 moving up slightly. Taking into account only the bottom six over the 5 years of the analysis shows that they on average move up around 0.0164 (~0.75 points). This however is small enough to ignore for the most part, although some further investigation into this may be interesting.

So, what does this all mean then?

• There can be significant change in the shape of the Championship table from season to season
• This change can be quite large, particularly the relegation places, where the last relegated team's points total can vary as much as 12 points (in the last 15 seasons)
• The table after 35-36 games is very similar to the final table, with changes very unlikely (less than ~5%) to be more than ±5 points from what would be expected, and most likely to fall within ±2 of what would be expected
• The bottom six appear to move up on average between the 35-36 game mark and the end of the season, but less than a point, and not enough to be considered particularly major

   

So, what does this mean then? Well, it means that a interpolating table created from the current table should be a good approximation of the final table. That is, getting the table by points per game should be a good guide of the final table, as such it can be used to replace the general table in calculations such as the one used to calculate the probability of our finish as done earlier this season for the playoffs, and recently to show how unlikely a true relegation battle is. Below is that a plot of the results, done as a probability density, that is, the left hand axis represents the likelihood of finishing in a position, whilst the bottom axis represents the position. The green region is automatic promotion, the blue is the playoffs whilst the red is the relegation places:

"k2wAHQw" alt="k2wAHQw">

Figure 4: A plot of the final position against probability of getting that position at the end of the season

In order to find the probability here, a range has to be selected, as the probability is the sum of the area under the curve. For example, the chances of us finishing 12th or above here are 6.17% (76-5), whilst relegation is 1.77% (388-7). Even losing the next 3 games will only increase this probability of relegation to 20.71% (23-6). As things stand though, the chances of a finishing in the bottom 6 are now 18.71% (13-3). Overall, even using this corrected form, relegation is still extremely unlikely.

As one final aside, using what was mentioned before, the likely "safe" points total is 48-49 points based on the current league table, with 54 being safe to 95% confidence, whilst 45 could also be safe, but less than 5% probability.

So to summarise that, taking into account of the Championship table at this point in time, it is extremely unlikely that we will be dragged into the relegation battle proper, only around a 18.71%, whilst actually being relegated is current only around a 1.77% chance. In terms of actual points on the board, 49-50 should be safe, whilst 54 would almost certainly be safe.

Might be a joke that passes some people but.....

 

"http://www.davegorman.com/images/DGORMAN_DVD" alt="DGORMAN_DVD">

[TroyDyer]

Ok. I can't say that I care about graphs and charts. I do care that once again we're a laughing stock. 

[Albert]

Ok. I can't say that I care about graphs and charts. I do care that once again we're a laughing stock.

Is there an echo Troy?

[TroyDyer]

My computer is actually retarded. 

 

Or maybe it feels strongly about it. God knows. Either way, it's annoying. 

 

Apologies. 

[cheron85]

Ok. I can't say that I care about graphs and charts. I do care that once again we're a laughing stock. 

 

Why? I don't see too many people laughing at us... In fact most opposition managers this season have mentioned how difficult they find playing us and how intimidating it is going to PP... When cardiff came they pretty much played 5-5-0

[Gritstone Ram]

Interesting. I've never heard that phrase before.

If "ifs" and "buts" were candy and nuts, wouldn't it be a Merry Christmas.

and I never want to hear it again, its bollux.

How about if 'ifs'and 'buts' were cows nuts. wouldn't it be bullocks.

[curb]

