Rounding error

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David Blower
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Rounding error

Post by David Blower » Mon Dec 30, 2013 11:18 pm

Does this play a part in possible inaccurate grades?

For example imagine player A having a grade of 100. This would be 100 to the nearest whole number, when the actual grade is somewhere between 99.5 and 100.5 The amount of points needed for this is 3000 as 3000/30=100. But in reality the actual amount of points got by the player could be anything in between 2985 and 3014 inclusive.

I know from my experience of mathamatics that if you round up or down at an early stage, several stages down the line when you get to your final answer the margin can be pretty big, but I'm not suggesting the ECF introduces decimal points into the grading system, I'm quite happy with whole numbers.

But I do wonder what affect it has.

Andrew Camp
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Re: Rounding error

Post by Andrew Camp » Mon Dec 30, 2013 11:35 pm

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Roger de Coverly
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Re: Rounding error

Post by Roger de Coverly » Tue Dec 31, 2013 12:10 am

David Blower wrote: But in reality the actual amount of points got by the player could be anything in between 2985 and 3014 inclusive.
I doubt that's a problem as the underlying statistical theory suggests that grades are only accurate to 8 ECF points anyway over 30 games. To clarify a little, a higher grade says you are a "better" player but there's only confidence in the statistical sense in that verdict if you are at least 8 points higher.

International FIDE Elo used to reflect this as well, by rounding so that every rating finished in a 5 or 0. One well known Grandmaster whose name began with S, objected to this as the tie-break was then alphabetic order, so he could miss out by being ranked below others above him in the alphabet, but equal to him in rating.

Ratings and grades now matter for seeded pairings. It's a shame really that no one developed an accepted computer method of doing random or semi random pairings.

David Sedgwick
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Re: Rounding error

Post by David Sedgwick » Tue Dec 31, 2013 10:12 am

Roger de Coverly wrote:International FIDE Elo used to reflect this as well, by rounding so that every rating finished in a 5 or 0. One well known Grandmaster whose name began with S, objected to this as the tie-break was then alphabetic order, so he could miss out by being ranked below others above him in the alphabet, but equal to him in rating.
I don't think that's quite right. The tie-break was the number of games played in the previous rating period and he missed out on an invitation to a top event in favour of a Grandmaster who had played slightly more games.

That tie-break is still used, but is less likely to be important with ratings rounded to the nearest whole number.

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John Upham
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Re: Rounding error

Post by John Upham » Tue Dec 31, 2013 10:19 am

I'd like to see an in-depth analysis of this critical matter from Robert Jurjevic.

Perhaps David and Robert could commence a pilot study of rounding errors in the Clarke grading system since its inception?

I look forward to the outcome.
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