Secretariat and Man o’ War: Applied Statistics and the Forbidden Comparison (Second Edition)

By Charles Justice

I began this book with the express purpose of making it the definitive comparison of Secretariat and Man o’ War. I feel that I’ve succeeded. By engaging the discipline of applied statistics to compare the legendary achievements of these two horses, I am being completely honest about my two primary audiences—the serious Thoroughbred racing fan and those desiring a clearer comparison of runner quality that only the lens of basic statistics can provide.

The statistics in this book are basic and are completely explained as the text progresses. They are not difficult—provided one is motivated to compare Thoroughbreds on an objective rather than subjective level and to spend a modicum of extra time learning the minimal eight-grade-level computations the statistics require.

I personally wish all readers well on their journey into what is possibly a groundbreaking area, thereby showing their willingness to accept a very modest challenge.

• Language: English
• Publisher: AuthorHouse
• Release date: Aug 8, 2023
• ISBN: 9781665545914

Charles Justice

DR. CHARLES JUSTICE has twenty years experience in applied statistics. His boyhood fascination with Thoroughbreds surfaced when Blood-Horse, Inc. published Thoroughbred Champions: Top 100 Racehorses of the 20th Century in 1999. Finding scant evidence that the book’s selection were made using more than general opinion, he published his own analysis in 2008 of 50 of its top-ranked horses—The Greatest Horse of All: A Controversy Examined. A second related book, Beyond Greatness: Four Thoroughbred Legends followed in 2011.

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Secretariat

and

Man o’ War

Applied Statistics and the

Forbidden Comparison

Second Edition

Charles Justice

AuthorHouse™

1663 Liberty Drive

Bloomington, IN 47403

www.authorhouse.com

Phone: [phone]

© 2021 Charles Justice. All rights reserved.

No part of this book may be reproduced, stored in a retrieval system, or transmitted by any means without the written permission of the author.

Published by AuthorHouse   08/04/2023

ISBN: 978-1-6655-4178-7 (sc)

ISBN: 978-1-6655-4591-4 (e)

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Because of the dynamic nature of the Internet, any web addresses or links contained in this book may have changed since publication and may no longer be valid. The views expressed in this work are solely those of the author and do not necessarily reflect the views of the publisher, and the publisher hereby disclaims any responsibility for them.

Related books on

Thoroughbred racing

by Charles Justice

The Greatest Horse of All: A Controversy Examined Beyond Greatness: Four Thoroughbred Legends

Dedication

In memory of my father

Charles Joseph Justice, Sr.

1914 – 1987

and my grandparents

Joseph Marion Justice 1884 – 1949

Bess Margaret Graham Justice 1884 – 1973

Tribute

The maple leaf silhouette, used as a ‘text break’ symbol throughout this book, is intended to represent the central emblem of the flag of Canada.

This symbol was chosen to honor two gentlemen who played indispensable roles in shaping Secretariat’s amazing career—Lucien Laurin, his trainer, and Ron Turcotte, his jockey for 18 of 21 career races including the Triple Crown victories.

The maple leaf also recognizes that the Canadian International Stakes, run at Woodbine Race Track in Toronto, Ontario on October 28, 1973, was the final competition of Secretariat’s career.

Acknowledgments

Special thanks go to the following individuals, each for contributing in their own unique way to make this book a reality:

Buddy Dow of Author House for his consistent professionalism and individual help in the entire publication process, including intensive file editing and for suggesting the new cover for this, the second edition.

Dementi Milestone Publishing for granting permission to paraphrase portions of Secretariat’s Meadow by Kate Chenery Tweedy and LeeAnne Ladin.

Abigail Anderson for permission to paraphrase portions of the article A Living Flame: Will Harbut and Man o’ War featured on her website: www.thevaulthorseracing.wordpress.com

Melissa Ullmann, Marketing Manager of Daily Racing Form for her assistance in obtaining permission to use published data of Secretariat and Man o’ War from the North American Dirt Records given in their Champions and American Racing Manual publications.

Betsy Baxter, Archives Technician of Keeneland Association, Inc., who researched and resolved a vital question regarding Man o’ War.

Sara Boncha, Associate Subsidiary Rights Manager of Disney Publishing Worldwide, for permission to quote Ron Turcotte from William Nack’s biography Secretariat.

Jim Crandell, Manager, Dr. Baden Clegg Pty Ltd., Wembly, Western Australia, who shared several extensive and informative email discussions of the Clegg Impact Soil Tester and its potential application in determining absolute track surface speed.

Patricia Zline, Rights and Permissions Assistant of The Rowman & Littlefield Publishing Group, Lanham, Maryland, for permission to quote from Speed and the Thoroughbred by Alexander MacKay-Smith.

