Finally, A Post About Horseshoes and Cricket

By Daniel Adler

Which athlete is the furthest from the rest of his sport? ¬†Barry Bonds and his four seasons with on-base-percentages above .500 springs to mind. ¬†So does Wilt Chamberlain and his 1961-62 season in which he averaged over 50 points. ¬†However, according to a NY Times article, the greatest athlete outlier may be a 40 year old purchasing manager from Ohio. ¬†The article explains that in horseshoes, a “ringer” percentage of 70 percent is elite, 80 percent places a person in the top two in the world, and 90 percent means your name is Alan Francis.

How is it possible that one person rises so far above the rest of the field? ¬†It seems that Francis’ success on the whatever you call a horseshoe lane (pitch, field, alley, court?) is unrivaled in other sports. ¬†In most other games, there are certainly players whose play is far better than average, but the impressive thing about Francis is that there is not one person even close to his play. ¬†He seems to contradict our old friend (and Nassim Taleb’s enemy), the normal distribution.

One theory for how Francis can be so far away from anybody else is that there are just not many players of horseshoes. ¬†Imagine a world in which we select 100 random people to play baseball and nobody else. ¬†That is probably a large enough number that their batting averages would look like a normal distribution. ¬†However, imagine if one of those players by some stroke of luck happened to be Albert Pujols, who we know is a very skilled player when compared to a universe of millions of baseball players (i.e. today’s baseball environment). ¬†Pujols would not only be the best of the group, but he would be the best by a huge margin, much like Francis is in horseshoes. ¬†When the universe of players is smaller, the gap between the players at the top end is bound to be larger. ¬†Furthermore, if we actually have a one in 500 million type player in a sport with few participants, we are going to have a huge gap.

Another player with similarly outlandish statistics is cricket player Donald Bradman. ¬†His cricket batting average fell 4.4 standard deviations above the mean (approximately 1 in 185,000), eclipsing the outlier-ness of Pele, Ty Cobb, Michael Jordan, and others. ¬†It would be interesting to see where Francis falls in this pantheon of distinguished athletes. ¬†As for Bradman’s performance in comparison to other elite players, he appears to have an even greater edge than Francis, with a test career batting average of 99.94 compared to the an average of 60.97 for the next best player.

Maybe we should all head to Cedar Rapids, Iowa for the Horseshoe World Championships so we can tell our grandkids that we saw Jim Francis, the greatest athlete ever…or at least Jim Francis, a great athlete in a small sport. ¬†Is he a one in a million talent in a sport of 100,000 or is he perhaps a one in a billion talent in a sport of 100,000?

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  • In the 1980s, Stephen Gould wrote an article on how the shrinking standard deviation of batting average over time prevents .400 hitters. Basically, as the average MLB player became better over time, the SD shrunk and .400 hitters became less and less likely.

    • Thanks, for your reply David. Very interesting phenomena. I wonder if we are seeing an increasingly small standard deviation in other sports. Considering that relatively few people play horseshoes, we are probably far from the limit of human ability (unlike baseball in which Gould posits those good enough to make the majors are all in a narrow band).

      I wonder how the standard deviations have changed since Gould wrote the article. With baseball no longer being the sport of choice for many of our country’s top athletes, are we still at a point where the talent level is high enough for ever smaller standard deviations, or is the spread perhaps getting larger? I would imagine additions from Latin America and Asia probably mean that the overall talent level is just as high if not higher in MLB now, even if the American born talent level is off a bit.

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