Comparison of Magnus Carlsen, Levon Aronian, and Vladimir Kramnik in
Major Round-Robin Tourneys or Matches, 2010--2012, 6 games minimum.
IPR and IPR-versus computed using Rybka3 depth-13 50-PV data, with
all moves weighted equally and probability-matching of tied-value moves.

This writeup copyright (c) Kenneth W. Regan, 19 December 2012.


Carlsen:
IPR  #mv IPRv Diff Event
2829 357 2609  220 Bazna 2010
2726 366 2850 -124 Bilbao GSF 2010
2798 322 2642  156 London Classic 2010
2887 379 2683  204 Nanjing Pearl Spring 2010
2918 273 2732  186 Bazna 2011
2872 306 2620  252 London Classic 2011  
2718 369 2589  129 Moscow Tal Mem 2011
2841 384 2683  158 Wijk Tata 2011
2855 340 2644  211 Biel 2012
2812 338 2582  230 London Classic 2012
2802 332 2560  242 Moscow Tal Mem 2012
2648 391 2647  001 Sao Paulo-Bilbao Final Masters 2012  (whole event 2690)
2797 571 2738  059 Wijk Tata 2012
-------
2808 average, median 2812, average 2807 for 2011-2012. 
2660 avg.vs., median 2644  average 2644 for 2011-2012


Aronian:
IPR  #mv IPRv Diff Event
2787 408 2777  010 Linares 2010
2917 286 2744  173 Moscow Tal Mem 2010
2884 224 2776  108 Shanghai 2010
2737 257 2733  004 London Classic 2011
2840 389 2741  099 Moscow Tal Mem 2011
2758 344 2716  042 Sao Paulo-Bilbao GSF 2011  (whole event 2624)
2820 375 2671  149 Wijk Tata 2011
3002 169 2604  398 Aronian-Kramnik match
2680 335 2850 -170 London Classic 2012
2739 274 2693  046 Moscow Tal Mem 2012
2704 315 2543  161 Sao Paulo-Bilbao Final Masters 2012 (whole event 2690)
2760 427 2423  337 Wijk Tata 2012
-------
2802 average, median 2760-2787, average 2782 in 2011-12
2689 avg.vs., median 2693-2716, average 2664 in 2011-12

Not counted:

2926 309 2736  190 Aronian at Istanbul Olympiad 2012


Kramnik:
IPR  #mv IPRv Diff Event
3086 200 2893  193 Bilbao GSF 2010
2659 365 2762 -103 London Classic 2010
2554 270 2650 -096 Moscow Tal Mem 2010
2712 207 2798 -086 Shanghai 2010
2775 331 2626  149 Dortmund 2011
2705 184 2587  118 Hoogeveen Unive Crown 2011
2839 282 2576  263 London Classic 2011
2660 332 2923 -263 Moscow Tal Mem 2011
3016 322 2826  190 Wijk Tata 2011
2604 168 3002 -398 Aronian-Kramnik match
2851 314 2762  089 Dortmund 2012
2991 316 2677  314 London Classic 2012
2773 323 2809 -036 Moscow Tal Mem 2012
-------
2787 average, median 2773, average 2802 for 2011-2012
2761 avg.vs., median 2762  average 2754 for 2011-2012

Not counted:
2745 343 2775 -030 Kramnik at Istanbul Olympiad 2012


Conclusion: Carlsen +148, Aronian +113, Kramnik +26.  Have not normalized for
the average Elo of opponents, nor weighted by the number of moves.  But much
of Aronian's "gain" is from his match with Kramnik and freakish-low IPR-versus
at Wijk 2012.  The medians show Aronian and Kramnik allowing many 2700+
IPR-versus performances by opponents, Carlsen almost none (3 of 13).
That seems to be the root of Carlsen's current 50-60 Elo bulge over both.