Just how fast was Secretariat?

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.

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