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PostPosted: Sat Jul 14, 2012 1:42 pm 
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I've been seeking to provide some numbers for this question, too.

I started with a fundamental principle: That a county should be able to field a full team without dipping into the next grading band down. For example, a U180 team should be able to field a team filled entirely with players graded 160-179. The reason for this is that at the national stages, a strong county ought to be able to field teams in every section without one team stealing players from another. (Yorkshire and Lancashire do this at the moment with admirable success.) For that reason, I've ignored the U100, on the basis that there is no section below it creating a floor.

So I've totted up the number of players in the wrong band playing for a team. There are two potential things that may distort this:
(1) A reserve. Neil Graham, for example, leaped from the concession stand to fill in when a Nottinghamshire player was absent.
(2) Improvement. A county may be putting in someone graded 70 into the Under 120 because he's genuinely improved significantly from the start of the season, and they don't have an Under 100 team to put him in. This could be resolved by looking only at players under the limit of the section minus 20 who are on boards at the bottom, but I decided not to do that for this, because this only occurred to me after I'd got the data for two sections out of four, and I was too lazy to go back and correct everything. I don't think this will be that significant.
(3) Some reports had January grades, not July grades. I couldn't be bothered to change them, so didn't. This only affected two games out of everything, so far as I could tell.

First, the Under 180 section. The following table shows everyone who qualified for the national stages, sorted by the number of players available within that boundary.

Image

This makes the far-from-startling discovery that the biggest counties went the furthest in the tournament. It also shows that the counties that reached the Final used far fewer players from other sections than other teams.

Why did Surrey dip into the < 160 players so much? Given their size, they had enough bums to put on seats within the boundary. They can't blame their Open team for taking the players away; only 1 player in the Open was under 180 last season. I'm not sure I can think of an explanation for that.

On average, 4.25 boards were below 160. That's about 26%.

Next, the Under 160.

Image

There's a much less intuitive relationship here between progression through the event, and the number of players from the wrong section. This can be explained by Kent losing to Yorkshire in their opening match; both of which ought to have gone far in the competition had they avoided each other. The Semi Finalists were about as good as each other in terms of putting out players in the right section.

On average, 3.01 boards were below 140. That's about 18%.

Image

Same again, this time Under 140. The counties with the most players from below 120 were Leicestershire and Yorkshire. Neither county made it beyond the Quarter Finals.

This time, an average of 1.75 boards were below 120, which is just 11%.

Image

Finally, the Under 120. Again, Staffordshire and Norfolk went out early, and they had the most players under 100.

2.02 boards under 100 on average, 17%.

I've attempted to summarise the above as a table.

Image

It seems to me that there is a problem with the Under 180 section, in so much as the counties that field teams in it have to dip into the pool of players below 160 too much. I would argue that the Under 160 and Under 120 were also too high, whereas the Under 140 figure is probably reasonable. This would suggest to me one of two things: Either (a) There are too many sections, or (b) The teams are too big.

I'm going to see if there's a relationship between the size of the county, and the number of players in other sections they have to use. I'd be amazed if there wasn't, but I think it's worth doing to clarify!

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PostPosted: Sat Jul 14, 2012 2:23 pm 
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You need to remember here that the sizes of squads that county captains call upon isn't static. It changes as players move in and out of grading bands, and it changes as a captains builds up contacts and persuades people to play county chess.


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PostPosted: Sat Jul 14, 2012 2:27 pm 
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As promised, here are the graphs...

Image

Image

Image

Image

The U180 and U160 show that as the number of eligible players for a team goes up, the number of players 20 points below them in the team goes down. On the other hand, the U180 and U160 favour the bigger counties. By contrast, the U140 and U120 are seemingly uncorrelated in this regard. I would expect there to be this correlation, but I don't see it. I leave others to come up with reasons for it not existing, or indeed, a reason why it shouldn't exist in the U180/U160!

Sometimes, adding together collections of random points can help to form something that is a pattern. So I tried it. I added together all sections in one graph, and looked for a pattern.

Image

I don't see anything the other graphs didn't show. The R^2 value is approximately the mean R^2 value of the above four R^2 values.

Anyway, conclusions from these posts:
(1) The number of eligible players for a section is related to the number of players playing up from another section; but only really in the U160 and U180.
(2) The sections are too tight. In the light of (1), I'd be prepared to accept that U140 is doing fine. If the U120 was the bottom section, and was expanded to 16 boards, then I think that would be fine too. (This would mean doing away with the U100, which is hardly flooded with entries now.) The U160 and U180 is probably one section too many though, and it might be better to replace them with a U170 section.

I invite comments on these conclusions.

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PostPosted: Sat Jul 14, 2012 2:30 pm 
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Christopher Kreuzer wrote:
You need to remember here that the sizes of squads that county captains call upon isn't static. It changes as players move in and out of grading bands, and it changes as a captains builds up contacts and persuades people to play county chess.