After some comments by Ramblur it became obvious that my previous posts tended to pave over the current Championship table in favour of the general Championship table constructed from averages over the last 15 seasons. This is all well and good early in the season, or as a rough guide, but at the end of the day, 19th in 2008-09 isn't the same as 19th in 2009-10, 2010-11, etc. I have previously used in discussions a system using the results a team has had during the season to find the probability of getting to a certain position within the table, this however used the general Championship table, rather than the current season's table, which can be rather different. With the difference between the important positions such as the playoffs, promotion and relegation can vary by as much as 12 or more points from season to season, it is of course important, especially in a situation where every point may matter to be a bit more precise in this area. As such I've decided to redo some of what I originally did, especially with these odd mentions of relegation creeping into the forum.Now, I realise that a lot of people don't like walls of text, in fact the above may well have been a bit much for some people, so I'll do things a little differently this time. If this is all a bit much, skip to the bold sections for key points, and look under the figures for a quick description.Now, having gone through a lot of past data, it's hard to get across the key points at times, especially with things like the shape of the table. One way to show what is meant by shape is to plot the points or points per game of teams in various positions against the league place. For the sake of consistency throughout, teams will be sorted only by points per game as the teams can be left nameless, the key is how the league shapes up by points per game in order to take games in hand out of the equation for the time being. Below is a plot of the general league table (the red line) and the current league table (blue diamonds) as league position against points per game."dkvhoL3" alt="dkvhoL3">Figure 1: A plot of league position against points per game, with the red line being the 'general league table', that is, the average league table from the last 15 seasons, whilst the blue diamonds are this season at this pointAs can be seen in the above the lower part of the table is quite flat, however, midtable, whilst flat, is around it's average level. Compare this to last season:"In5pv1P" alt="In5pv1P">Figure 2: As with figure 1, this is a plot of league position against points per game. As before, the red line is the 'general league table', whilst the blue diamonds are now the final league table for the 2011-12 seasonCarefully note how the midtable is quite compact, whilst there is a layering effect towards the end, with a break between the mid table and the relegation battlers, before another break between them and the teams that were relegated. Also note that points deductions are included within this table.The question after this of course becomes how the general league table relates to the final league table. This is quite difficult to really show, but the league tables don't change a huge amount after the middle of the season, the teams in various position may change, but the overall shape stays roughly the same. The real question for now though is whether or not the table will change, shape wise at least, from what it roughly is now. Rather than offer piles of previous seasons tables comparing them, below is a plot showing points per game at around the end of the 3rd quarter of the season (so, around ~35-36 odd games in) as compared to the points per game at the end of the season. The bottom axis is the points per game for the end of the 3rd quarter, whilst the other is the points per game at the end of the season. This is using data for 5 seasons from 2007-08 to 2011-12. The red diagonal line represents 1:1 correspondence, that is, if they stayed identical:"ABsPus6" alt="ABsPus6">Figure 3: A plot of points per game after ~35-36 games against points per game at the end of the season. Here the red line represents a 1:1 relationWhat is clear from this is that whilst there is a small amount of movement off the 1:1 line, any movement is very small indeed. In fact, the average change is only ±0.0423 points per game (~2 points over a season), with a standard deviation of ±0.0335 points per game (~1.5 points over a season). From this you can say that within 95% confidence that the change to the final table won't be more than ±0.109 (~5 points) from what was found from the quarter 3 table. That's still a fair bit to vary, but that is either way and taking into account 95% of cases. There seems to be a slight bias towards the bottom 6 moving up slightly. Taking into account only the bottom six over the 5 years of the analysis shows that they on average move up around 0.0164 (~0.75 points). This however is small enough to ignore for the most part, although some further investigation into this may be interesting.So, what does this all mean then?

• There can be significant change in the shape of the Championship table from season to season
• This change can be quite large, particularly the relegation places, where the last relegated team's points total can vary as much as 12 points (in the last 15 seasons)
• The table after 35-36 games is very similar to the final table, with changes very unlikely (less than ~5%) to be more than ±5 points from what would be expected, and most likely to fall within ±2 of what would be expected
• The bottom six appear to move up on average between the 35-36 game mark and the end of the season, but less than a point, and not enough to be considered particularly major

So, what does this mean then? Well, it means that a interpolating table created from the current table should be a good approximation of the final table. That is, getting the table by points per game should be a good guide of the final table, as such it can be used to replace the general table in calculations such as the one used to calculate the probability of our finish as done earlier this season for the playoffs, and recently to show how unlikely a true relegation battle is. Below is that a plot of the results, done as a probability density, that is, the left hand axis represents the likelihood of finishing in a position, whilst the bottom axis represents the position. The green region is automatic promotion, the blue is the playoffs whilst the red is the relegation places:"k2wAHQw" alt="k2wAHQw">Figure 4: A plot of the final position against probability of getting that position at the end of the seasonIn order to find the probability here, a range has to be selected, as the probability is the sum of the area under the curve. For example, the chances of us finishing 12th or above here are 6.17% (76-5), whilst relegation is 1.77% (388-7). Even losing the next 3 games will only increase this probability of relegation to 20.71% (23-6). As things stand though, the chances of a finishing in the bottom 6 are now 18.71% (13-3). Overall, even using this corrected form, relegation is still extremely unlikely.As one final aside, using what was mentioned before, the likely "safe" points total is 48-49 points based on the current league table, with 54 being safe to 95% confidence, whilst 45 could also be safe, but less than 5% probability.So to summarise that, taking into account of the Championship table at this point in time, it is extremely unlikely that we will be dragged into the relegation battle proper, only around a 18.71%, whilst actually being relegated is current only around a 1.77% chance. In terms of actual points on the board, 49-50 should be safe, whilst 54 would almost certainly be safe.

Might be a joke that passes some people but.....

 

"http://www.davegorman.com/images/DGORMAN_DVD" alt="DGORMAN_DVD">

Did you have to quote the whole post?

