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sholker [printed: August 29, 2007 8:03 AM] [saved: August 29, 2007 8:19 AM] C:\Documents and Settings\sholker\Desktop\Sholk\Presentation\Sholk Molecular Diagnostics Presentation Final.ppt
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Speculative repetitions
• I recently captured a 1,760% ROI with a contrarian pari-mutuel bet on the outcome
of a thoroughbred horse race
• The following work outlines the thinking behind this specific bet, but more generally,
points to a speculative approach that works in pari-mutuel pools, capital markets,
and other speculative games in which humans handicap the future
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Betting opportunity
• On September 5, 2013, seven 2-year old colts competed in the 2013 Whirling Ash
Stakes, a one-mile horse race at Delaware Park
• The race was Daily Racing Form’s “Race of the Day”, which meant DRF provided
free past performance data for each competing horse
• After pre-race review of the past performance data (Appendix I), I thought five of
the seven horses had a realistic chance of winning, with the 1a, 3 and 4 horses
having the best chances
Horse # Horse name ML odds* on win bet
1a Jessethemarine Yes Yes 8-to-1**
2 No Fruit Degroote Yes No 2-to-1
3 Divorce Party Yes Yes 4-to-1
4 Interchange Yes Yes 6-to-1
5 Tashir No No 10-to-1
6 Son of Sparta No No 8-to-1
7 Mr. Viber Yes No 3-to-1
* Morning Line ("ML") odds are the forecasted, pre-race, pre-betting odds on a win bet, as estimated by DRF staff
** The 8-to-1 morning line odds on the 1a horse assumed the 1 horse would also run; however, the 1 was scratched pre-race
Source: Daily Racing Form
Potential winner? Likeliest to win
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Summary
• I knew the downside for each $2 win bet made on a horse that didn’t win the race,
but didn’t know the potential upside should one of these horses win until other
bettors began making wagers and setting the actual odds about 30 minutes prior to
the race
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Bet value determines maximum acceptable bet price
• Regardless of what each individual bettor believes when making a win bet, the
resulting odds imply a consensus expectation regarding each horse’s likelihood of
winning
• Though I favored three horses (1a,3,4), I believed there were five horses
(1a,2,3,4,7) that could realistically win
• Recognizing my limited ability to predict the future, I ascribed to each horse a rough
1-in-5 chance of winning the race, or 20%
• Therefore, if I expected to at least break even over a large number of similar races,
the lowest profit I could accept on a successful win bet on any of these horses was
$4, or “4-to-1 odds”
Probability of single
horse winning x(Payoff returned with $1 win bet
upon single horse winning) + (Probability of other
four horses winning) x(Payoff upon one of other
four horses winning) =Break-even expected
value over many races
20% x α + 80% x -$1 = $0
α = $4
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Translate bet price to mkt. expectation of bet success
• Just prior to race start, bettors moved the final odds on the five potential winners to
as low as 1.6-to-1 and as high as 17.6-to-1
• After adjusting these final odds to account for the 23% track takeout*, I found the
implied consensus probability of each of the probable winners winning was as high
as 32.5% and as low as 4.2%
*Takeout is the portion of each bet taken by the racetrack to cover operating costs - Delaware Park’s advertised
takeout rate is 17% for win pools, but the final odds suggest the takeout was 23% for this race
Horse # Horse name Implied win %
1a Jessethemarine 17.6 to 1.0 1.0 in 18.6 5.4%
2 No Fruit Degroote 4.9 to 1.0 1.0 in 5.9 16.9%
3 Divorce Party 1.6 to 1.0 1.0 in 2.6 38.5%
4 Interchange 2.1 to 1.0 1.0 in 3.1 32.3%
5 Tashir 6.0 to 1.0 1.0 in 7.0 14.3%
6 Son of Sparta 33.9 to 1.0 1.0 in 34.9 2.9%
7 Mr. Viber 7.5 to 1.0 1.0 in 8.5 11.8%
Source: Equibase, Daily Racing Form Check 122.0%