Contents

Foreword

General Considerations

Limitations on Statistics

Overview of Book

Data Sources

Preface to the Second Edition

Prologue

In The Beginning

Gene Pools and Other Bets

The Percent of Possible Stakes Winners

Using the Genetic Arguments for Practical Data Comparisons

Chapter One

Introduction - Establishing the Basics

The World of Thoroughbred Racing

Background Basics

Distance

Time

Mass versus Weight: Other Names for Impost

Average Speed

Acceleration

Momentum and Kinetic Energy

Chapter Two

The Statistician’s World

Populations and Samples

Descriptive and Inferential Statistics

Mean or Average of a Sample

Range

Standard Deviation and Variance

The Normal Distribution

Correlation

Simple Linear Regression

Test for Two-Sample Significant Difference

How the t-Test is used

Hypotheses and the t-Test

Chapter Three

Introduction

The Argument about Era Differences

Facts against the Era Comparison Controversy

Applying the Work-Energy Theorem

Thoroughbred Improvements over Three Centuries

The Distribution of Talent among Foals

Track Variant and Foal Crop Relative Ability

Track Variants: Man o’ War’s 6-f Races

Chapter Four

Man o’ War

Juvenile Year Anomaly: The Sanford Stakes

A Closer Look: the Sanford and Four other Six-Furlong Races

First Anomaly of the Sophomore Year

Second Sophomore Anomaly: The Lawrence Realization Stakes

Final Sophomore and Career Anomaly

Life after Track Glory

Chapter Five

Secretariat

The Races

Secretariat’s Sophomore Season

Let the Anomalies Begin

Big Red’s Final Anomalies

The Arlington Invitational

The Whitney Stakes

The Marlboro Invitational

The Woodward

Man o’ War Stakes

The Canadian International

Old Champions Never Die

Chapter Six

Juvenile Year Correlations

Basic Juvenile Year Data

Correlations with Time for Six Furlongs: Man o’ War

Correlations with Time for Six Furlongs: Secretariat

Coding the Correlation Sequences

t-Test Results for the Ten Race Parameters

Six Furlongs versus all Races

Chapter Seven

Test for Significant Difference at Six Furlongs

Setting Boundaries for Man o’ War’s Time Adjustments

Unbiased Time Adjustments to the Raw Data

Adjusting Running Times for Data Comparability

The Uniform Distribution of Thoroughbred Ability: I

The Uniform Distribution of Thoroughbred Ability: II

The Sequence of Time Adjustments

The Adjustment Process for the Six-Furlong Races

Explanation of the Impost Adjust Procedure

Confidence Intervals and Impost Values

A Second Type of Confidence Interval

Linear Regression and the Trapezoidal Adjustment Method

Chapter Eight

Handicapping Man o’ War and Secretariat as Juveniles

Freedom from Era Effect Guaranteed using z-Scores

Using Specific Race Results to Derive z-Scores

Peer Quality Factor

Z-scores and Time Adjustments Relative to the World Record

Chapter Nine

Man o’ War and Secretariat—Sophomore Year Comparisons

Basic Sophomore Year Data

Correlations with Time for Nine Furlongs

Test for Significant Difference at Nine Furlongs

Shapiro-Wilk Normalcy Results: Ten Major Race Parameters

Adjusting Running Times for Data Equality

The Sequence of Time Adjustments

Raw Data Comparisons and Simulations

t -Test Results and a Reference Baseline

Adjustment Method 1: Comparison of Track Records

Nine-Furlong Boundaries for Man o’ War

Simulation Results of the Adjustments

The Time Adjustment Giving Man o’ War the Obvious Advantage

Chapter Ten

Adjustment Method 2: The Trapezoidal Time Adjustment

The Relationship of z-Scores to the Nine-Furlong World Record

What White Stockings (or Socks) Prove

Chapter Eleven

An Extraordinary Triple Crown

Enter Two Faces of Linear Regression

Inter-Event Regression

Intra-Event Regression

Secretariat’s Belmont Stakes: June 9, 1973

Signatures of Greatness

About Track Speed

A Related Issue

A Matter of Energy

Temporary Resolution of Track Speed

Asides and Final Thoughts

Epilogue

Embracing the Statistical Gauntlet

The Challenge Continues

Science and Beyond

Coda

References

Appendices

A: Basic Data: Man o’ War and Secretariat

B: Calculating the Standard Deviation and Variance

C: Calculating the Pearson Product-Moment Correlation Coefficient r

D: The Output Data from LINEST Linear Regression

E: Reference Table for Selected t Values of a One Tailed Distribution

F: The Possible Combinations of Null and Alternate Hypotheses

G: Generating the Normal Distribution with Excel

H: The t-Test for Two Samples with Equal Variances

I: Justification for the 50/50 Division of Track Variant

J: Time versus Impost Trends: Six Standard Distances

K: Calculating Confidence Intervals

L: Adjusting Linear Trends to World Record Trend

M: The Appropriateness of Using Linear Regression to Predict Performance

Foreword

General Considerations

This book presents a detailed comparison of the racing records of Man o’ War and Secretariat. These two colts are generally considered the greatest North American Thoroughbred runners of the past century.

