Making Parimutuel Odds With Fibonacci Numbers

Donald A. Swanson

This work describes a subjective method of making an odds line from the analysis of a thoroughbred horse race. Symbols are chosen by the handicapper to represent the race analysis. Fibonacci numbers are used to convert symbol combinations into weighted percentages.

1. Symbols

The leftmost column in figure 1 shows the seven symbols used in the method. The left side symbol part is the base (+, N, Ø). The right side symbol part (+, -) is the modifier. Descriptions are names for the symbols. The symbols are usually hand-written with a forward slash "/" as a separator, for example: (N- / ++ / Ø+). Memorize the symbols and descriptions. The rightmost column shows the matching Fibonacci numbers which will be used to calculate the weighted percentages.

Figure 1.
Symbol Description Weight
++ double plus 21
+ plus 13
N+ neutral plus 8
N neutral 5
N- neutral minus 3
Ø+ doubtful plus 2
Ø doubtful 1

2. Contender Percentage And Confidence Levels

The race is analyzed to decide which horses will be contenders. The handicapper will have some level of confidence that one of the contenders will win the race. A symbol is selected to represent the confidence level. Figure 2 shows the symbols and matching confidence levels. Non-contenders get a Ø.

Figure 2.
Symbol Confidence Level
++ maximum
+ high
N+ moderate high
N moderate
N- moderate low
Ø+ low
Ø minimum

cp - contender percentage
nc - number of contenders
fs - field size
wt - weight

cp = (wt * nc) / ((wt * nc) + (fs - nc))

Four contenders in a nine horse field with moderate confidence.
4 / 9 / N
N / N / N / N / Ø / Ø / Ø / Ø / Ø
5 + 5 + 5 + 5 + 1 + 1 + 1 + 1 + 1
cp = 20 / 25 = .80
cp = (5 * 4) / ((5 * 4) + (9 - 4)) = .80

One contender in a twelve horse field with maximum confidence.
1 / 12 / ++
++ / Ø / Ø / Ø / Ø / Ø / Ø / Ø / Ø / Ø / Ø / Ø
21 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
cp = 21 / 32 = .66
cp = (21 * 1) / ((21 * 1) + (12 - 1)) = .66

3. Factor Symbols And Combinations

Races with two or more contenders will use one to three factors which must be arranged from left to right in order of importance, for example: class, form, distance. Factors can be two-part compounded, for example: form-age, form-surface, distance-surface.

The N symbol can be extended to NN making the neutral base symbols (N+, NN, N-). The factor symbols are the right side symbol parts (+, N, -) matched up with Fibonacci numbers 8, 5, 3 respectively. Figure 3 shows the six factor symbol combinations, descriptions, and weighted percentages. Factor symbols have no separator slash "/" between them. A combination is chosen that indicates the relative importance of each factor.

Figure 3.
Symbols Description Percent Doubled
N  N  N neutral 33,33,34 66,34
+  N  N plus 44,28,28 -
N  N  - minus 38,38,24 76,24
+  N  - plus minus 50,31,19 -
+  -  - two minus 56,22,22 56,44
+  +  - two plus 42,42,16 84,16

Weighted percentage calculation for the (+ N -) combination.

8 + 5 + 3 = 16
8 / 16 = .5
5 / 16 = .3125
3 / 16 = .1875

Factors can be doubled, for example: speed, speed, form making a two factor race. The factor symbol representing the doubled factor must be duplicated in the combination as shown in figure 3. A single factor can be tripled (N N N) making a one factor race.

4. Selecting Symbols For Each Contender And Factor

Each contender is given one symbol for each factor. Symbol selection starts with consideration of (+, N, Ø) before moving up or down to the appropriate symbol. The handicapper should mentally move toward N when uncertain. The relative difference between the symbols is the degree of certainty that one horse will outperform the other(s). The range is 0 to 6 degrees. For example: N versus N is zero degrees and + versus Ø is five degrees.