[RodleyRam]

probabilities and charts are all well and good. Basically we need some good result and we'll be fine, it's in our hands, I'd like to see us going out to try and get as many points on the board as we can.

 

We shouldn't be looking over our shoulders because that implies we're at the mercy of others, we aren't!

 

We'll get the points we need to stay up, but will that be enough to show progress this season?

[Albert]

probabilities and charts are all well and good. Basically we need some good result and we'll be fine, it's in our hands, I'd like to see us going out to try and get as many points on the board as we can.

 

We shouldn't be looking over our shoulders because that implies we're at the mercy of others, we aren't!

 

We'll get the points we need to stay up, but will that be enough to show progress this season?

I guess the question is what is meant by progress?

The most obvious is points on the board, but that's a very simplistic measure. This season we have been scoring in more games than we have before, we're not being beaten convincingly, that is, even when we lose, we aren't losing badly and this shows on our goal difference (which is only at around parity even in our poor form) as compared to previous seasons (around the -10 mark). We aren't keeping as many clean sheets though, which is a worry. As things stand as well, it's clear that the reason we've not picked up as many points is due to us drawing more and winning less, not losing more. With 9 to play if we lose 4 or less we will be on the same number, or better, in terms of losses as compared to last season. Of course, then we get on to other matters such as bringing through young players and the squad in general. There are some positives, but in a bad run very few people are really going to be that interested in such things.

[Bris Vegas]

Can you make a graph to show how we've fluctuated between mediocre and feckin dire under NC?

[davenportram]

I did say chances are LOL.

BUT YOU ARE RIGHT

If Barnley lose to Watford and a 3 point result from WOLVES VS BRISTOL occurs then the gap will be 4 points prior to the Rams late kick off against Leicester..

PS Barnsley have played 36 and the Rams 37 as it stands. Millwall have played 35 . Does this come into your equation .

don't forget Peterborough too if they lose or draw, Barnsley lose then we will be at least 4 points from relegation regardless of the Wolves Bristol result.

seeing as Alberts graph shows a 1 in 5 chance of being in the bottom 6 then we should look at the bottom 3 and make sure we stay clear of that

[Albert]

Can you make a graph to show how we've fluctuated between mediocre and feckin dire under NC?

I'm not sure if this is what you meant, here's a graph of average points per game done as a 10 game average over Nigel's management (first 10 games included) with the red dotted line showing the average points per game for relegation with the dotted purple being the playoffs and the green being promotion, these over a whole season of course (the last match is not included in this plot):

"jE0jfkP" alt="jE0jfkP">

[Bris Vegas]

I'm not sure if this is what you meant, here's a graph of average points per game done as a 10 game average over Nigel's management (first 10 games included) with the red dotted line showing the average points per game for relegation with the dotted purple being the playoffs and the green being promotion, these over a whole season of course (the last match is not included in this plot):

"jE0jfkP" alt="jE0jfkP">

 

Thanks..

 

Any chance you can do one for league positions?

 

I think we'll come out as one of the most consistant teams in the league over the past 2 years.. Ranging from 8th to 15th.

[RodleyRam]

I guess the question is what is meant by progress?

The most obvious is points on the board, but that's a very simplistic measure. This season we have been scoring in more games than we have before, we're not being beaten convincingly, that is, even when we lose, we aren't losing badly and this shows on our goal difference (which is only at around parity even in our poor form) as compared to previous seasons (around the -10 mark). We aren't keeping as many clean sheets though, which is a worry. As things stand as well, it's clear that the reason we've not picked up as many points is due to us drawing more and winning less, not losing more. With 9 to play if we lose 4 or less we will be on the same number, or better, in terms of losses as compared to last season. Of course, then we get on to other matters such as bringing through young players and the squad in general. There are some positives, but in a bad run very few people are really going to be that interested in such things.

I'm inclined to agree with you, I've seen more positives this season across a number of areas. Although we've scored more goals and more often as you say I think there's been critical points where we've failed to score at important times. Our 'Game Management' has been poor at times and we lack a certain amount of experience to make the most of opportunities when it really counts.  Does that point towards the need for a regular goal scoring forward that we can rely on to 'win' us matches? Maybe.

 

We've also been worse defensively this season, the loss of a commanding CB and some frailty down the left are the root causes in my opinion. As much as I like Keogh, he's not dominant enough to grab our defense and midfield by the scruff of the neck and force clean sheets out of them like Shackell and Barker could. With a Shackell or a Barker type player he'd be better and that doesn't point to him being a poor defender, it just highlights that he needs a proper, consistent partner.

 

I'm definitely one for looking at the positives and there are a lot of them, ultimately though history will have this season down as fewer points and a lower league position. If Clough stays next season only then will we be able to see whether this softer progression can be turned into consistent result, which ultimately is the only statistic that REALLY matters for a football club.