James' Blog

Predicting the Premiership, 2011-12 edition

Jameswgrayson — Mon, 31 Oct 2011 05:16:20 +0000

In an improvement over last season I’m only a quarter of a season late with this.

Team	Exp pos	Exp points	Exp ±
Arsenal	1	72	+26
Chelsea	2	68	+25
Manchester United	3	68	+23
Tottenham Hotspur	4	61	+12
Liverpool	5	60	+11
Manchester City	6	59	+12
Everton	7	58	+8
West Bromwich Albion	8	56	+2
Fulham	9	54	+3
Newcastle United	10	54	+2
Wigan Athletic	11	53	-3
Bolton Wanderers	12	52	-1
Sunderland	13	48	-7
Aston Villa	14	47	-8
Stoke City	15	45	-8
Swansea City	16	43	-12
Wolverhampton Wanderers	17	41	-16
Norwich City	18	38	-17
Queens Park Rangers	19	37	-16
Blackburn Rovers	20	35	-21

So the main discrepancy here is obviously Manchester City. It’s worth mentioning once more that this is a basic model that relies solely on last seasons performance.

Once again this model has predicted that Wigan and Arsenal will be much higher than they are at this point. I’m at a bit of a loss to explain this. They’re both teams that play passing football and so I’d expect that if any teams in the league were to utilise the benefit from whatever skill lies in shooting percentage it would be those playing passing football that style of football but obviously this isn’t the case.

And to this point Norwich are doing pretty well although I don’t expect them to be in the top half of the table come the end of the season.

I may revisit this at the end of the season to see how it pans out at the end of the season.

Predicting future performance – revisited

Jameswgrayson — Mon, 31 Oct 2011 04:31:34 +0000

A long time ago I took a look at a range of statistics to determine which was the best predictor of future performance. I did this by looking at the performance of a team one season and seeing which statistic showed the least regression towards the mean.

I now have a much larger data set (702 sets of back-to-back seasons) on which to base a more concrete conclusion and the results are as follows. The initial post demonstrated that using ratio’s (such as shots on target ratio) regress far less to the mean than differential or pythagorian values and so these are what I will report. The updated table appears as follows:

Factor	R²	Regression towards the mean
Goals	0.332	42.4%
Shots on target	0.462	32.1%
Total shots	0.473	31.2%
Sh%	0.109	66.9%
Sv%	0.128	64.2%
PDO	0.067	74.1%

To give these values a bit of context, the points a team earns regress ~45.4% towards the mean over consecutive seasons (it’s important to note that I didn’t include seasons where teams were promoted or relegated so the inevitable drop off/improvement the following year). Therefore if we want to know how a team will perform in the future then using points is less accurate than goals or shots.

Two of the ratio’s clearly stand out as being much better at predicting future performance than the rest. In this case it turns out that the best predictor is in fact the ratio of the total shots in the games a team plays. From now on (as in the few posts that remain) I’ll switch to use total shots ratio to predict future performance.

Finally I threw sh%, sv% and PDO in there to once again reiterate just how much they fluctuate from season to season. All three of these are vastly more luck driven than skill driven.

The comparitive strength of the four English leagues

Jameswgrayson — Mon, 31 Oct 2011 04:06:54 +0000

In a set of posts I’ve compared the strengths of the neighbouring English leagues and now I want to go one step further and use that to determine how all of the leagues compare to one another.

The table below is a recap what I’ve found so far:

One goal in		is worth		goals in
	the championship		~0.64		the premiership
	league one		~0.74		the championship
	league two		~0.84		league one

By multiplying the numbers together we can then compare all of the leagues to the premiership:

One goal in		is worth		goals in the premiership
	the championship		~0.64
	league one		~0.47
	league two		~0.39

I think the take away message from these two tables is that the gap between divisions gets narrower as we move towards the lower divisions (the number suggest the gap between league two and league one is roughly half the size of that between the championship and the premiership).

I don’t expect anyone to be surprised by this, for example I can think of many more examples of teams being promoted from the conference and league two in consecutive seasons than from league one and the championship, but I think it’s nice to show the relative strengths numerically.

I think this would give a relatively good estimation for individual players transferred between leagues but I simply don’t own the data necessary to back that up conclusively.

How much is a goal in league two worth in league one?

Jameswgrayson — Mon, 31 Oct 2011 03:43:12 +0000

There last couple of months were pretty hectic so this place got neglected. I’ve had a look back at the data I have and realistically there’s only a handful (probably around ten) more posts I can squeeze out of it so I’m going to finish with a bit of a sprint.

