The Continuum Theory - Evaluating Performances

Which is a better performance? Running 3rd as a 4-1 (3rd) choice or running 4th at odds of 50-1 (9th)choice? With multiple variables such as odds, and number of betting entries, how does a handicapper compare performances across years to determine positive or negative performances?

The continuum theory proposes to answer this question by comparing horses expected finish to their actual finish with the result either a positive or negative number, with a continuum of 0, being equal to an expected finishing performance.

Once we have determined the continuum number for each horse’s performance. We can than begin to answer such questions as?

Has Todd Pletcher over-achieved or under-achieved in the Kentucky Derby?
What horse has over-achieved by betting odds the most in the Kentucky Derby?
How have horses who won as first time starters performed in the Kentucky Derby, compared to horses who have won as 2nd time starters?


I did not stay at a Holiday Inn last night, but I did propose this mathematical question to a financial analyst collegue, who then told me “The continuum Theory would work very well” to analyze this question.

First let’s dive into the formula, then we will put forth some disclaimers and caveats, before we begin to take a look at some of the numbers and try to answer some questions in regards to positive and negative Kentucky Derby performances

Once we are familiar with the formula we can then introduce the continuum theory and how it can be applied to determine positive and negative efforts. These positive and negative numbers can than be used to determine short term and longer impacts with multiple variables.

First let’s walk through a couple of examples. In 2004, Smarty Jones went off the 4-1 favorite and finished 1st.

Continuum = (Expected Finish (by odds) – Finish)* Odds

Smarty Jones = 1 (favorite) 1 – 1 (1st) 0 * 4 = 0
Limehouse = 14 (14th favorite – 4 (4th place) 10 * 41.70 = 417 (positive)
The Cliff’s Edge = 4 (4th favorite) – 5 (5th place) -1*8.20 = -82 (negative)

So in the example above Smarty Jones finished with a continuum of 0. He finished in the same position as was forecasted by the public. Limehouse exceeded expectations with a 4th place finish, when the public predicted him to finish in 14th place by the “odds”. That is a 417 positive continuum. The Cliff’s Edge finished 5th overall as the 4th favorite, but with 8.20 odds he ends up with a -82 negative continuum.

We than can compute the continuum for every horse for each year.  I originally calculated the continuum theory for all starters since 1981 to match my database of past performances.   This posed a problem with races prior to 2001 when they stopped coupling horses and eliminated "field" entries.  In the 80's and 90's there were many years of 5 or 6 "field" entries and those horses had unusually low continuum theories because 5 or 6 horses get lumped with the same odds.

So for purposes of staying consistent we will concentrate on all results since since 2001. Let's take a look at some of the numbers:

From 2001 through 2007 there have been 129 starters in the Kentucky Derby.  6 horses have a continuum of Zero, meaning they have done finished exactly where the "odds" valued them to finish.  Of those 6, Smarty Jones and Street Sense were favorites.

The worst performances, based on the continuum of expected finishing position and their actual finish by odds?  the winner is High Limit who finished with a -247, Cowtown Cat pushed the challenge last year with a (negative) -217.

On the flip side who overachieved the most?  Well you may guess Giacomo, who shocked the world at 50-1 in 2005.  But that is 6th on the list.  According the continuum theory, that same Derby, Closing Argument finished with a positive 1288.  Fans who hit the Superfecta last year with Sedgfield will be happy to know that he is second with 1029.  Deputy Glitters, Startac and Invisible Ink round the top 5 over achievers based on odds and final performance.

Now that we have developed a way at measuring performances individually, we can than group variable and see if patterns emerge.

How has Todd Pletcher done?  Since 2001 Todd has had 15 starters in Louisville.  With 5 horses showing positive scores, 1, horse with a zero, and 9 horses showing negative shores.  Positive 5, Negative 9.  That's a rough looking scoreboard, but there's always 2008!

How about horses who have 10 or more lifetime starts, entering the Derby.  Since 2001, 18 horses have have 10 or more lifetime starts, 10 show positive continuum numbers and 8 show negative.  Most of them within a pretty narrow range.

How about lightly raced horses.  We will define a lightly raced horse as having 5 or fewer career starts leading into the Derby.  Since 2001 32 horses have 5 or fewer career starts.   21 of them have negative continuum numbers.  2 are zero and 9 are positive.  A ratio of 2 to 1 being negative.  Might want to take a look again at horses like Dennis of Cork and other lightly raced winners.  Barbaro did prove the exception in 2006 with his victory, despite only 5 lifetime starts.

For those of you who like Majestic Warrior, or possibly Colonel John, who might only get 2 starts leading into this years Derby, here's another way of looking at that strategy.  Street Sense did break the "2-start" jinx last year, but I will have more on him later this week.  He was trained a lot differently than other horses have been prepared in recent years.  Getting back to the 2-starts.  59 horses have started in Kentucky with 2 races as a sophomore.  Here are the results.  16 horses show positive continuum numbers.   6 Horses have a continuum of Zero. That leaves 37 horses with negative results, a 2-1 ratio not in favor of the 2 start rule.  Tread lightly if backing those horses.

The continuum theory is not a "ranking" of numbers it's a way to look at the results and see if any trends and what ratio of positive horses to negative horses by group or individually.  So when someone highlights the fact that Invisible Ink finished 3rd as a longshot for Todd Pletcher, you can counter back, Cowtown Cat has the 2nd worst continuum number for negativity.