I’m a fan of Secretariat. I’m not sure why, but a lot of people are fascinated by this horse. I think that when you see greatness – something that is just clearly apart from all others, it just brings emotions out. Even Jack Nicklaus cried watching Secretariat win the Belmont in 1973, that should tell you something.
You can google quite a lot about how fast Secretariat was (37.7 mph / 2:24 flat for the Belmont), or even how big his heart was (22 pounds, when the average horse heart is about 9 pounds, and the next biggest horse heart on record is ~15 pounds), but those numbers, especially the speed numbers, are clinical. They don’t give the context to let you appreciate. Enter statistics:
It is a very easy statistical problem to look at all the Belmont winner times since 1925 (ever since the track was at its current 1.5 mile length). Secretariat is the record holder at 2 minutes and 24 seconds flat. The next closest horse is 2 minutes and 26 seconds flat. There are about 90 horses between 2:26 to 2:33. Here is the list:
YEAR HORSE time (seconds) Z score percentage 1973 Secretariat * 144.00 -3.01 99.870% 1992 A.P. Indy 146.00 -1.83 96.674% 1989 Easy Goer 146.00 -1.83 96.674% 2001 Point Given 146.40 -1.60 94.515% 1988 Risen Star 146.40 -1.60 94.515% 1957 Gallant Man 146.60 -1.48 93.080% 2015 American Pharoah * 146.70 -1.42 92.263% 1994 Tabasco Cat 146.80 -1.36 91.373% 1978 Affirmed * 146.80 -1.36 91.373% 1985 Creme Fraiche 147.00 -1.25 89.370% 2021 Essential Quality 147.10 -1.19 88.250% 1990 Go And Go 147.20 -1.13 87.049% 1984 Swale 147.20 -1.13 87.049% 1968 Stage Door Johnny 147.20 -1.13 87.049% 2004 Birdstone 147.40 -1.01 84.400% 2009 Summer Bird 147.50 -0.95 82.950% 1999 Lemon Drop Kid 147.80 -0.78 78.102% 1983 Caveat 147.80 -0.78 78.102% 2006 Jazil 147.90 -0.72 76.325% 1991 Hansel 148.00 -0.66 74.472% 1972 Riva Ridge 148.00 -0.66 74.472% 2018 Justify * 148.20 -0.54 70.549% 2003 Empire Maker 148.20 -0.54 70.549% 1987 Bet Twice 148.20 -0.54 70.549% 1982 Conquistador Cielo 148.20 -0.54 70.549% 1948 Citation * 148.20 -0.54 70.549% 1943 Count Fleet * 148.20 -0.54 70.549% 1975 Avatar 148.20 -0.54 70.549% 2019 Sir Winston 148.30 -0.48 68.489% 1965 Hail To All 148.40 -0.42 66.370% 1964 Quadrangle 148.40 -0.42 66.370% 1959 Sword Dancer 148.40 -0.42 66.370% 2016 Creator 148.50 -0.36 64.197% 2014 Tonalist 148.50 -0.36 64.197% 2005 Afleet Alex 148.60 -0.30 61.977% 1979 Coastal 148.60 -0.30 61.977% 1953 Native Dancer 148.60 -0.30 61.977% 1950 Middleground 148.60 -0.30 61.977% 1937 War Admiral * 148.60 -0.30 61.977% 2007 Rags to Riches (f) 148.70 -0.25 59.717% 1997 Touch Gold 148.80 -0.19 57.424% 1996 Editor's Note 148.80 -0.19 57.424% 1969 Arts And Letters 148.80 -0.19 57.424% 1967 Damascus 148.80 -0.19 57.424% 1962 Jaipur 148.80 -0.19 57.424% 1998 Victory Gallop 149.00 -0.07 52.770% 1981 Summing 149.00 -0.07 52.770% 1976 Bold Forbes 149.00 -0.07 52.770% 1955 Nashua 149.00 -0.07 52.770% 1951 Counterpoint 149.00 -0.07 52.770% 1974 Little Current 149.20 0.05 48.078% 1961 