Consider the fractions run by Blame and Zenyatta in that unforgettable 2010 Breeders' Cup Classic:
Blame 24.6 24.5 23.7 24.6 24.9
Zenyatta 26.3 23.7 23.7 24.5 24.1
The times are given in seconds and tenths. Even pace for a final time of 2:02.3 could be represented by quarters of 24.4, so it easy to see that Blame ran the more evenly.
(This, as many of you will know, is a rather coarse form of analysis, as ideal pace over 10f at Churchill Downs is not exactly five equal quarters of 24.4, but licence is asked for ease of explanation. And the same applies to the comparison with the 2009 Classic at Santa Anita below.)
If Blame and Zenyatta were clones, the runner-up could be proclaimed the better horse with confidence. Her first quarter of 26.3 represents by far the biggest deviation from even pace, so it is axiomatic that she used her energy less efficiently.
Zenyatta, who broke in something of a tangle, could not recover the ground she lost early. But should her jockey Mike Smith have moved earlier, as many asserted?
First, compare Zenyatta's sectionals from 2010 with those from 2009 Classic at Santa Anita, run on the track's Pro Ride surface which was faster than the Churchill Downs dirt:
2009 26.9 23.3 23.3 23.9 23.2
2010 26.3 23.7 23.7 24.5 24.1
When Zenyatta won the 2009 Classic, she actually ran the first quarter slower than in 2010, but her final quarter was her fastest and represented genuine top-notch acceleration.
In 2010, by contrast, Zenyatta could muster a final quarter of only 24.5 which was slower than she was running earlier in the race.
In other words, she was not limited by the maximum speed reasonably attainable - as many implied after her vain, late charge - she was tiring. Her finishing flourish was made to look more impressive because it was framed against a slow final quarter in general.
Had Smith been more vigorous in the early stages, Zenyatta would have run the final quarter even slower. Moreover, there is no reason to suggest it would have been a more successful move: the energy cost of recovering that fleeting losing margin would have been higher for her at 23.7 per quarter early than at 24.1 per quarter late.
But why did Zenyatta have to lag behind at all? Some accused Smith of showboating, of assuming that tactics which Zenyatta could overcome against slower females in California would work against some of the best horses in the world.
I believe the answer lies in the concept of psychological flow. In the last part, I detailed scientific research which has concluded that the vigour of an animal's physical response to a stressor is closely related to the control it can exert over it. (Control is a psychological term for freedom of choice.)
From an early stage of Zenyatta's career, it was clear she had an idiosyncratic style of racing. It could be said that the vigour of her finishing response was dependent on the freedom she had to race within herself early.
If you watch closely down the back stretch of the 2010 Classic, Zenyatta was carrying both her head and tail in a pointed fashion. And though Smith could have been more vigorous, neither was he sat still.
Zenyatta was expressing her control over the stressful experience of racing by doing things in her own time - just like she always did.
And Smith learned that a jockey had to work with and not against her in this regard. He had to allow her freedom to run within the envelope of her psychological needs.
We should never forget how tough racing is for the top-class horse. As Aidan O'Brien and others have learned from the evidence provided by heart-rate monitors: the great ones are those not just of the deepest talent but the most committed response.
Horses like Zenyatta are operating right on the edge of the thoroughbred's capabilities. It has been shown, for instance, that the tensile force on their cannon bones is very close to that required to shatter them.
Moreover, their heart-rate and blood pressure is near to the maximum their systems can sustain without fatal consequences. And all the while they are not fully cognisant of what we are trying to achieve by stressing them.
If a horse needs some control over this massive stress; if it will only go so close to the level of effort which is enough to badly hurt it; if it needs to express some sense of "self" in the turmoil of exertion. Well, it is hardly surprising, is it?
Racing makes its special connection with us because horses are not insentient like cars. And, when great performances against the clock are encountered, there is always a feeling that the horse has given something special on both a physical and psychological plane.
Every time I watch my favourite horse Ghostzapper win the 2004 Classic at Lone Star (the link is here) there is always a point just after the turn for home when he palpably seems to let go.
If you compare the way he is moving 50 yards out to earlier in the race, there is evident freedom in his action and a release of the tightness in his physique.
This is something special. And it is my connection with racing, as much an any pleasure which analysis can supply.
If you remember the formative races of Ghostzapper's career, he would lag behind early, even though he had tremendous speed. It wasn't so much the lesser distance of races: this was the way he needed or wanted to run.
This is the implication of Flow psychology: to get maximal effort from the top-class racehorse - to encourage them to bring it all - we don't have to drive them against their will, we don't have to bully them. Instead, we must allow them just as much freedom, or control, as the tactical constraints of a race will allow.
This may not hold so well at the other end of the class scale, but in its purest form it is an important plank of the ethical defence of racing: that there is something to be had from running for the horse.
In general, I am no fan of Smith as a rider - he has never seen a wide trip he didn't like. But he understood Zenyatta the athlete so fully, and he had a strong grasp over his role as her partner. As a result, he rode her so beautifully and so effectively throughout her career.
To pin Zenyatta's sole defeat on her regular rider because he did not push her harder when we thought he should appeals as extremely unfair. And, not for the first time, it may be evidence of a superficial approach to racing analysis; that some of us often have a limited and simplistic philosophy where animals are involved.
As far as the science of sectionals is concerned, all this might appear nebulous. But it is actually fundamental and can be summarised in one line:
When comparing a horse with the ideal, first remember to compare it with itself.
And that's the point I was driving at in this series. Horses tend to have a sectional imprint which is common to their best efforts and is characteristic of themselves.
While ideal pace exists for any course and distance, there is a distribution around it which represents the horse population and their individual needs.
Many, like Blame, are close to the mean while few, like Zenyatta, depart greatly from it.
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I hope you have enjoyed the series and found something in common within your own experience. Many thanks to all who have read it and made such generous and enlightening remarks.