Actual odds on win bet Implied win probability
Horse # Horse name Implied win %
1a Jessethemarine 22.9 to 1.0 1.0 in 23.9 4.2%
2 No Fruit Degroote 6.4 to 1.0 1.0 in 7.4 13.6%
3 Divorce Party 2.1 to 1.0 1.0 in 3.1 32.5%
4 Interchange 2.7 to 1.0 1.0 in 3.7 26.8%
5 Tashir 7.8 to 1.0 1.0 in 8.8 11.4%
6 Son of Sparta 44.0 to 1.0 1.0 in 45.0 2.2%
7 Mr. Viber 9.7 to 1.0 1.0 in 10.7 9.3%
Source: Equibase, Daily Racing Form, analyst adjustments Check 100.0%
0% takeout odds on win bet Implied win probability
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Win bet pricing discrepancy for Horse 1a
• Most of the probable horses had win odds below or close enough to the 4-to-1
minimum requirement to make them uninteresting as betting candidates, but Horse
1a had been bet up to 17-to-1 odds, implying bettors thought he had a ~4% chance
of winning the race
• With the market effectively telling me Horse 1a couldn’t win the race once if it were
run 20 times, I decided to re-check the logic behind my estimate he might win 4 of
20 theoretical runs
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Past speed is the best predictor of future speed
• I agree with the widely held view that the speed at which a horse has run in past
live races is the best predictor of its speed in future live races, while still recognizing
that horses regularly gain and lose racing speed, often unpredictably, over their
careers
• The most widely used estimate for a horse’s speed in a past race is the Beyer
Speed Figure, which distills an individual horse’s effort at one distance and under
one track condition into a single figure which can then be reasonably* compared
with Beyer figures recorded by other horses at different distances and over different
tracks
• With this in mind, I went back to the past performance data to see if Horse 1a could
be reasonably expected to run faster than its competitors over one mile
* The Beyer figure appears to be less reliable in predicting the horse’s future speed in longer route races
(usually 8-12 furlongs) if the figure was recorded by the horse in a short sprint race (usually 4.5-7 furlongs), and
vice versa, because many horses often show ability at one distance but not the other
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Horse 1a had competitive speed
• Horse 1a had recorded a career-best Beyer figure of 64, which was equal to Horse
5’s best figure and second only to Horse 4’s Beyer figure of 67
• The Beyer figure can be converted to horse lengths at a rate of ~2.5 points per 1
horse length for shorter sprint races and ~2.0 points to 1 length for longer route
races*; therefore, based on Beyer speed figures alone, the finish for the Whirling
Ash Stakes might have reasonably been expected to look like this:
*Source: http://www1.drf.com/help/help_speedrate.html
Projected finish - 2013 Whirling Ash Stakes (based on Beyer speed figures)
4
7 1a
6 5
3
2
Finish
Horse # Horse name
Beyer speed figure earned Beyer speed figure
4 Interchange 67 5.5 furlongs 2.1 - to - 1
1a Jessethemarine 64 5.5 furlongs 17.6 - to - 1
5 Tashir 64 5.5 furlongs 6.0 - to - 1
3 Divorce Party 62 8.5 furlongs 1.6 - to - 1
2 No Fruit Degroote 61 5.5 furlongs 4.9 - to - 1
7 Mr. Viber 56 5 furlongs 7.5 - to - 1
6 Son of Sparta 43 8 furlongs + 70 yards 33.9 - to - 1
* A furlong is equal to 1/8 mile. The Whirling Ash Stakes was raced over 1 mile, or 8 furlongs
Source: Daily Racing Form, Equibase
Final odds to win
2013 Whirling Ash Stakes
Best earned Race distance for best
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Win bets on similar horses trade at dissimilar prices
• The past performances suggested Horse 4 was only slightly faster than Horses 1a
and 5, yet had an implied win probability of ~25%, vs. 10% for Horse 5 and ~4% for
Horse 1a
• I recognized that Horse 1a had recorded his best and only Beyer figure at 5.5
furlongs vs. the 8 furlongs he would run in the Whirling Ash Stakes, but Horses 4
and 5 had also never run further than 5.5 furlongs – why did bettors think these
horses were so much more likely to handle the added distance?
