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James Willoughby: Understanding sectionals, and what they told us at York

By James Willoughby
Sun 16 May 2021

By James Willoughby

Course Track wins award

It's not the races a good horse wins that you remember; it’s not the winning distances, the ratings or the things that people said. It is captured by the moment, a few seconds abstracted from everything else: that’s the only frame that good horses need to show they are special.

For me, that horse was Dayjur in the 1990 Nunthorpe at York – the way he dipped his shoulder outside the furlong pole like a big cat and went again. Standing there three rows deep on the rail, I heard an expletive punctuate the din, broken into two syllables for emphasis. Then, moments later, when the shouting gave way, I realised in horror it must have been mine.

Here's the race that still makes James purr 31 years on

This week at York, there was no Dayjur on the racecourse. And not many jaws to drop, in any case. But it was still a meeting for marvel, only now we have the capacity to measure as well as react. The era of sectional times has dawned.

Tracking horses by means of the GPS system does not come without difficulties. Satellite-based radio navigation systems use geometric calculations that exist on the edge of a knife. These satellites are in middle Earth orbit and the distances they span are eye-watering. They were not designed to pinpoint one racehorse in a field of many travelling at 40mph. As a result, the racing fan needs to be a little patient and desist from cheap shots; catching lightning in a bottle is not an easy thing.

The engineering task required to produce sectional times is awesome. People who specialise in the technology know this and that is why Course Track won a prestigious Sports Technology Award this week.

Course Track uses two sensors placed in pockets either side of a horse’s saddle-cloth because one will not do the job. Walls, cars and trees get in the way, sometimes the sensor is belted by a jockey’s whip. Even when it isn’t, the sensor has to deal with the motion of the horse. Nobody designed GPS originally to do this.

The raw data from the sensors needs to be combined optimally by data scientists. Course Track has some very good ones on the job, but at the moment the raw data needs to be passed by human observers, to combat sensor errors. This is going to get better and better as time goes on, because the highly qualified people that Course Track has on the job are domain experts who work with technical racing data in a betting context every day. My own meagre abilities are dominated by theirs.

Making sense of sectionals

How do you know you can get anything out of sectionals? I have a simple test: have you ever purchased, or even picked up, a popular science book? If the answer is ‘yes’, the chances are you are just the type to get a ton out of this data. If the answer is ‘no’ it doesn’t mean anything other than you probably rely on instinct or visual learning to make sense of the world and that numbers are likely not your bag. In this latter group is one person I rely on to understand racing most every day.

But let’s get into this now, enough of the chat. How do we start to think about sectionals? How would you explain them to someone else, once you understand the fundamental ideas.

Raw Course Track data is collected in what is called a continuous manner. The electronic sensors measure their position ten times a second using an algorithm called a Kalman filter which is common in robotics and missile systems. Without going too deep, a Kalman filter helps to estimate the position of the sensor by combing the measurement of where it is made from space with where it should be based on the last few positions calculated. It is principled guessing, no less, which is why it is silly to think that any GPS system can establish ‘truth’.

The maths involved is undergraduate level, but solving problems like this is how mankind has progressed in ways inconceivable 100 years ago. Critics of sectional timing say that undulations and variable going render them inapplicable in British and Irish racing, but at the same time they rely on mobile phones and computers...

Everything is numbers and the scientific method which deals with them is mankind’s greatest achievement. But science has nothing to work with except for measurement and this involves the messy, chaotic world in which we live. Rainfall, wind and clerks moving the rails aren’t going to stop science in its tracks now.

So, if you are one of those people curious to pick up books that teach something new, you might now wonder to what the popular science of sectionals amounts?

Well, that continuous data we talked about is bewildering for the end user of sectionals. So we chop it up, which is called ‘discretising’. Now we have left behind the real world of the split-second and entered a new stroboscopic framework. We need to present sectionals like this for now, but it won’t always be the case.

