Ranking Athletes at the Olympics
The Weighted Ranking Systems ( more details )
simple point system (3:2:1) — gold  3 points, silver 2 points, and bronze  1 point.
New York Times weighted point system (4:2:1) — gold  4 points, silver  2 points, and bronze  1 point.
1908 London point system (5:3:1) — gold  5 points, silver  3 points, and bronze  1 point.
Luchies  Olympic Formula (LOF)  point system (5:3:2) — gold  5 points, silver  3 points, and bronze  2 point.
Topend Sports point system (6:2:1) — gold  6 points, silver  2 points, and bronze  1 point.
Topend Sports Ranking Method
My compromise weighting method ( Topend Sports 6:2:1 ranking system ) incorporates both gold and total medal counts -  it  gives the most credit for gold medals (6 points), but then still some credit for the minor medals - so if an athlete has a large number of the minor medals without the corresponding golds then they may still rank well. As this method gives the most points for gold medals, it most closely matches the ranking for the gold medal only system.
There are a couple of examples on this table where the Topend system appears to give a better result. This system rates Gymnast Nikolai Andrianov (7-5-3=15) on equal with another gymnast Sawao Kato (8-3-1=12), which on face value seems fair. Also Carl Lewis on 9-1-0=10 ranks the same as canoeist Birgit Fischer on 8-4-0=12.
Not All Sports Are Equal
One things that is clear from this table is that athletes from the sports of swimming, gymnastics and athletics are highly represented, as a result of the  many more medals available in these sports, particularly if you compare it to the team sports such as football, handball and hockey where there is only one of each medal available at each Olympiad. Not only are there more medals  available in some events than others, and the number of events in which medals are available overall have changed over time. Because of this, we had done additional analysis to compare only within each sport, and find the highest ranked athletes from each sport .
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about Olympic Medals
Old Comments
Of course we tend to focus on the glamour sports & perhaps don't have an appreciation of the 2nd & 3rd tier. Perhaps a different table is to mark the all-time best Olympic performing moments such as these (from  KIM L., 4 July 2012)
1984 LA S.O. American Mary Lou Retton nails a perfect 10.0 on the last event (vault) to win the All-Around;
1984 LA S.O. Swiss marathoner Gabriella Anderson-Schiess in a state of heat exhaustion struggles through a horrifying last 500 meters to finish the inaugural womens marathon to the delight of the American crowd;
1984 Sarajevo W.O. GB's Jane Torvill & Christopher Dean skate to Ravel's Bolero to score perfect 10s across the board to win the ice dance gold;
2008 Beijing S.O. American swimmer Michael Phelps becomes the most decorated Olympian of all time after winning 8 golds-the most ever in 1 Olympiad to add to 6 other medals;
1988 Seoul S.O. American trackstar sizzles to golds in the 100/200 in world & Olympic record time-records that still hold today to go with her 4 by 1 gold, her 200 silver, & 4 by 4 silver;
2008 Beijing O.G. Jamaica's sprint sensation Usain Bolt thunders to new world marks in the 100/200 & helps his team win the 4 by 1 relay;
1988 Seoul S.O. American diver Greg Louganis becomes the most decorated diver with his 4th gold won in the platform on his last dive;
1984 Sarajevo W.O. in the epic battle of the Brians, American figure skater Brian Boitano outduels Canadian rival Brian Orser for the gold;
1984 LA S.O. American Joan Benoit dazzles the hometown crowd by winning the first Olympic marathon;
1968 Mexico City S.O. American long jumper Bob Beamon jumps the unbelievable 29 plus feet at high altitude to establish a record that would hold for 20 years;
Australian swimmer Dawn Frasier becomes the only swimmer to pull off 3 consecutive gold medal wins in the 100 freestyle over 3 Olympiads;
1972 Munich S.O. Mark Spitz becomes the 1st swimmer & athlete to win 7 gold medals in 1 Olympiad;
1976 Montreal S.O. Romanian gymnast Nadia Comaneci becomes the 1st gymnast to score a perfect 10 & win the all-around title plus 3 event golds;
