|2016-10October 2016 | |- style="text-align: center;" |1010 (tie) | 2816 | style="text-align: left;" | Veselin Topalov |2015–07July 2015 | |- style="text-align: center;" |1010 (tie) | 2816 | style="text-align: left;" | Hikaru Nakamura |2015-10October 2015 | |- style="text-align: center;" |1010 (tie) | 2816 | style="text-align: left;" | Ding Liren |2018-11November 2018 | |- style="text-align: center;" |1313 | 2810 | style="text-align: left;" | Alexander Grischuk |2014-12December 2014 | |- style="text-align: center;" |1414 | 2804 | style="text-align: left;" | Alireza Firouzja |2021-11December 2021 | |- style="text-align: center;" |1515 | 2798 | style="text-align: left;" | Anish Giri |2015-10October 2015 | |- style="text-align: center;" |1616 (tie) | 2793 | style="text-align: left;" | Teimour Radjabov |2012-11November 2012 | |- style="text-align: center;" |1616 (tie) | 2793 | style="text-align: left;" | Ian Nepomniachtchi |2022-10October 2022 | |- style="text-align: center;" |1818 (tie) | 2788 | style="text-align: left;" | Alexander Morozevich |2008-07July 2008 | |- style="text-align: center;" |1818 (tie) | 2788 | style="text-align: left;" | Sergey Karjakin |2011-07July 2011 | |- style="text-align: center;" |2020 | 2787 | style="text-align: left;" | Vassily Ivanchuk |2007–10October 2007 | |- style="text-align: center;" |} Average rating over time The average Elo rating of top players has risen over time. For instance, the average of the top 10 active players rose from 2751 in July 2000 to 2794 in July 2014, a 43-point increase in 14 years. The average rating of the top 100 players, meanwhile, increased from 2644 to 2703, a 59-point increase. Many people believe that this rise is mostly due to an anomaly known as ratings inflation, making it impractical to compare players of different eras. Elo said it was futile to attempt to use ratings to compare players from different eras and that they could only measure the strength of a player as compared to their contemporaries. He also stated that the process of rating players was in any case rather approximate - he compared it to "the measurement of the position of a cork bobbing up and down on the surface of agitated water with a yard stick tied to a rope and which is swaying in the wind". Chessmetrics Many statisticians besides Elo have devised similar methods to retrospectively rate players. Jeff Sonas' rating system is called "Chessmetrics". This system takes account of many games played after the publication of Elo's book, and claims to take account of the rating inflation that the Elo system has allegedly suffered. One caveat