The term North American is stressed because no attempt is made herein to consider the racing records of the many fine horses from other continents and countries. I am keenly aware that horses of equal caliber to Man o’ War and Secretariat may have raced outside North America, but it presents challenge enough to concentrate on these two horses exclusively for present purposes of applying data comparison methods.

Comparing Man o’ War with other horses—whether of North American or other origin—is greatly frowned upon by his fans. Indeed, a general mantra-like expression has evolved among his advocates which admonishes that horses from different eras cannot be compared. This dogmatic statement is actually one of the great motivators of my attempt herein to present a rational, systematic and objective comparison of the racing records of Man o’ War and Secretariat.

Limitations on Statistics

Of necessity, basic statistics must be used to achieve an unbiased, objective and scientific comparison between or among racing records, often referred to as past performance records.

Even statistics, however, cannot define or compare an inherent level of greatness regarding these or any other horses. Many people wish to deny or overlook this fact.

Thus, zealous fans immediately excoriate statistics without considering that all it properly does is allow the dispassionate comparison of data records.

That is all statistics was developed over many decades to do—objectively compare data. At its worst, it is applied by statisticians who generate and use biased data. Notice that it is the human element, the statisticians, who misinterpret and misapply statistics.

The statistics as a discipline does not and cannot bias data. Statistics is a purely mathematical approach which allows pattern recognition in what otherwise might be only numeric chaos. It harbors none of the hidden agendas which may haunt the subconscious mind of the investigator applying it.

Data, as used herein, simply indicate the results a given horse achieved at a given time and place and under particular conditions. Such factual data does not, a priori, define the absolute performance level of which a horse was capable. The reader must always remember this.

If data transcended mere fact, then it might be reasonable to speak of comparing relative greatness. However, factual data shows only what a horse did under an isolated, specific competition.

If horse A ran one mile in 93.00 seconds while horse B ran the same mile under the same conditions in 93.45 seconds, then, obviously, horse A was declared the winner, and his winning time was, by direct subtraction, 0.45 seconds faster than horse B’s.

These are the bare facts of one hypothetical situation. They state nothing about whether horse A was more capable, in general, than horse B, nor do they necessarily predict that horse A would always beat horse B if they ran multiple races at the same distance and under identical conditions in the future.

I use and apply statistics only within the foregoing interpretive framework when comparing the records of Man o’ War and Secretariat. I respect both colts highly. I favor neither. I come to this study with no ulterior motives or hidden agendas. This is a highly relevant fact.

Having stated the above, one must still realize that multiple random factors always interact to produce data, especially in Thoroughbred racing. Horses do not control these factors. They perform as their jockeys are capable of shaping a good ride under the pre-race instructions of the owner and trainer and under the track limitations on racing day.

The final result, barring accident, mishap or bad racing luck, depends greatly on the horses’ actual health on race day. Many horses, including Secretariat, have run when they should not have been asked to run, and they lost.

Overview of Book

Following an initial overview in the Introduction, all statistical methods used herein are thoroughly explained as the text proceeds and a particular application is required. Chapters 1 thru 3 are devoted basically to these explanations.

Chapter 1 provides an elementary introduction to key terms used in Thoroughbred racing for those new to the sport. Chapters 2 and 3 explain the basic statistical concepts used throughout the book for the data comparisons. Even readers absolutely new to statistics should be enabled to read the book with understanding provided these chapters are read diligently.

Chapters 4 and 5 are biographical, being devoted to the lives and track achievements of Man o’ War and Secretariat, respectively.

Chapters 6 thru 10 contain the statistical crux of the data comparisons. In these chapters the various statistical tests explained in Chapters 2 and 3 are applied.

Chapter 11 serves as an overview of what has emerged relative to the two champions, while an Epilogue provides a philosophical statement concerning the book’s implications for further research into comparative Thoroughbred statistics.

The textual structure generally follows the format of my previous books on Thoroughbred racing and data comparison: The Greatest Horse of All: A Controversy Examined and Beyond Greatness: Four Thoroughbred Legends.

