Donald A. Swanson

This work describes a subjective method of constructing 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.

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 | 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 - 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.

Symbol | Word Description |

+N | positive neutral |

-N | negative neutral |

+Ø | positive doubtful |

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.

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 = 20 + 5 = 25

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 = 26 + 6 = 32

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 = 21 + 5 = 26

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.

Symbols | Word Description | Percentage | Doubled |

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

+ 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 |

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

8 + 5 + 3 = 16 // factor weight sum 8 / 16 = .5 // weight/sum = percentage 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 also 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

Factors: class, form-surface, distance with (+ N -) weight.

8 + 5 + 3 = 16 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 second column. The 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 // 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

Rounded odds are converted into fractions.

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

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

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

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

In the example below the distance-surface factor compound is doubled.

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

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

#2 | N- / Ø+ | 232 | .213 | 7 / 2 |

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

Donald A. Swanson

This method uses second call positions of race winners to measure positional tendency at a given distance. Second call position and field size data are retrieved from the result charts. The four furlong position is used for sprints. The six furlong position is used for routes. Maiden races are not representative and should not be used. Calculate figures for each distance and surface. It takes about fifteen races to get a good indication. The user should become familiar with track circumference and start / finish locations.

n = 0 // number of races repeat input 2nd call position (c2) input field size (fs) n = n + 1 list(n) = (c2 / fs) * 10 until done sort the list() in ascending order average the entire list() total = 0 for i = 1 to n total = total + list(i) next i a1 = int((total / n) + .5) average the low third of the list() total = 0 lt = int((n / 3) + .5) for i = 1 to lt total = total + list(i) next i a2 = int((total / lt) + .5 average the high third of the list() total = 0 ht = (n - lt) + 1 for i = ht to n total = total + list(i) next i a3 = int((total / lt) + .5) display as (a2,a3)a1 for example: (3,8)5 or [1,5]3

Interpret the figures using the table below.

Low Third | High Third | Average |

1 (+) 2 (Ø) |
5 (+) 6 (Ø) |
2 (+) 3 (N+) 4 (N-) 5 (Ø) |

- Brohamer T. (1991) Modern Pace Handicapping, William Morrow & Company
- Scott W.L. (1989) Total Victory At The Track: The Promise And The Performance, Liberty Publishing Company

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