I have remembered these things.

I'm only comparing one season's worth of data. Players can't move in and out of grading bands in one season, because eligibility is based on one grading list.

I see the ability of the captain (i.e. his contacts and ability to get people to play) as a variable, which I would say is responsible for some of the anomalies on this page. There's absolutely no way I can model this, so I haven't tried to!

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PostPosted: Sat Jul 14, 2012 2:35 pm 
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Alex Holowczak wrote:
The U160 and U180 is probably one section too many though, and it might be better to replace them with a U170 section.


On a personal level, my grade next season is likely to be 170... :( (not that anyone should let such thing influence their opinions, as any grading boundaries will always affect some unlucky people). When would any grading bands for the forthcoming season be decided by, by whom, and at which meetings?


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PostPosted: Sat Jul 14, 2012 2:39 pm 
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Christopher Kreuzer wrote:
Alex Holowczak wrote:
The U160 and U180 is probably one section too many though, and it might be better to replace them with a U170 section.


On a personal level, my grade next season is likely to be 170... :( (not that anyone should let such thing influence their opinions, as any grading boundaries will always affect some unlucky people). When would any grading bands for the forthcoming season be decided by, by whom, and at which meetings?


The grading boundaries for the forthcoming season are fixed at what they were last year. That was decided at April's meeting, since no one proposed anything to that effect.

It's important you've mentioned this, actually. I should make it explicit: The grade boundaries for 2012/13 are the same as 2011/12. This is purely for the sake of interest, despite the National Controller being the person who is publishing it!

This may well lead to a proposal for 2013/14's rules, but if so, the proposal should come from counties or a Union, not me.

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PostPosted: Sat Jul 14, 2012 2:54 pm 
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You've done some very interesting research there Alex.

I don't think it's surprising that the U180s have to dip into the U160s at a higher rate than any other sections, there are simply fewer players to choose from!

I think a case could be made for reducing the number of sections to Open and Minor, U170s, U140s, U120s, U100s but increase the number of boards for the top two competitions to 20 boards. This would allow at least a similar number of people to play in the competition whilst ensuring that more people play in the "correct" section.

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PostPosted: Sat Jul 14, 2012 3:08 pm 
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Andrew Bak wrote:
I don't think it's surprising that the U180s have to dip into the U160s at a higher rate than any other sections, there are simply fewer players to choose from!


Indeed it makes sense. If you think of the grades of chessplayers as normally distributed, then there are going to be fewer players at the top and bottom than there are in the middle. The data shown in the other thread supports the tail at the top, but not the tail at the bottom. I think this is for two reasons:
(1) The number of Under 100s is artificially inflated by juniors who play junior-only chess
(2) The tail doesn't really kick in until a much lower number than 100

I'd have to test which of these it really is, but I'm sure it must be one of them.

The sections as they are assume a linear relationship for grades, which isn't backed up by numbers.

Andrew Bak wrote:
I think a case could be made for reducing the number of sections to Open and Minor, U170s, U140s, U120s, U100s but increase the number of boards for the top two competitions to 20 boards. This would allow at least a similar number of people to play in the competition whilst ensuring that more people play in the "correct" section.


Perhaps:
Open/Minor: 20 boards
U170/U140/U120: 16 boards

That'd generate 88 boards of activity at Finals Day, whereas there are 104 now. So it's still a reduction, but I think it'd be a fairer reduction to get people playing in the correct sections. Given we have hardly any counties play at U100 (7 this year in the entire country even at the Union stages, 6 qualified for the national stages, 2 of which defaulted), I'm not sure it'd be a massive disaster to see it disappear. Increasing the U120 from 12 to 16 arguably gets around the problem.

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PostPosted: Sat Jul 14, 2012 3:55 pm 
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Alex Holowczak wrote:
Andrew Bak wrote:
I don't think it's surprising that the U180s have to dip into the U160s at a higher rate than any other sections, there are simply fewer players to choose from!


Indeed it makes sense. If you think of the grades of chessplayers as normally distributed, then there are going to be fewer players at the top and bottom than there are in the middle. The data shown in the other thread supports the tail at the top, but not the tail at the bottom. I think this is for two reasons:
(1) The number of Under 100s is artificially inflated by juniors who play junior-only chess
(2) The tail doesn't really kick in until a much lower number than 100

I'd have to test which of these it really is, but I'm sure it must be one of them.


Test complete.

I've ignored 0 grades.

Image

This looked wrong to me, because the left hand side of the graph looks to be too flat, and not a true normal distribution. I figured juniors were the problem, so I removed them.

Image

And this looks much more like a normal distribution to me. Albeit, the left side of the curve is still much flatter. I suspect this is explained by players who are new to the game and haven't found their true ability yet, whereas the right is caused by things like the London Chess Classic and Gibraltar giving the likes of Carlsen and Ivanchuk a grade.