Hereafter when either of these books is cited, the acronyms GHA and BG are used. Similarly, DRF and ARM always mean Daily Racing Form and American Racing Manual, respectively.

It is suggested that only those potential readers particularly interested in Thoroughbred racing and the comparative study of racing records acquire this book. It is primarily for the serious student of Thoroughbred racing and data comparison. Others should not apply.

That being stated, if a reader approaches the book comfortable with eighth-grade level mathematics and with a positive, unbiased mindset, he or she will have little or no trouble understanding the basic statistical methods used herein. This is not rocket science by any stretch of the imagination!

Appendix A gives a condensed summary of the complete racing records of both Man o’ War and Secretariat, a table of world-record times from five thru thirteen furlongs and a summary of Farley’s (337) track-speed estimate for the tracks Man o’ War ran.

As preliminary aid to those unfamiliar with Thoroughbred racing, one furlong is one-eighth of one mile. Thus, six furlongs is three-quarters of one mile, and ten furlongs is a mile and a quarter.

The statistical methods explained and used herein include:

1) Applying and interpreting the normal distribution with detailed use of its two major parameters, the mean (average) and the standard deviation; 2) Correlation and its interpretation;

3) Hypothesis testing using the t-test; and 4) Linear regression as performed by Microsoft Excel’s© 2003 LINEST function.

If potential readers distinctly dislike or even fear mathematics on any level, they too are discouraged from purchasing this book. It is, to reiterate, impossible to do more than a superficial and subjective comparison of two or more Thoroughbred past performance records without at least using basic statistics.

These admonitions apply whether the horses being compared are Man o’ War and Secretariat or Joe Place and Larry Show.

Enough such inadequate, qualitative comparisons—perhaps more properly called ‘anecdotes’—exist and prove little, if anything. To paraphrase President Barak Obama in one of his initial campaign speeches, the world doesn’t need another superficial comparison.

Data Sources

The data used herein for all analyses are taken directly from two major and trusted sources: the 2005 revised edition of Champions and the 2012 edition of the American Racing Manual. Both books are published by the Daily Racing Form.

Serious readers who wish either to check the conclusions herein or to explore additional possibilities are encouraged to obtain these books and perform their own research. Microsoft’s Excel 2003 application, including Lumenaut’s© add-on for the Shapiro-Wilk Normalcy check, was used exclusively to perform all analyses. Both are readily available and popular computer packages.

Readers should also consider that the data used herein are not the author’s personal possessions. Some reviewers chose to assume as much regarding my previous books. The data herein are the numbers recorded as a result of two horses running fifty-three years apart—Man o’ War in 1919 and 1920 and Secretariat in 1972 and 1973.

The author was not yet born when Man o’ War raced, but he was fortunate to have seen Secretariat run.

As a researcher interested in comparing these data and hopefully clarifying some misunderstood issues related to these two great champions, I only used the data in standard statistical applications. I also assumed that it was accurate as I found it.

The data were in no way modified or made a means by which to advance my own favorite horse, as some might choose to conclude. I believe that an honest and close reading will obviously support that statement.

Actually, if pressed about what horse was my favorite, I would definitely lean toward the great Native Dancer, now largely marginalized by racing pundits. He actually had a better record than either Man o’ War or Secretariat, having lost only the Kentucky Derby—and that by a head—in his 22 career races. But that is another story.

In conclusion, readers will never find stated herein that either Man o’ War or Secretariat was the better horse. Again, as stressed in GHA and BG, data analysis can never disclose a horse’s inherent greatness. Those who think otherwise completely misunderstand the nature of statistical methods and objectives.

Statistics only suggests the acceptance or rejection of hypotheses—as readers will discover if they do not already know this—concerning whether one sample seems to differ or not differ significantly from another. That is all statistics does or can do. This idea is thoroughly examined, explained and illustrated throughout the text.

If you, therefore, are someone seeking affirmation of your predilections about one of these horses versus the other, this also is not the book for you.

Such multiple caveats having been clearly stated, I wish those well who desire to enter and seriously consider the past performance records of the two Thoroughbred runners generally considered the greatest colts in the history of North American racing.

Charles Justice

Bloomington, Indiana

January 6, 2013

Preface to the Second Edition

This edition, published by Author House, is the second edition of the book Secretariat and Man o’ War: Applied Statistics and the Forbidden Comparison

The first publication in 2013 was under the auspices of Dementi Milestone Publishing of Manakin-Sabot, Virginia.

When their first printing sold out, in late 2021, I opted to re-publish using Author House of Bloomington, Indiana.

