Donald A. Swanson

This work describes a subjective method of making a pari-mutuel 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.

The leftmost column in figure 1 shows the seven symbols used in the method. There are three one-part symbols and four two-part symbols. The left side symbol part is the base (+, N, Ø). The right side symbol part (+, -) is the modifier. Word descriptions are names for the symbols. Each symbol is matched up with a Fibonacci number. Symbols are hand-written with a forward slash "/" as a separator, for example: N- / ++ / Ø+.

Symbol | Description | Weight | Number |
---|---|---|---|

++ | double plus | 21 | 7 |

+ | plus | 13 | 6 |

N+ | neutral plus | 8 | 5 |

N | neutral | 5 | 4 |

N- | neutral minus | 3 | 3 |

Ø+ | doubtful plus | 2 | 2 |

Ø | doubtful | 1 | 1 |

Absolute Analysis - Evaluate a single horse in isolation or against todays race conditions. 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.

Relative Analysis - Compare two or more horses against each other. Symbol selection starts with consideration of N versus N before expanding toward the top and bottom. In figure 1 rightmost column the symbols are numbered 1 to 7. The difference between the symbols is the degree of certainty that one horse will outperform the other(s). The range is 0 to 6 degrees.

Reversing the two-part symbols can be helpful in situations with unknowns. A developing horse might be taking a large rise or drop in class or trying a new distance or surface. A positive reverse read is modified neutral or doubtful depending on the absolute and relative analysis of todays race.

Symbol | Description |
---|---|

+N | positive neutral |

-N | negative neutral |

+Ø | positive doubtful |

The analysis of contenders versus non-contenders is relative. Non-contenders get a Ø. The handicapper will have some level of confidence that one of the contenders will win the race. Confidence levels can be thought of as moderate, high, or maximum. A symbol subset is chosen to represent these levels, for example: (N, +, ++). If the confidence level is high then the relative analysis is + versus Ø.

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 = .800

cp = (5 * 4) / ((5 * 4) + (9 - 4)) = .800

Two contenders in an eight horse field with high confidence.

2 / 8 / +

+ / + / Ø / Ø / Ø / Ø / Ø / Ø

13 + 13 + 1 + 1 + 1 + 1 + 1 + 1

cp = 26 / 32 = .813

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

One contender in a six horse field with maximum confidence.

1 / 6 / ++

++ / Ø / Ø / Ø / Ø / Ø

21 + 1 + 1 + 1 + 1 + 1

cp = 21 / 26 = .808

cp = (21 * 1) / ((21 * 1) + (6 - 1)) = .808

Races with two or more contenders 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. The six factor symbol combinations and word descriptions are shown in the table below. Factor symbols are written plain without the separator slash.

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. A single factor can be tripled (N N N) making a one factor race.

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 2 second column. Symbols can be converted into 1 to 7 numbers for entry into a hand-held calculating device.

Horse | cls / fm-sur / dst | 1 - 7 | Weights |
---|---|---|---|

#1 | + / N / N | 1644 | 13 / 5 / 5 |

#2 | N- / N+ / + | 2356 | 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 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 the table below with percentages and fractional odds.

2 / 8 / + | cls / fm-sur / dst | 1 - 7 | + N - | |
---|---|---|---|---|

#1 | + / N / N | 1644 | .471 | 6 / 5 |

#2 | N- / N+ / + | 2356 | .342 | 2 / 1 |

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

2 / 10 / + | cls / dst-sf | 1 - 7 | + - - | |
---|---|---|---|---|

#1 | N+ / N | 154 | .552 | 4 / 5 |

#2 | N- / Ø+ | 232 | .213 | 7 / 2 |

- 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
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