Firstly I want to finish a series of posts I’ve previously started looking at the effect of relegation/promotion on a teams ability to score/prevent goals. Firstly I did this for those going to and from the premiership and then to and from the championship. For the final part I’ll look at the teams promoted to and relegated from league one. This time I’m using a sample size in excess of 7000 games.

Initially I’ll look at teams that were relegated from the league one in ‘year 1′ and consequently spent ‘year 2′ in league two:

Year	League	Games	Goals scored	Goals per game
‘Year 1′	League one	1840	2005	1.090
‘Year 2′	League two	1840	2415	1.313

So to calculate how much a goal scored in the league one is worth in the championship:

^{Goals for per game (league one)}/_{Goals for per game (league two)} = ^1.090/_1.313 = 0.830

How about the other way around, teams that are promoted in ‘year 1′ and spend ‘year 2′ playing in the league one?

Year	League	Games	Goals scored	Goals per game
‘Year 1′	League two	1840	2874	1.562
‘Year 2′	League one	1840	2436	1.324

^{Goals for per game (league one)}/_{Goals for per game (league two)} = ^1.324/_1.562 = 0.848

For the third time in three posts the two ratios give similar numbers. By taking the average of these numbers I’m going to estimate that a goal in league two is worth ~0.839 goals in the league one. By following the same process for goals conceded and I got values of 0.779 and 0.746 (for relegation and promotion respectively), an average of ~0.763, which is significantly smaller than the value obtained goals scored.

In the next post I’ll combine the numbers from this and the previous two in the series to compare the relative strength of the four English leagues.

Hey Lincolnshire Echo. Did you make up a quote from Steve Prescott or just forget that he’d said it?

Jameswgrayson — Tue, 27 Sep 2011 05:31:34 +0000

Some are going to regard the following as pedantic but given how much press there was regarding the ticket prices at Lincoln over the summer I think it’s important to find out which version is actually true.

I was reading through some of the articles from the Echo website to catch up on Lincoln’s season (it wasn’t much fun) and I came across this article from September 14th in which Steve Prescott talks about this seasons attendance figures. There’s one line in particular that caught my eye which reads as follows

“Prescott would not divulge just how low the gates were below their original budgeted target – which is not the 3,200 figure speculated by some supporters”

The reason that that sentence stands out to me is because I distinctly remember reading this article from July 2nd where Steve Prescott is quoted as saying

“We were working on a budget regarding the gates. We’re hoping we can get an average crowd of 3,200.”

In the span of ten weeks a direct quote from the board member responsible for setting the budget has regressed to simply some made up numbers by fans.

So I’m interested to know which version of the story is true, did Steve Prescott say the quotes that are attributed to him in the initial article? If yes then why is it now simply attributed as speculation from fans? If no then why were the Echo allowed to print it?

Why the motions at the Lincoln City EGM will probably fail

Jameswgrayson — Fri, 08 Jul 2011 07:42:30 +0000

*I’m pretty apathetic towards the issue in general, this article has nothing to do with whether I think the motions should be approved, simply an explanation of why, mathematically, they probably won’t be*

I obtained the latest Annual Return for Lincoln City Football Club Company Limited using the excellent WebCHeck service operated by Companies House. Part of this is a complete list of shareholders in the club, in total there are 4,221,334 ordinary shares owned by ≈1,300 shareholders (I’m not going to count the exact number). I’m of the understanding that these are classed as ‘ordinary motions’* meaning a simple majority is required (votes representing >50% of the shares) for them to be passed but I’d welcome clarification on this.

From this I’ve been able to split the shareholders into groups. The current members of the board (which comprises of B Dorrian, R Bates, D Beck, K Cooke, J Foster, D Leonard, J Powell & S Tindall) & their associated companies (Lindum Group Limited and Lincolnshire Co-operative) own a total of 760,523 shares, or an 18.0% share in the football club. These shares are obviously going to be used to keep the Directors in their position

Lincoln City Supporters Trust is the single largest shareholder, owning 25.4% of the shares. Given the situation the Supporters Trust find themselves in (with two members representing it’s interests at board of directors) I doubt that there’s a big motivation to challenge the leadership at this time. (I might be proved wrong – the details of lasts nights’ board meeting have yet to be released)

And herein lies the problem for those attempting to oust the board**. Add the shares owned by the Directors to those owned by the Supporters Trust and 43.4% have been accounted for***. Of the remaining 56.6% owned by others (including the dissenters), 90% would have to vote for a motion for it to pass.

This would require the 60 largest shareholders to all attend the EGM and vote the same way and that’s highly improbable.

