OK, I need to revisit the rating performance calculation issue for Ivanchuk. I think we were all off base with how it's determined. After Round 5, Chessbase reported that Ivanchuk's performance was +797 points. And after Round 6, Chessbase reported that with Ivanchuk's Round 6 draw, his performance was now "only" +415 points. So clearly, either Chessbase is wrong, or I'm wrong in my understanding of the calculations. After looking at the FIDE handbook, I think Chessbase was right, and I was wrong.
Apparently the way it should be calculated is as follows:
1) Calculate the average elo of Ivanchuk's opponents for the rounds played. (If this is being done after Round 6, then you have to add Radjabov's rating twice, since Ivanchuk played him twice. After summing the 6 rating numbers, you then divide by 6.)
2) Using the table in the FIDE handbook, section B.02.10.1.a, calculate the difference points (dp) according to Ivanchuk's percentage score (p=Points obtained/Number of games).
Apparently, this table is just an approximation of the exact equation:
dp = -400 x log(1/p - 1)
(in the above equation, the x means multiply)
3) Then Ivanchuk's performance is obtained by adding the results of 1) and 2) above. That is, Performance = Average ELO of Rivals + dp
I used this method to calculate the Round 6 performance for Ivanchuk and Topalov (I used the exact equation instead of the chart), and I got within 2 points of the value Chessbase got for Ivanchuk and within 1 point of the value Chessbase got for Topalov.
For example, for Topalov after Round 6, the average elo of his opponents was 2736.8333. Topalov's percentage score was 4.5/6, or 0.75. Plugging these numbers into the dp equation, we get dp = 190.85. Therefore, Topalov's performance was 2736.8333 + 190.85 = 2927.68, which is about 160.7 points above his rating of 2767. Chessbase gave a value of +160, which is about the same as I got, considering roundoff error.
The curious thing you can see from the table is that at a percentage score of about 0.92, the value for the difference points is 400 points. And as the percentage score goes above 0.92, the difference points continue going up. (At a p of 0.99, the dp is 677.) And for Ivanchuk after Round 5, his p was 1.0, which is undefined for the equation, and it basically means that the difference points have an infinite value. (I suspect this is the reason that the Chessbase report for Round 5 carried the title, "MTel R5: Ivanchuk aiming for infinity with 5.0/5".) 🙂
The only thing I don't understand is how Chessbase came up with the +797 performance number for Ivanchuk after Round 5. (Technically, his performance was infinite.) It appears that they arbitrarily assigned a value of 800 for the dp, correlating to a p of 1/1.01, or 0.990099. If you use these arbitrary numbers, you get a +797 performance as Chessbase reported.
Dang, I hope I don't get any questions on this - my head hurts. 🙂