Let’s go. Here is the stroboscopic world of the two-year-old race on the opening day of the Dante Festival 2021, in which Project Dante fulfilled his nominative determinism, to use a phrase beloved on Twitter:

The first thing a good data scientist like you does is to plot the data. Let’s focus on Project Dante’s row, the stroboscopic world of furlongs. “Start, F2, F3, …, F5” are his furlong-times. Let’s translate those to speeds into mph:

If you absorb the lesson of this graph, the rest of sectional times as a study is just filling in the details. On the graph are three lines. Let’s start with the red one: this is Project Dante’s average speed for the race which is about 39mph.

Stop right there. Yes, 39mph. This is a two-year-old racehorse on rain-softened ground in May. His average speed from a standing start for five-eighths of a mile was nearly 40mph. Gulp. You want to get someone you know to have a guess at this. Project Dante is no Battaash and this is not July or August. Let’s hear it for the thoroughbred. This is awesome.

The next line to consider is the dotted orange one. This line is fitted to the points described by Project Dante’s sectional times; first, we calculated the equivalent miles per hour using speed = distance/time then interpolated between points to create a continuous measure of estimated speeds. Where the orange line is above the red one, Project Dante was travelling faster than his average speed.

Now, all this is necessarily simplified in the same way all subjects are. The key point to understand comes from basic physics, or classical mechanics as it is known to the initiated: the kinetic energy of a moving body is proportional to the square of its velocity (or speed). Maximising its energy use is not the only consideration for the horse in running the fastest time possible, but it is an important one.

What this squared law tells us is this: small deviations in speed for the horse result in much larger deviations in energy use. Every science (or pseudoscience, in this case) requires a fundamental law. For the science of sectionals, this is:


“When a horse’s speed varies the least, it will almost always run the fastest time of which it is capable”


Some of the world’s great jockeys understand this principle perfectly. Ryan Moore even said similar to me once unbidden. Moore is a truly great rider with the greatest racing brain of his generation; his is able to adhere to the theory while mindful of the positional requirements of a race, the race strategy, that which mathematicians call the ‘game theoretical considerations’ of winning.

I cannot speak for any other rider, but when you back a horse ridden by Moore, you can be content that he understands this and is a master of applying it. But, as a punter, you cannot have everything in this world because you have to pay a hefty premium in terms of reduced odds when backing Moore’s horses. Our job is to find less well-celebrated riders who understand the same ideas and can enact them at high speed with a cool head on the back of a horse. Personally, I cannot even do my 12-times table while riding a bike.

Back to the graph. Where the orange dotted line veers away from the red dashed one lies inefficiency. Notice the green line now which is an arbitrary energy function. Forget about its computation, but notice that small deviations in the orange dotted line result in large deviations in the green one. These are the artefacts of exceptions to the fundamental law. Generally speaking – and allowing for the layout and relief of the course – the closer a horse stays to its average speed for the race, the better it will perform.

The Expected Goals principle for horse racing

Hopefully, as a sports fan, you have absorbed the principle of Expected Goals in football. Of course, this is no new idea. It was stolen by football analysts from the sport of ice hockey. The idea is that adding up rare events like goals and determining the best team by the higher total (the way the result of the game is resolved) means that you mistake luck for skill in many instances.

The skill in scoring goals, it turns out, is mostly in getting golden chances, rather than in the ability to tuck them away. In other words, the best teams and players are better identified by adding up the probabilities of a goal, given the location, angle and speed of shots, rather than the count of goals that went in.

What football analysts are doing here is what the brilliant baseball analyst Bill James first realised when studying the sport he loved as an enthusiastic amateur: it isn’t the realisation of events that is important, it is what should have happened on average.

James sparked a revolution in sports analytics which has since been driven largely by one principle: the desire to extract from a game (or in our case, a race) the signal of true ability as apart from the noise of the event. James was like a goldminer panning through dirt to get to nuggets of information which would then predict future events better than what actually happened.

This cannot be stressed enough: the job of the racing analyst should be to do the same. From time immemorial, some of the best analysts in our sport have tried to do just this from visual images. And many do a cracking job as well. What tracking and timing does is not to invalidate their instinctual judgments, their intuition, their domain knowledge and experience, but to subject it to scientific rigour.

In the graph, the green line is basically our key to horse racing’s Expected Goals equivalent. If we took the same graph for every horse in every race and, after allowing for the context of the race (the going, the distance, the layout of the track etc), calculated the area under the graph, we have a horse’s Expected Goals equivalent which we could call ‘Expected Lengths’ for instance.