*I’ve come to this conclusion because the Companies Act 2006 states in Part 13, Chapter 1, Section 283, 6, a that

the resolution is not a special resolution unless the notice of the meeting included the text of the resolution and specified the intention to propose the resolution as a special resolution

From reading a transcript of the letters sent to shareholders I’m pretty sure that this clause wasn’t fulfilled, thus the resolutions are classed as ordinary resolutions (requiring a simple majority).

**A quick note to Bob Dorrian, requisitioners isn’t a real word, you’ve made that up

***If I add in the shares owned by associated directors this figure rises further still, to 50.5%, making a majority dissent impossible. I have no insight as to which way there would vote though

How much has the cost of tuition in the UK actually changed?

Jameswgrayson — Sat, 02 Jul 2011 08:08:59 +0000

A couple of months ago the Government announced a rise in tuition fees paid by students to attend British Universities. I’m not interested in the politics but I’d like to put some numbers to the changes and see whether the move will actually leave students worse off over the life of their student loan. Monetarily the two main changes from the current system were

a) Universities can charge tuition fees up to a total of £9,000 per annum (up from £3,375 that will be charged for the 2011-12 academic year)
b) Students will repay their loan at a rate of 9% on any income above a threshold of £21,000 (as opposed to the current threshold of £15,000)

I’m looking to calculate the effect that these changes will have on the amount that students pay over the life of their student loans. To prevent this post from becoming more boring than necessary I’ve outlined the assumptions I’ve made at the end of the post.

I’ve looked at the numbers for the three different paths taken by most University students (three year Batchelor’s degree, four year Masters and Masters followed by a PhD). I’ve also factored in a couple of variables; the graduates starting salary and the rate at which their salary increases.

The average graduate starting salary is ~£25,000 and so I’ve looked at starting salaries that range from £17,500 – £32,500. The values for salary inflation range from 2 – 6% per annum. This covers a range of incomes that are below inflation (2 &3%), at inflation (4%) and above inflation (5 & 6%).

Each of the tables below show the difference (in 2012 £’s) in the amount that graduates will pay over the life of their loan under the new system as opposed to the current system for each combination of these variables.

Basically if a cell is green then the student will pay less under the new system and vice versa. I’ve rounded the results to the nearest £1000 as the model I’m using is pretty crude. Down the left of each table is the graduates starting salary and across the top is the rate of salary inflation.

First the most popular degree choice; Batchelor’s students:

	2%	3%	4%	5%	6%
£17,500	-£6,000	-£6,000	£1,000	£10,000	£12,000
£20,000	-£7,000	-£3,000	£6,000	£13,000	£13,000
£22,500	-£4,000	£3,000	£12,000	£13,000	£11,000
£25,000	£0	£8,000	£12,000	£12,000	£12,000
£27,500	£4,000	£12,000	£12,000	£13,000	£12,000
£30,000	£9,000	£13,000	£12,000	£12,000	£13,000
£32,500	£12,000	£13,000	£13,000	£13,000	£12,000

Then for Master’s students:

	2%	3%	4%	5%	6%
£17,500	-£6,000	-£7,000	-£5,000	£3,000	£15,000
£20,000	-£7,000	-£7,000	£1,000	£11,000	£18,000
£22,500	-£7,000	-£3,000	£6,000	£17,000	£17,000
£25,000	-£5,000	£2,000	£13,000	£17,000	£19,000
£27,500	-£1,000	£7,000	£17,000	£17,000	£16,000
£30,000	£3,000	£12,000	£17,000	£18,000	£17,000
£32,500	£7,000	£17,000	£18,000	£16,000	£16,000

And finally for Master’s students who go on to study a PhD:

	2%	3%	4%	5%	6%
£17,500	-£5,000	-£5,000	-£6,000	-£4,000	£3,000
£20,000	-£6,000	-£5,000	-£6,000	£2,000	£9,000
£22,500	-£6,000	-£6,000	-£1,000	£7,000	£16,000
£25,000	-£6,000	-£4,000	£3,000	£12,000	£16,000
£27,500	-£9,000	£0	£8,000	£17,000	£18,000
£30,000	-£3,000	£4,000	£13,000	£17,000	£18,000
£32,500	£0	£8,000	£17,000	£19,000	£17,000

First impressions are that the three tables mirror one another very nicely and there isn’t a lot of green there. The new system appears to benefit students who have a low starting salary and receive below inflation wage increases. I don’t think many graduates will find that a particularly pleasing proposal.

