How High Can Magnus Go?

Still a teenager, the Norwegian superstar Magnus Carlsen rocketed to the top of the world rankings at the end of 2009.  Three years later, he has yet to reach orbit.  Indeed, Number One continues to climb, breaking records set by his one-time mentor, the great Garry Kasparov.  How high will he go?
 

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The chess media focuses on the new record rating of 2861, but equally impressive is the 51 point gap that almost suddenly opened up between Carlsen and his followers.  For perspective, consider that reigning world champion Viswanathan Anand occupied the top spot merely a year and a half ago.  Today, the nearest challengers are ex-champion Vladimir Kramnik and Levon Aronian.  Indeed, Carlsen separated himself not just from the veterans Anand and Kramnik, but from an entire constellation of younger super-duper-Grandmasters.  A popular saying suggests that more competition provides good motivation; if it doesn't kill you, it makes you stronger!

However, the current 51 point lead hardly counts as a record.  A couple of years before his retirement, Kasparov pulled 79 points ahead of Kramnik.  Further back in history, Bobby Fischer at 2785 was the only player rated above 2700 before the 1972 clash, fully 125 points ahead of defending champion Boris Spassky.  One could draw several conclusions: 1. Fischer was just that good.  2. The competition was weaker than today.  3. Modern players are all overrated. 

What do these numbers suggest about Magnus Carlsen's future rating?  The Elo rating system invented by the Hungarian born but American educated Arpad Elo relies on a statistic formula to correlate the difference in skill (more precisely: head-to-head performance)  between two players to the difference in their chess rating.  **  In principle, a 2700 should score equally well against a 2800 as a 1300 would do versus a 1400. 

Thus the most significant number for our Norwegian hero is not 2861, but rather 51.  According to the Elo formula, the higher rated Kramnik, Aronian, Anand and other mere mortals become, the more likely Carlsen will reach even closer to the stars.

Of course, any talented young player who dutifully studies the game will naturally improve through age, experience and knowledge.  At 22, Carlsen should expect another decade of full speed ahead before he reaches maturity, albeit at an astronomically high elevation.  Historians will compare his peak separation from the rest of the world to the golden standard set by the greatest chess Grandmasters of all time: Kasparov and Fischer.

The answer seems obvious: Magnus Carlsen will shoot into an unprecedented orbit.  By now, 2900 seems a foregone conclusion; it is merely a question of how soon?  Even the oft critical Kasparov has publicly conceded this point, provided that his former protégé maintains his sharp concentration and work ethic.  Indeed, the real question is: Will Magnus be the first human to break 3000?  Stay tuned.

** The greater the rating difference, the larger the burden falls on the top player to win.  For example, a player rated 70 points higher than the opponent must score 60% to hold this rating.  As the difference reaches 200 points, the higher ranked one needs to win 75% to break even.