Reversing the neutral base two-part symbols can be helpful in situations with unknowns. A horse might be making a large rise or drop in class or switching to a new surface. For example: the "form-surface" factor compound where a horse with positive form is trying grass or dirt for the first time should be given the +N symbol (surface modifies form).

Figure 4.
Symbol Description
+N positive neutral
-N negative neutral

5. Example Race Calculation With Weighted Percentages And Odds

Two contenders in an eight horse field with high confidence.

cp = (13 * 2) / ((13 * 2) + (8 - 2)) = .813

Three factors are chosen: class, form-surface, distance with the (+ N -) combination.

8 + 5 + 3 = 16
(8 / 16) * .813 = .407
(5 / 16) * .813 = .254
(3 / 16) * .813 = .152

Each contender gets three symbols one for each factor as shown in figure 5 second column.

Figure 5.
Horse cls / fm-sur / dst Weights
#1 +  /  N  /  N 13 / 5 / 5
#2 N- /  N+  / + 3 / 8 / 13

13 + 3 = 16
(13 / 16) * .407 = .331  (#1)
(3 / 16) * .407 = .076    (#2)

5 + 8 = 13
(5 / 13) * .254 = .098    (#1)
(8 / 13) * .254 = .156    (#2)

5 + 13 = 18
(5 / 18) * .152 = .042    (#1)
(13 / 18) * .152 = .110  (#2)

Sum the three percentages for each contender.

.331 + .098 + .042 = .471  (#1)
.076 + .156 + .110 = .342  (#2)

Sort the percentages (pct) in descending order before converting into odds.

odds = (1 / pct) - 1

(1 / .471) - 1 = 1.123  (#1)
(1 / .342) - 1 = 1.924  (#2)

Select the increment (inc) for rounding off.

if odds < 0.3 then inc = 20
elseif odds < 1 then inc = 10
elseif odds < 2 then inc = 5
elseif odds < 5 then inc = 2
else inc = 1

odds = (int ((odds * inc) + .5)) / inc

(int ((1.123 * 5) + .5)) / 5 = 1.2  (#1)
(int ((1.924 * 5) + .5)) / 5 = 2     (#2)

Convert rounded odds into fractions.

n = .5  // numerator
d = 0   // denominator
while int(n)<> n
  d = d + 1
  n = odds * d
end
print n,"/",d

Finished calculation shown in figure 6 with percentages and fractional odds.

Figure 6.
2 / 8 / + cls / fm-sur / dst +  N  -
#1 +  /  N  /  N .471 6 / 5
#2 N- /  N+  / + .342 2 / 1

A two factor race with the distance-surface factor compound doubled.

Figure 7.
2 / 10 / + cls / dst-sf +  -  -
#1 N+  /  N .552 4 / 5
#2 N-  /  Ø+ .213 7 / 2

References

  1. Baker M. (2009) Converting Decimal To Fractions, http://www.sitepoint.com/forums/showthread.php?608881-Converting-Decimal-to-Fractions&s=bffaeae0b7abc90fc14be8f602ff922b&p=4208775&viewfull=1#post4208775
  2. Cramer M. (1987) The Odds On Your Side: The Logic Of Racetrack Investing, Cynthia Publishing Company
  3. McNeill D. & Freiberger P. (1993) Fuzzy Logic: The Discovery Of A Revolutionary Computer Technology And How It Is Changing Our World, Simon & Schuster
  4. Mitchell D. (1988) Winning Thoroughbred Strategies: With The Right Strategy, You Can Think Like An Investor, Not A Gambler!, William Morrow & Company
  5. Quinn J. (1987) Class Of The Field: New Performance Ratings For Thoroughbreds, William Morrow & Company
  6. Quirin W.L. (1979) Winning At The Races: Computer Discoveries In Thoroughbred Handicapping, William Morrow & Company
  7. Scott W.L. (1984) How Will Your Horse Run Today?, Amicus Press
  8. Scott W.L. (1989) Total Victory At The Track: The Promise And The Performance, Liberty Publishing Company

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