Those most affected are those who earn an average salary and receive pay rises at or above the level of inflation. It should come as no surprise that this group will account for the largest number of any students. It seems like the Government knew what they were doing…

In conclusion I can guarantee that 40 years in the future we’ll hear the Government of the time complaining about writing off huge swathes of student loans the reality is that they will have received vastly more under the new student loan system than the one that is currently in place.

Regardless of what the Government promise student loans are guaranteed to rise in the future, it’s too easy to sell. Spin an aging population a line about it being a choice between increasing taxes/cutting pensions (which affect the vast majority of the electorate) or raising student loans (which affects a tiny proportion, many of whom are too young to vote) and there’ll only ever be one winner.

I’ll round off by mentioning a two points. Firstly the most that I’ve being paid back in these scenario’s is ≈£40,000 in real terms (ie the value of the £ in 2012) and that is for someone earning (in real terms) ≈£45,000 thirty years after starting their job. And secondly the difference between doing a PhD or not make very little difference (less than £1000 using this model) as to how much money you will pay in total and this is true for both the current and new systems.

*The assumptions made for this post are as follows:

1) The interest rate for student loans is determined using the Retail Prices Index (RPI), which over the past 20 years has averaged 3.86%. I’m assuming that it continues at this pace for the foreseeable future. I’m also assuming that tuition fees and student loans will increase at this rate for each year of study.
2) The student comes from an affluent background and studies outside of London (Where higher maintenance loans are available). Basically this means that the student receives the available maintenance loan but none of the ‘means tested’ portion.
3) An employee’s salary will rise at a fixed percentage each year. This isn’t a perfect model (salaries tend to increase at a faster rate at the beginning of a career than the end) but is a pretty good starting place.
4) Loans are written off 40 years after graduation.

The market for Rob Green

Jameswgrayson — Fri, 24 Jun 2011 03:59:28 +0000

When West Ham were relegated the fans were warned to expect the club to lose several of its international players, including some key pieces along the spine of the team, namely Rob Green, Matthew Upson, Scott Parker and Carlton Cole. Whilst it’s difficult (at least for me) to evaluate where the outfield players end up I think the story is different for goalkeepers. Typically teams have two or three, and there are only 20 places in the league for first choice goalkeepers. I’m not sure what price West Ham have in mind but at a guess I’d say the figure is in the region of £7m. I’m also going to guess that Rob Green expects to be the first choice keeper at whichever club he joins.

To identify which teams may be interested I’ve split the premiership teams into three categories depending on how well set they are between the posts

Firstly these are the teams that look to have a clear and/or settled first choice ‘keeper

Blackburn Rovers (Robinson) Bolton Wanderers (Jaaskelainen) Chelsea (Cech) Everton (Howard) Fulham (Schwarzer) Manchester City (Hart) Manchester United (De Gea – providing the deal goes through) Newcastle United (Harper) Stoke City (Begovic/Sorensen) Tottenham Hotspur (Friedel/Gomes) Wigan Athletic (El Habsi)

Next is the group of teams where the ‘keepers appear to be on more shaky ground, or are rumoured as transfer targets

Arsenal (Szcezny) Liverpool (Reina) Sunderland (Gordon/Mignolet) West Bromwich Albion (Carson) Wolverhampton Wanderers (Hennessey/Hahnemann)

Of these I wouldn’t expect Arsenal to consider Green (I don’t actually think Arsenal will look to buy any keepers). Liverpool appear to be going through a movement to get more English players into the set up so that could be a possibility, but only if the rumours that Reina wants to leave are accurate. The persistent rumours coming out of West Brom suggest that Carson is likely gone, and the situation at Sunderland has been up in the air for a couple of seasons. If Wolves were looking to upgrade at the back I don’t think they’d be looking to spend the amount that West Ham are asking.

Which leaves one team that is actively looking
Aston Villa

I think this job is going to go to Ben Foster. Common knowledge seems to suggest that Alex McLeish is looking to bring his back room staff with him from Birmingham, with the goalkeeping coach being a part of that package. The rumours that Foster would also move make a lot of sense.

Of the newly promoted teams a dream move back to Norwich could be possible but again money is an issue, plus the fact that they seem pretty settled with Ruddy between the posts. I don’t think QPR or Swansea will actively be looking to change their ‘keepers either – I can’t think of the last time a team was promoted and changed goalies and I doubt this year will be an exception.

So in conclusion there aren’t many starting jobs available in the premier league next season. If West Ham want to sell Rob Green, and it seems they need his salary off the books, then I think they would have to accept a low offer. If Green is determined to play in the premiership he may have to accept a lower salary as well as potentially being the second choice where he goes. An alternative strategy for the club would be to wait to see if injuries hit one of the premier league clubs in August but there’s a lot of risk there.