• Furthermore, Horse 1a was co-owned and trained by trainer John Rigattieri, who
prior to race start had entered horses in 231 races in 2013 and recorded 52 wins;
according to Equibase, this 23% win rate was in the Top 11% among all trainers in
the US with 100+ starts in 2013
Source: Daily Racing Form
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Behavioral analysis confirms bet mispricing
• Put differently, a top-performing trainer that had won over 20% of his races in 2013
was entering a horse that he owned and trained (and whose chance of success at
8 furlongs he likely knew better than any bettor) and that appeared to have
comparable speed to the other logical winners, yet bettors implicitly ascribed only a
4% probability to the horse winning
• The market appeared too pessimistic so I bought a Horse 1a win bet at odds of
17.6-to-1; I didn’t think the horse had a great chance of winning but thought it was
greater than that implied by its odds
• How did it turn out? Horse 4 appeared to win by a nose over Horse 1a, with
Horse 5 finishing a distant third, seven lengths behind (see Appendix II for final race
results and press)
Actual finish - 2013 Whirling Ash Stakes (with final win odds)
7 2
6 3
5
Source: Equibase, Daily Racing Form
Finish
1a
4
(7.5-to-1)
(33.9-to-1)
(1.6-to-1)
(4.9-to-1)
(6.0-to-1)
(2.1-to-1)
(17.6-to-1)
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Illegal bump disqualifies Horse 4, Horse 1a wins
• Horse 4 won by a nose, after having lost the lead briefly to Horse 1a inside the final
100 yards
• However, the horse was disqualified and placed second after track stewards
confirmed it had illegally bumped Horse 1a in the stretch, giving Horse 1a the win
Bets canceled pre-race due to changing
odds and improved thinking
Illegal bump
from Horse 4
interferes with
Horse 1a’s run
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Takeaways
• As long as takeout rates at US racetracks are 17%-25%, even talented horse
bettors are likely to lose money over time – only bet an amount you’re willing to
take a substantial haircut on in exchange for the challenge
• When speculating, don’t love the horse - know the horse, its relative speed and its
human connections’ talent and incentives as well as you can, but focus on
identifying illogical bet pricing and the circumstances under which it occurs
• If the evidence suggests a horse bet is worth more than its price, only take the bet if
your value estimate is much higher than that price - your forecast is imperfect and
you must get paid enough the few times you win to make up for the many inevitable
small losses (unlike speculating in the stock market, you either lose your full bet or
win a multiple of it; unjustifiably high odds provide your “margin of safety” over time)
• When people with proven talent and properly aligned incentives know a horse
better than any other bettors and are betting on it when others aren’t – you should
carefully consider betting with them
• I may have gotten lucky - Horse 1a may have had less than a 4% chance of
winning in the instant before race start
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Appendix I: DRF past performance data
Scratched prior
to race start
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Appendix I: DRF past performance data (cont.)
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Appendix II: Official race results
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Appendix II: Press coverage of race results
• Summary article with video replay of race: http://www.drf.com/news/delaware-dq-
gives-longshot-jessethemarine-win-whirling-ash
Delaware: DQ gives longshot Jessethemarine win in Whirling Ash By: John DeVivo
“Jessethemarine, the second longest shot on the board at 17-1, came up short by a head following a
stretch-long duel but walked away a winner, thanks to the disqualification of Interchange in Thursday’s
$50,250 Whirling Ash Stakes for 2-year-olds at Delaware Park.
Jessethemarine, with Jose Caraballo aboard, briefly took a narrow lead over pacesetter Interchange in
deep stretch of the one-mile dirt race only to see Interchange, under Victor Carrasco, fight back to
narrowly reach the wire first in 1:38.70.
Following a stewards’ inquiry and a claim of foul by Caraballo as the result of a bumping incident inside
the eighth pole, Interchange, the 2-1 second choice in a field of seven, was disqualified and placed
second. It was another seven lengths back to Tashir in third. Divorce Party was a dull fifth as the 8-5
favorite.
Jessethemarine ($37.20), racing beyond 5 1/2 furlongs for the first time, is now 2 for 3 for trainer John
Rigatierri, who owns the son of With Distinction in partnership with Manfred Roos.”