1968 Grenoble W.O. French skier Jean Claude-Killy becomes the Games' most decorated skier by winning all 3 alpine golds in the downhill, slalom, & giant slalom;
1960 Rome S.O. Ethiopian marathoner completes the 1st of his 2 gold medal marathon performances by running barefoot;
1952 Helsinki S.O. Czech Emil Zatopek completes the distance triple gold-winning the 5k, 10k, & marathon;
1960 Rome S.O. American sprint genius Wilma Rudolf, born w/ polio, sets the women's standard by winning the gold at 100, 200, & 4 by 1;
American sprinter/jumper Carl Lewis retires as one of the most decorated Olympians, winning medals in the sprints, relay, & 3 times in the long jump;
1976 Montreal S.O. Finnish legend Lasse Viren completes the historic double-double winning consecutive 5k/10k in 2 Olympiads;
Finn distance sensation Paavo Nurmi sets the standard in distance racing as one of the most decorated Olympians of all time;
American speed skater Bonnie Blair proves to be one of the most decorated Winter Olympians & winning her specialty the 500 3 times in a row;
1988 Calgary W.O. German figure skater Katarina Witt completes her 2nd consecutive gold in the ladies long program showing what grace under pressure is all about;
British rower Steven Redgrave becomes the most decorated Brit & goes down in history with the most rowing medals capsulated by his last gold;
1996 Atlanta S.O. American Michael Johnson becomes the best 200-400 specialist w/ double golds including a world record at 200-he would then go on to break the 400 record in winning at Sydney;
1912 Stockholm American Indian Jim Thorpe sets the standard in winning the decathlon;
1948 London S.O. Dutch girl Francia Blankers-Koen becomes one of the most celebrated inaugural woman in track w/ 4 golds;
American speed skater Dan Janson a veteran favorite who had failed to medal several times even though he was favored finally wins his gold medal in the 1000;
the speed skating feats of American Eric Heiden & Norwegians Bjorn Dailey & Olang Olav-Koss;
1984 Sarajevo W.O. Russian dominance continues with a lavish pairs performance by Ekaterina Gordeeva & Sergei Grinkov;
1992 Barcelona S.O. the UK's Derek Redmond pulls a hamstring halfway thru the 400 but is walked on to the finish by his dad who jumped the stands & made his way to the track;
1936 Berlin S.O. American legend Jesse Owens wins 4 golds;
1956 Melbourne S.O. American decathlete wins his 2nd decathlon gold;
1952 Oslo W.O. American figure skater Dick Button wins his 2nd gold medal;
1932 LA S.O. American Babe Didrikson rockets to the stuff of legends by winning several t&f medals;
1968 Mexico City S.O. American swim star Debbie Meyer wins the 100,200, & 400 freestyle events;
1968 Mexico City S.O. American standout Tommy Carlos runs a sub-20 second 200 to win the gold with a record that would stand for years to come;
1984 LA S.O. Brit star Seb Coe completes a rare double winning his 2nd consecutive gold at the 1500 distance;
1972 Munich S.O. American Dave Wottle comes from well behind the pack to outkick the field in winning the 800 at the tape;
1972 Munich S.O. Russia's Olga Korbut dazzles the crowd with a daring unseen move on the bars only to lose the all-around but later come back to win 3 events;
1968 Mexico City S.O. American innovator Dick Fosbury introduces a new high jumping style in winning the gold;
1988 Seoul East German Kristin Otto swims 6 events & wins 6;
Swedish figure skating star Sonje Henne becomes the 1st skater to win 3 gold medals;
1984 Sarajevo W.O. the Russian heraldry in pairs is marked by the 2nd win by Irina Rodnina & new partner Aleksander Zaitsev;
a feat unheralded-American t&f star Al Oerter goes into the record books winning 4 consecutive discus gold medals;
1984 LA S.O. American Evelyn Ashford drives home to the gold medal breaking the streak of victories led by steroid-using nations;
1984 LA S.O. German high jumper wins her 2nd high jump gold at age 28, 12 years after her first one;
1972 Munich American wrestling legend Dan Gable leads a US rout;
American women's soccer wins the inaugural gold;
Canadian women's ice hockey wins the inaugural gold;
1980 Lake Placid the American hockey team pulls the upset of all time beating the Russians & then defeating Finland for the gold.
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