# Making Pari-Mutuel 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+). Symbol selection starts with consideration of (+, N, Ø) before moving up or down to the appropriate symbol. Memorize the symbols and descriptions. The rightmost column in figure 1 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. Symbol selection starts with consideration of (N+) before moving up or down to the appropriate symbol. 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 an eight horse field with moderate high confidence.
4 / 8 / N+
N+ / N+ / N+ / N+ / Ø / Ø / Ø / Ø
8 + 8 + 8 + 8 + 1 + 1 + 1 + 1
cp = 32 / 36 = .889
cp = (8 * 4) / ((8 * 4) + (8 - 4)) = .889

## 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-surface, jockey-trainer, form-age, 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 and weighted percentages. A symbol combination is chosen that indicates the relative importance of each factor.

Figure 3.
Symbols Percent Doubled
N  N  N 33,33,34 66,34
+  N  N 44,28,28 -
N  N  - 38,38,24 76,24
+  N  - 50,31,19 -
+  -  - 56,22,22 56,44
+  +  - 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. 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, 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 / 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 = 0.5  // 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 / dst +  N  -
#1 +  /  N  /  N .471 6 / 5
#2 N- /  N+  / + .342 2 / 1

Figure 7 is a two factor race with the distance factor doubled.

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

## References

1. Cramer M. (1987) The Odds On Your Side: The Logic Of Racetrack Investing, Cynthia Publishing Company
2. McNeill D. & Freiberger P. (1993) Fuzzy Logic: The Discovery Of A Revolutionary Computer Technology And How It Is Changing Our World, Simon & Schuster
3. Mitchell D. (1988) Winning Thoroughbred Strategies: With The Right Strategy, You Can Think Like An Investor, Not A Gambler!, William Morrow & Company
4. Quinn J. (1987) Class Of The Field: New Performance Ratings For Thoroughbreds, William Morrow & Company
5. Quirin W.L. (1979) Winning At The Races: Computer Discoveries In Thoroughbred Handicapping, William Morrow & Company
6. Scott W.L. (1984) How Will Your Horse Run Today?, Amicus Press
7. Scott W.L. (1989) Total Victory At The Track: The Promise And The Performance, Liberty Publishing Company

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