The player rated 400 points higher than their opponents wouldn't be expected to get 5/5 95% of the time Craig. The 95% expectancy would mean the strong player would average 4+3/4 (4.75) out of five, eg half the time getting 4.5 and half the time 5/5. Not that far from reality?
Not that I'm disagreeing with you...a statistician IS at hand - Jeff Sonas, who has written several articles about rating theory vs practice. Here's the first one
http://en.chessbase.com/post/the-elo-rat...ncy-tables
According to this 2011 article:
1) The true theoretical expectancy of the stronger player at a 400 difference is 92% (eg see the first graph on the link).
2) Rating differences of less than 400 slightly exaggerate the expectation of the higher player compared with practice, which continues up to the 400 point - supporting the feeling expressed by Craig and Steve (See the fourth graph).
3) Because of the 400 cutoff, the stronger player is favoured at differences of more than 400 as their score continues to increase with the rating difference (going up to at least 98% for 600 plus, after which the data gets a bit sparse), while the expectation actually used is fixed at a lower value by the cutoff. This favours the stronger player but is kind of pairing is probably rarer.
Careful what you lobby for - for aspiring GM norm hunters, does the difference between expectation and reality not work in your favour when you play a GM rated much higher than you are!?
Hope helpful.
Cheers
[/quote]
Not that I'm disagreeing with you...a statistician IS at hand - Jeff Sonas, who has written several articles about rating theory vs practice. Here's the first one
http://en.chessbase.com/post/the-elo-rat...ncy-tables
According to this 2011 article:
1) The true theoretical expectancy of the stronger player at a 400 difference is 92% (eg see the first graph on the link).
2) Rating differences of less than 400 slightly exaggerate the expectation of the higher player compared with practice, which continues up to the 400 point - supporting the feeling expressed by Craig and Steve (See the fourth graph).
3) Because of the 400 cutoff, the stronger player is favoured at differences of more than 400 as their score continues to increase with the rating difference (going up to at least 98% for 600 plus, after which the data gets a bit sparse), while the expectation actually used is fixed at a lower value by the cutoff. This favours the stronger player but is kind of pairing is probably rarer.
Careful what you lobby for - for aspiring GM norm hunters, does the difference between expectation and reality not work in your favour when you play a GM rated much higher than you are!?
Hope helpful.
Cheers
[/quote]