Chess Scotland Noticeboard

Daniel Rocks · Posted: Tue Feb 13, 2007 5:06 pm Post subject: 200^ Rule

Hi, I have a question...

I have played 43 games this season and gone from 1287 to 1578. How is my grade calculated now?, is it calculated based on if I was an un-graded player? (eg) If I played an average opposition of 1650 and scored 1650... I would be graded 1650? Or, since I have played 30+ games, do I get penalised for the number of games I have played.

Thanks,

Sad geek (aka Rocksy)

HLang · Queen Joined: 08 Feb 2007 Posts: 151 Location: Oxford

200-up rule: see http://www.chessscotland.com/grading/gradeexp.htm. (Maybe this link could be a sticky at the top of the board?)

You will be treated as ungraded. It's unlikely (though possible) that someone who's gone up more than 200 points won't have played close to 30 games anyway.

Now some more general points - I've been trying to think of a way to explain about this "you get penalised for playing 30 + games" myth.

You're never penalised for playing more than 30 games. In fact, if you are already graded and improving, you are "penalised" by the system until you reach 30 games. This is because a few results are a less accurate estimate of your playing strength than a lot of results, so there's an extra "damping factor" in the system for < 30 games so that grades don't fluctuate too wildly.

The myth that you "get less points for a win after you've played 30 games" probably comes from people typing their results into the grading spreadsheet. The assumption that the grading system makes is that the best estimate it can get of your strength is (more or less - I'm simplifying a bit) your average performance for the whole season compared with your current grade. Each individual result (good or bad) changes your average performance (and therefore your change in grade) less when you've played more games[1]. But the order you play the games in doesn't matter - it's not that later results affect the average performance less than earlier ones.

Did you ever do that thing in school where they measured everyone's height and plotted it on a chart with height along the x-axis and number of people along the y-axis? You're supposed to get a normal / Bell / Gaussian distribution. But with a small number of people it looks blocky, and probably not like it would if you measured more people.

And then as you measure more heights in the population, it gets more and more like the theoretical distribution, until, if you zoomed out, you'd see a smooth-looking Bell-shaped curve, with the average height at the centre of the curve. The more heights you measure, the less each "odd" height sticks out like a sore thumb. Finally, note that the order we measure the heights in doesn't matter - we'll still get the same graph at the end as long as we measure the same group of people.

It's kind-of similar with rating performances. Once your average performance is based on a large number of games, each "odd" good or bad result that is above or below that average affects the average less.

Footnote:

[1] The average of 2.2 and 10 is 6.10 (the numbers added together and divided by 2).

The average of 2.2, 2.2, 2.2 and 10 is 4.15 (the numbers added together and divided by 4).

The average of 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2, 2.2 and 10 is 2.85 (the numbers added together and divided by 12).

The average of 29 lots of 2.2 plus a single 10 is 2.46 (the numbers added together and divided by 30).

The average of 149 lots of 2.2 plus a single 10 is 2.25 (the numbers added together and divided by 150)

With more numbers to take an average of, the "outlier" (the 10 in this case) has a smaller effect on the overall answer.

Now, suppose that I'm working out these averages to determine how much someone's grade should change in a simplified system I've just invented to help explain this. How am I going to stop that naughty 10 (a single result - maybe the opponent's phone went off, or they were ill on the night, or blundered) from making the change in grade far too high?

So I go off and do a bit of maths, deciding on the standard error that is acceptable on this grade. And realise that 30 results is the number required for the error on the grade to be within two standard deviations[2]. So I introduce a damping factor - if the player has played less than 30 games, I will divide the numbers added together by 30 instead of by the number of games.

Note that this also applies to damp out a single bad result (e.g. the average of 2.2, 2.2 and -10) - maybe your phone went off, or you were ill, or blundered and lost to someone much weaker than you.

NB: I've deliberately chosen to use numbers that don't look like grades to illustrate this so that I can't get pedanted.

[2] I'm not sure if you've done any stats in maths. If not, then these two sentences might not make sense.

Daniel Rocks · Posted: Wed Feb 14, 2007 4:33 pm Post subject: average opposition

Ok, given that my average opposition is 1550 from 43 games... If I played someone graded 1250 and I won, would my grading go down?,

DR

HLang · Queen Joined: 08 Feb 2007 Posts: 151 Location: Oxford