The changes to the book from the original in no way change its conclusions—that no real era difference exists between Secretariat and Man o’ War, or between any two Thoroughbred horses, to prevent them from being equitably compared despite how many years separate them.

A statement was added to the Prologue giving the exact time span required for horses to evolve from their progenitor (Eohippus) to the modern horse.

The third section of Chapter Three, dealing with the Work-Energy Theorem, was revised to make reading more smooth and meaningful.

The Index was expanded by adding necessary items inadvertently omitted previously.

Figure L.2 in Appendix L was deleted because it was redundant.

An additional appendix, M, was added to refute some charges by readers of the first edition that Linear Regression was not the most accurate type of analysis to describe and predict Thoroughbred performance.

It is, especially if one wants predictions that make practical sense!

For readers familiar with statistics, I refer to the test status of the Null Hypothesis by the term ‘accept’ vice ‘not reject’ as most texts use. I believe this is easier for beginners to understand.

Last, the cover was completely redesigned. This will be obvious to the casual observer.

Other than these changes and corrections of typos, nothing significant in the book was changed.

Charles Justice

Bloomington, Indiana

April 27, 2022

Each of us is all the sums he has not counted.

~ Thomas Wolfe

Prologue

Despite many gratuitous warnings that comparisons of Man o’ War and Secretariat are forbidden by the very era separating them, I choose to compare their racing records herein.

I do not believe that an era difference existed on any conceivable level between Man o’ War and Secretariat. I do not, in fact, believe that an era difference exists anywhere within Thoroughbred racing history, from the publication of the General Stud Book by James Weatherby in 1791 to the present.

This point will be expanded and illustrated as the book progresses.

In The Beginning

If one compares Man o’ War’s six six-furlong juvenile (two-year-old) race times to the times for Secretariat’s three six-furlong juvenile races, the first and most readily gathered fact is that their respective averages were 72.2 s and 70.47s, respectively, where ‘s’ means seconds.

Subtracting the latter time from the former shows that 1.74s, on average per six-furlong race, separates the two colts.

The same procedure applied to Man o’ War’s two nine-furlong sophomore races and Secretariat’s four nine-furlong sophomore races discloses a difference between their average times of: 110.4 s - 108.04s, or 2.36s.

Therefore, if an era difference actually existed between the colts—some ethereal quality of time’s passing which rendered their races inherently different, like the proverbial apples and oranges—then it changed character from one year to the next since the difference of the average times between six and nine furlongs is not proportional to Farley’s estimate, i.e., about 2s slower per mile (337).

However, neither the colts nor their race parameters were inherently different. They were both Thoroughbred horses, descended from overlapping and intermingled ancestors (Ainslie 79) dating back to more than three centuries ago. (Mackay-Smith 173) They both ran equal measured distances and they were both timed for those distances by technologically similar devices.

Their running feats were recorded for posterity’s admiring gaze on durable materials using suitable mineral-spirit-based substances—because they happened to consistently apply their skills better than any two North American Thoroughbreds of the past century.

The previous 333 words having been written, this book could be terminated forthwith, for my major point is established— that all the rooftop shouting, over many years by people highly perturbed that anyone would compare Man o’ War to another horse, has been wasted. I continue writing mainly to develop the case.

There is not and never was an era difference of any substance separating Man o’ War and Secretariat or any other great Thoroughbred runner. The fact that relatively small time differences, 1.74 s and 2.36 s are all the time adjustment required to make the average times of these champions equivalent belies any statement that their records cannot properly be compared.

What is meant by equivalent? It means precisely, for these studies, that 1000 random simulations of both Man o’ War’s and Secretariat’s six-furlong and nine-furlong races, using adjusted run times for Man o’ War based on the above two numbers, predict that he would win, on average, 504 of 1000 of the six-furlong races and 484 of 1000 of the nine-furlong races—provided that Secretariat received no counterbalancing compensation.

By any reasonable standard, those results would be interpreted as judging the two colts equally adept at running the respective distances. Neither was better, if a qualifying term must be used.

However, the rest of the story should be told because it’s important.

Gene Pools and Other Bets

The gene pool of the Thoroughbred is subject to extensive inbreeding and has been since the Irish Hobby, the English Running Horse and the Turkoman Arabian strains were introduced and combined. (Mackay-Smith 1) Thus, its genes tend to remain relatively constant over long time periods, just ten horses having contributed over half the genes found in modern Thoroughbreds. (Cunningham 94)

Specifically, it is now known that the evolution of the horse from its progenitor, Eohippus or Dawn Horse, took about 52 million years (Tufts Univ.) and not just the roughly three-hundred years that the Thoroughbred was bred in earnest. It certainly required far more than the paltry 53 years separating Man o’ War and