Either way, it sure as hell ain't linear. Given the peak of the graph is between 120-140, I think it explains why the U140 as a section limit works even as a 20-point boundary, it's the mean of the graph. (By calculating the mean, rather than reading it off the graph, you get 127 with juniors, 120 without.)

Edit: This isn't quite right. See below!

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Last edited by Alex Holowczak on Sat Jul 14, 2012 4:09 pm, edited 1 time in total.

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PostPosted: Sat Jul 14, 2012 4:00 pm 
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Alex Holowczak wrote:

Perhaps:
Open/Minor: 20 boards
U170/U140/U120: 16 boards

That'd generate 88 boards of activity at Finals Day, whereas there are 104 now. So it's still a reduction, but I think it'd be a fairer reduction to get people playing in the correct sections. Given we have hardly any counties play at U100 (7 this year in the entire country even at the Union stages, 6 qualified for the national stages, 2 of which defaulted), I'm not sure it'd be a massive disaster to see it disappear. Increasing the U120 from 12 to 16 arguably gets around the problem.


When I made my original post, I originally had just a U140 and then a U110 section, for similar reasons that you gave. Since the grades got revised a couple of years ago, there aren't that many players U100 any more.

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PostPosted: Sat Jul 14, 2012 4:17 pm 
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I've redone the graph, taking out * players, which are active players without grades. (They annoy me when I import them to Tournament Director, and they've come back to bite me again.)

These are the two corresponding graphs. They're much closer to the normal distribution! Maybe a little triangular for my liking...

Image

Image

The same point holds though. Grades are normally distributed, and aren't linear.

The means by calculation are 133 and 136 respectively. Again, in the 120-140 section.

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PostPosted: Sat Jul 14, 2012 4:21 pm 
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Andrew Bak wrote:
Since the grades got revised a couple of years ago, there aren't that many players U100 any more.


There are loads of U100 players. Here's a breakdown from the masterlist used in the other thread:
U100: 1873
100-119: 1816
120-139: 2130
140-159: 1912
160-179: 1312
180+: 1083

There are plenty of players who can play in an Under 100 team. Each county has loads. Yorkshire has 72 we know about, and probably many more we don't.

The only reason I can think of them not doing well is a lack of captains who are in that grade range (or who are willing to run it).

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PostPosted: Sat Jul 14, 2012 5:16 pm 
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Looking at the results from the union stages, it might be worth considering merging the U180 and the Minor Counties and having a single U190 (or U195 or U200) competition. The big counties would be able to run Open and U190 teams, while the smaller counties could choose whichever competition they feel most comfortable with.

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PostPosted: Sat Jul 14, 2012 5:23 pm 
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Ian Kingston wrote:
The big counties would be able to run Open and U190 teams


I doubt this, or at the very least there would be so much overlap that those running Open and U190 teams would end up fielding weakened U190 teams that would lose to counties who were not fielding Open teams and able to field full-strength U190 teams. Though I'm not sure how many players there are in the 180-189 bracket. There is the issue that counties with large numbers of 180+ players sometimes have to leave out players in the low 180s when fielding strong teams (i.e. some players in the low 180s don't get chances to play county chess). But for the smaller counties, the reverse is true.

PS. Has anyone ever considered scrapping the country boundaries and redrawing new boundaries that accurately reflect the location and sizes of the various centres of chess playing strength? Is there a way to divide the country neatly into areas of equal playing strength and population? (Yeah, I know I can hear the various county chess unions protesting even as I type.)


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PostPosted: Sat Jul 14, 2012 5:37 pm 
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Christopher Kreuzer wrote:
Ian Kingston wrote:
The big counties would be able to run Open and U190 teams


I doubt this, or at the very least there would be so much overlap that those running Open and U190 teams would end up fielding weakened U190 teams that would lose to counties who were not fielding Open teams and able to field full-strength U190 teams. Though I'm not sure how many players there are in the 180-189 bracket. There is the issue that counties with large numbers of 180+ players sometimes have to leave out players in the low 180s when fielding strong teams (i.e. some players in the low 180s don't get chances to play county chess). But for the smaller counties, the reverse is true.


I think Ian's suggestion was to turn the Minor into an U190. But you could enter both if you wanted. (I can't see in reality that anyone would.)

Christopher Kreuzer wrote:
PS. Has anyone ever considered scrapping the country boundaries and redrawing new boundaries that accurately reflect the location and sizes of the various centres of chess playing strength? Is there a way to divide the country neatly into areas of equal playing strength and population? (Yeah, I know I can hear the various county chess unions protesting even as I type.)


I don't see what that would achieve, because it wouldn't be a county competition anymore.

I'm perfectly happy with having counties of different size. There's no solution that fits everyone; there never can be.

The suggestion I've made re a U170, getting rid of U180/160, is that there aren't enough players of that ability to fit. The evidence for this can be seen from:
(1) The distribution of grades.
(2) The fact that 25% of players in the national stages of the U180 were actually < 160, so were eligible for another section.

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