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Correctly Calculate Payouts-to-Investments to Assess Reward-to-Risk

Arlington Park Communications | 03/24/2014 #

Some Players Don’t Carry the Math Far Enough

Sometimes fans are just a little fuzzy on doing all the math when assessing payouts versus investments.  Here’s an example of what we often hear.

“I like two horses in this race.  The exactas are paying $12 each way.  That’s not too bad, it’s 5-1.”  The fan’s math is as follows:  $12 for $2 equals $10 profit for your $2, or 5-1 when converted to the standard method of expressing odds. 

Is it 5-1, or is the fan’s math fuzzy?  Let’s carry the math far enough, correctly.  The fan has just implied that, since he likes two horses, he’s considering boxing them (betting 1-2 and 2-1) in the exacta.  He checks the probable payouts and learns the $12 figure applies each way, 1-2 and 2-1.

But those payouts are for $2.  If he makes a $2 exacta box, he invests $4 because he is making two wagers.  Therefore, if either of his two combinations wins, the payout will be $12 for $4, not for $2.  That $12 for $4 is the same as $6 for $2, or 2-1 odds.  

Suddenly, that imagined 5-1 reward-to-risk ratio isn’t nearly as attractive as the real 2-1 ratio.

Here’s a more complicated example, one that arose a week ago.  On June 22 Jere Smith, Jr.’s recently-acquired In All Directions won at 76-1 and keyed a Superfecta that paid $1,709.54 for 10 cents.  We’ll round it off to $1,700 for simplifying our analysis.

A fan was quick to point out, “$1,700 for a dime, that’s the equivalent of $17,000 for a dollar, or 17,000-1 odds.”  True.

Like so many fans after a long shot wins, he went on to say, “I can see how someone could like this horse.”  And, like so many fans, he didn’t bet the horse because he couldn’t see it before the race, but that’s a different story.    

“The next time I like a long shot like this, I’m gonna key him with the field in the supers – it will be a great bet, going after a 17,000-1 payout.”

Will it?  Do the math, correctly.

In All Directions ran in a 12-horse field.  What is the investment to key one horse with all others?  The first step is to calculate the number of combinations.

The process is called a chain multiplication and is illustrated as follows:  1 x 11 x 10 x 9.  This means there is one horse to run first, which (in a 12-horse field) leaves any one of 11 horses to run second, any one of 10 to run third, and there are only 9 horses left to give us the fourth finisher.  Multiply that out and the answer is 990 combinations.

Now multiply the number of combos by the betting unit.  If we are talking about a 10-cent superfecta, the cost of the ticket is $99 (990 bets x 10 cents [or .10] equals $99).  Again, we will simplify by calling it $100.      

Is that 17,000-1?  Hardly.  $1,700 back for $100 invested is…17-1!  Congratulations, fan, you turned a 76-1 into a 17-1.  

It all checks out, but is a little unfair.  We only have the luxury of probable payouts when dealing with exactas, quinellas, and daily doubles.  With any other wager, including superfectas, we are flying blind because we don’t have probable payouts to consider, therefore, we cannot calculate exact risk-reward ratios.

In the example used, the odds of the next three finishers under the 76-1 were, respectively, 5-2, 9-1, and 5-1.  The 9-5 favorite ran out.  Had there been more long shots under the 76-1 winner, the superfecta would likely have paid more.  However, as we know, horses tend to finish near the order of their odds, which tells us shorter odds horses will usually make up the finishers in the superfecta.

But don’t let that deter from going for the big payoff.  We’ve seen instances where a single 10-cent ticket has won the entire superfecta pool.  If that had happened in the example above, the payout would have been around $24,000.  You can calculate the odds equivalent. 

Now the 76-1 shot made for a 240-1 takedown.  And, as nice as the money is, there’s an additional boost to one’s psyche when you realize you have the only ticket and the entire pool is yours. 

No more fuzzy math.

Next handicapping contest is Saturday, July 9, Million Preview Day.

Email me at contests@arlingtonpark.com with suggestions for future blog stories.

     Scott

M. Scott McMannis

  • Handicapping Seminar and Contest Host, Arlington Park
  • Expert Selections Handicapper, arlingtonpark.com
  • Midwest Correspondent, The HorsePlayer Magazine
  • Owner and Publisher, The McMannis Speed Figure & Trip Note Service Newsletter
  •      And Arlington and Hawthorne Trainer Patterns