Sherluck 149.20 0.05 48.078% 1942 Shut Out 149.20 0.05 48.078% 1934 Peace Chance 149.20 0.05 48.078% 1947 Phalanx 149.40 0.17 43.412% 1938 Pasteurized 149.40 0.17 43.412% 2002 Sarava 149.60 0.28 38.836% 1977 Seattle Slew * 149.60 0.28 38.836% 1966 Amberoid 149.60 0.28 38.836% 1960 Celtic Ash 149.60 0.28 38.836% 1940 Bimelech 149.60 0.28 38.836% 1939 Johnstown 149.60 0.28 38.836% 1931 Twenty Grand 149.60 0.28 38.836% 2008 Da' Tara 149.70 0.34 36.601% 1993 Colonial Affair 149.80 0.40 34.411% 1986 Danzig Connection 149.80 0.40 34.411% 1980 Temperence Hill 149.80 0.40 34.411% 1956 Needles 149.80 0.40 34.411% 2017 Tapwrit 150.00 0.52 30.189% 1936 Granville 150.00 0.52 30.189% 1963 Chateaugay 150.20 0.64 26.217% 1958 Cavan 150.20 0.64 26.217% 1952 One Count 150.20 0.64 26.217% 1949 Capot 150.20 0.64 26.217% 1945 Pavot 150.20 0.64 26.217% 2012 Union Rags 150.40 0.75 22.532% 1971 Pass Catcher 150.40 0.75 22.532% 1935 Omaha * 150.60 0.87 19.159% 2013 Palace Malice 150.70 0.93 17.595% 1954 High Gun 150.80 0.99 16.115% 1946 Assault * 150.80 0.99 16.115% 2011 Ruler On Ice 150.90 1.05 14.718% 2000 Commendable 151.00 1.11 13.405% 1941 Whirlaway * 151.00 1.11 13.405% 2010 Drosselmeyer 151.60 1.46 7.207% 1930 Gallant Fox * 151.60 1.46 7.207% 1995 Thunder Gulch 152.00 1.70 4.495% 1944 Bounding Home 152.20 1.81 3.487% 1926 Crusader 152.20 1.81 3.487% 1927 Chance Shot 152.40 1.93 2.672% 1933 Hurryoff 152.60 2.05 2.023% 1932 Faireno 152.80 2.17 1.513% 1929 Blue Larkspur 152.80 2.17 1.513% 1928 Vito 153.20 2.40 0.815% 1970 High Echelon 154.00 (mud)
Its trivial in Excel to compute a mean of this data set (149.12 seconds) and a standard deviation (sample) of 1.699 seconds. From there you can see a Z score of each winner. I left out 1970 as the track was filled with mud (you can see that race here) . Leaving 1970 out moves Secretariat from a -2.93 to a -3.01, a true -3 Z score event. How rare is that? basic statistics says 99.7% of all data is between -3<Z<+3. So there is .3%, spread .15% in each tail — or that Secretariat happens less than .15% of the time. 99.87% of all Belmont winners will be slower. Put that in perspective with days: 1/0.13% is 770 — or it will take, on average, 770 years for a horse to eclipse Secretariat
Now this data is not perfect, normally you need 200 data points to have a good sample (What Carter Worth taught me). However, it is quite good. I’m sure we can bring in the 2nd and 3rd place finishers to get ~300 data points and still have about the same mean and standard deviation, but I’ll leave that exercise for someone else. Note this data is normally distributed, period. The central limit theorem states that no matter how horserace speeds are distributed, when I pull samples those are normally distributed.
For comparison here is how the top 45 finishers fare – note the 2:26 horses are a 1 in 30 year event. We will see 3 of those in our lifetime. But unless you are sticking around for the year 2750, you are not going to see Secretariat’s record taken down.
