Donald A. Swanson

This work describes a subjective method of constructing an odds line from the analysis of a thoroughbred horse race. It uses generic symbols matched up with Fibonacci numbers to solve the problem of computational stabilization and the favorite-longshot bias. 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+. Memorize the symbols and word descriptions by writing them down a few times.

Symbol | Word 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 - Evaluates 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 - Compares 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.

The relative analysis of contenders versus non-contenders is + versus Ø.

Four contenders in an eight horse field (4 / 8).

+ / + / + / + / Ø / Ø / Ø / Ø

13 + 13 + 13 + 13 + 1 + 1 + 1 + 1 = 52 + 4 = 56

cp = 52 / 56 = .929

nc - number of contenders fs - field size cp = (13 * nc) / ((13 * nc) + (fs - nc))

Races with two or more contenders use three factors arranged from left to right in order of importance. Factors can be two-part compounded, for example: form-age, form-distance, form-surface, distance-surface. Fibonacci numbers 8, 5, 3 are used for the factor weights.

Two contenders in an eight horse field (2 / 8).

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

The three factors chosen are speed, class, form-distance.

8 + 5 + 3 = 16 // factor weight sum f1pct = (8 / 16) * .813 = .407 // (weight/sum) * cp f2pct = (5 / 16) * .813 = .254 f3pct = (3 / 16) * .813 = .152

Each contender gets three symbols one for each factor as shown in figure 2 center column.

2 / 8 | sp / cls / fm-dst | |

Horse | Symbols | Weights |
---|---|---|

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

#2 | N- / N+ / + | 3 / 8 / 13 |

13 + 3 = 16 // factor 1 sum (13 / 16) * .407 = .331 // #1 (weight/sum) * f1pct (3 / 16) * .407 = .076 // #2 5 + 8 = 13 // factor 2 sum (5 / 13) * .254 = .098 // #1 (weight/sum) * f2pct (8 / 13) * .254 = .156 // #2 5 + 13 = 18 // factor 3 sum (5 / 18) * .152 = .042 // #1 (weight/sum) * f3pct (13 / 18) * .152 = .110 // #2

Sum the three percentages for each contender.

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

Sort the final 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

2 / 8 | sp / cls / fm-dst | ||

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

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

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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 A1 shows the six combinations and word descriptions.

Symbols | Word Description | Percent | Doubled | Tripled |
---|---|---|---|---|

N N N | neutral | 33 / 33 / 34 | 66 / 34 | 100 |

+ N N | one plus | 44 / 28 / 28 | - | - |

N N - | one minus | 38 / 38 / 24 | 76 / 24 | - |

+ N - | one plus one minus | 50 / 31 / 19 | - | - |

+ - - | one plus two minus | 56 / 22 / 22 | 56 / 44 | - |

+ + - | two plus one minus | 42 / 42 / 16 | 84 / 16 | - |

Factors can be doubled, for example: speed, speed, form-distance. The factor symbol representing the doubled factor is duplicated in the combination. The (+ N N) combination is redundant having the same percentage as the (+ - -) combination. The highest weighted symbol in the combination should be dominant. Each horse will get two symbols instead of three since there are now only two factors.

A single factor can also be tripled. Again the factor symbol representing the tripled factor is duplicated (N N N). Each horse gets just one symbol.

Scaling Percentage To Symbol Numbers 1 To 7.

pct - percentage from 0 to 1 conv - converted into a 1 to 7 number conv = int((((pct * 100) + 16.667) / 16.667) + .5)

Win / Place Percentage.

nc - number of entrants or contenders st() - number of starts this year plus last year wp() - number of wins and places this year plus last year wt() - Fibonacci numbers 1,2,3,5,8,13,21 for i = 1 to nc wp(i) = wp(i) / st(i) conv = int((((wp(i) * 100) + 16.667) / 16.667) + .5) wp(i) = wt(conv) next i

Earnings Per Start Percentage.

en() - earnings this year plus last year (earnings are rounded to the nearest thousand) high - highest value found cap = 180 // eps limited to USD-180k high = 0 for i = 1 to nc en(i) = en(i) / st(i) if en(i) > cap then en(i) = cap if en(i) > high then high = en(i) next i for i = 1 to nc en(i) = en(i) / high conv = int((((en(i) * 100) + 16.667) / 16.667) + .5) en(i) = wt(conv) next i

Recent Representative Speed Rating.

scale - scaling increment sr() - speed rating scale = 2.0 high = 0 for i = 1 to nc if sr(i) > high then high = sr(i) next i offset = (high / scale) - 7 for i = 1 to nc sr(i) = int(((sr(i) / scale) - offset) + .5) if sr(i) < 1 then sr(i) = 1 sr(i) = wt(sr(i)) next i

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Copyright © 2011-2014 Donald A. Swanson

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