How much is a league one goal worth in the championship?

Jameswgrayson — Tue, 14 Jun 2011 06:38:01 +0000

A while ago I had a look at how teams promoted to and relegated from the premiership perform in the following season to compare the strength of the premiership to the championship. Now I’m going to follow the same methodology but for teams promoted to and relegated from the championship.

This time the sample size is comfortably above 5000 games so I’d expect pretty consistent results.

First I’ll look at teams that were relegated from the championship in ‘year 1′ and consequently spent ‘year 2′ in league one:

Year	League	Games	Goals scored	Goals per game
‘Year 1′	Championship	1380	1406	1.019
‘Year 2′	League one	1380	1951	1.414

So to calculate how much a goal scored in the league one is worth in the championship:

^{Goals for per game (championship)}/_{Goals for per game (league one)} = ^1.019/_1.414 = 0.721

How about the other way around, teams that are promoted in ‘year 1′ and spend ‘year 2′ playing in the championship?

Year	League	Games	Goals scored	Goals per game
‘Year 1′	League one	1380	2236	1.620
‘Year 2′	Championship	1380	1691	1.225

^{Goals for per game (championship)}/_{Goals for per game (league one)} = ^1.225/_1.620 = 0.756

The two ratios match pretty well, as found in the previous post, and by taking the average I’m going to estimate that a goal in league one is worth ~0.738 goals in the championship. By following the same process for goals conceded and I got values of 0.799 and 0.711 for relegation and promotion which have a similar average as goals for (of ~0.755)although once more the spread of the two values is wider than for goals for.

Next time I visit this topic I’ll have a similar look at the next rung of the ladder, the teams promoted to and relegated from league one.

Predicting the 10-11 Premiership standings

Jameswgrayson — Mon, 06 Jun 2011 23:26:18 +0000

Yer yer I’m aware the season has finished. But by using what I’ve learnt thus far how would I have predicted the premiership table to look at the start of the season? These are the actual and expected numbers:

Team	Pos	Points	±	Exp pos	Exp points	Exp ±
Mancheter United	1	80	+41	3	70	+30
Chelsea	2	71	+36	1	80	+42
Manchester City	3	71	+27	7	57	+10
Arsenal	4	68	+29	2	72	+28
Tottenham Hotspur	5	62	+9	5	62	+16
Liverpool	6	58	+15	4	67	+21
Everton	7	54	+6	6	60	+11
Fulham	8	49	+6	9	49	-5
Aston Villa	9	48	-11	15	44	-8
Sunderland	10	47	-11	12	45	-9
West Bromwich Albion	11	47	-15	13	45	-11
Newcastle United	12	46	-1	18	38	-17
Stoke City	13	46	-2	20	34	-22
Bolton Wanderers	14	46	-4	14	45	-13
Blackburn Rovers	15	43	-13	9	50	-3
Wigan Athletic	16	42	-21	8	52	-8
Wolverhampton Wanderers	17	40	-20	16	42	-16
Birmingham City	18	39	-21	17	41	-14
Blackpool	19	39	-23	19	38	-21
West Ham United	20	33	-27	11	47	-8

So there’s a mixed bag. On the plus side I had the top seven correct and roughly in the right order. I also had the teams that finished 17th, 18th and 19th projected to finish 16th, 17th & 19th respectively. In all I would have got eight of the point totals correct to within two points.

On the other hand I’d also have been wildly wrong for some of the others. In particular Manchester City, Stoke, West Ham and Wigan all stand out as poor projections.

I think I can explain a couple of these. This is a very basic model and it doesn’t account for transfers so it is no surprise to see that it underestimated Manchester City and it’s £150m summer upgrade.

I also think there’s an element of scorer bias at the DW stadium as Wigan (as I’ve mentioned previously) always seem to have a lower points total than their SOTR suggests they deserve and that would skew this prediction (I’ll be looking at scorer bias in the near future).

To me West Ham were a complete surprise. I think in the end they were worse than expected and this was compounded by a pretty terrible PDO. If they had the same squad next season I’d expect them to do very well in the championship but obviously that won’t be the case.

Finally there is Stoke. Looking at how they’ve performed the last two seasons it appears possible that their style of play allows them to obtain good results whilst producing few shots on target (the opposite may also be true for Arsenal) but I only have two seasons of data for them so it is equally likely they have simply been lucky.

So there is the table the stats I have would have projected at the beginning of the season. Later in the summer I’ll put out the numbers for the 11-12 season and see how that looks.