This is a bit complicated. It involves calculus, a term you probably never wanted to read since leaving school. But, bear with me, because we are about to skim the subject only: if we integrate under the graph, or could add up the total area, we could take the horse’s actual performance and normalise it for the run of the race.

This is what Expected Goals is doing for a football game: normalising the result of the game by removing the randomness inherent in shooting. Some horses are totally thrown off form by the ride they received; others were given a ride which was effective in winning, but which denied them the chance to fully extend their superiority. With tracking data in hand, the analyst is now able to remove the randomness inherent in running the race and find, like James, the signal of talent which lies underneath the numbers.

Sometimes, as James warned, this will be Fools’ Gold – not the real thing. Just as the Expected Goals model can err by misunderstanding the particular skill of a small number of footballers and teams who have a different way of playing, it is possible to make an horrendous error in assuming that a horse who ran the race a certain way that looks inefficient is capable of doing things differently. Some horses are quitters, others take time to warm up, some will perform a feat of majesty then back off from the experience and never do it again because it hurt.

As we said, tracking and timing data isn’t a panacea for all mistakes made by the human eye. It still requires a heck of a lot of secondary skills that some of us who are into sectionals clearly are lacking.

A first step along the road

You know the old saying that it is better to give someone a rod and line than a few fish? Well, that’s what I believe in when it comes to sectionals. We need to open the subject out, to demystify it, starting with the provision of a few simple tools.

And that’s what the Course Track sectional output you will find on the results tab of this website does. Instead of that complex integration thing, we can cut through the maths and use a proxy for efficiency which is much easier to compute and understand.

We already know the average speed of a horse for the race by dividing the distance by the time taken. Now, with split times in hand, we can calculate the speed of the horse for any section of the race. If we choose a section of suitable length at the end of a race – say two furlongs for races up to a mile and three furlongs for longer races – we can compare the speed a horse finished with its speed for the race as a whole.

Let’s walk through the calculation of what we call a Finishing Split % using the Musidora Stakes winner, Snowfall. Her winning time was 2min 13.18sec for the 2288 yards (the rail was out on the round course, adding 32 yards to the original distance of the race of 2256 yards) which is an average speed of 34.62mph. She ran the last three furlongs in 34.73sec according to Course Track sectionals, which is 38.87mph.

So, Snowfall’s Finishing Split % for the last three furlongs was 38.87 / 34.62 * 100 = 112.28%.

Any Finishing Split percentage over 100% represents a relatively fast finish while those under 100% represent a slow finish. We can infer that a horse who finished particularly fast or slow (considering its race speed) must have run the first part of the race in the opposite manner. And if a horse finishes evenly (close to 100%) it must have run the rest of the race likewise.

Of course, this is often a simplification. And it can lead to errors. So, don’t let anyone who uses this technique tell you it is exact. Some races feature more than one change of race pace, which means that a horse who finishes evenly at the end may not have run the rest of the race likewise. What we need to do to know how efficiently a horse has really run is to use complex numerical estimation to consider every moment of the race – to integrate under that green line.

But this way is so much easier. It is a way in to the subject which is vital to spreading an understanding of sectionals and tracking which is vital to its longevity.

What do we do with the Finishing Percentage?

There are some complications even with this simpler technique, however. And it’s back to the old chestnut about the variety of British and Irish racecourses. We cannot assume that a horse who finishes at 100% of race speed has run efficiently firstly because race times here are measured from a standing start.

So, on a level track, a horse who gave an even effort (for that is what we really care about) for a mile would finish faster than race speed because it takes over two seconds to overcome a standing start. In other words, if you catch a horse running quarters of, say, 26.5, 24, 24, it has given an even effort, but its final furlongs will be faster than the average of the three because of the start.

More profound is the effect of the relief of the course. A horse who finishes evenly on a track with an uphill finish, for instance, must have saved something early because the later furlongs are stiffer than the early ones. Also, horses running over shorter distances use a higher proportion of anaerobic energy to middle-distance horses and stayers which must be used early while is it available. And so an even effort for them means running harder than average early.

For every course and distance in the country, there exists a narrow range of Finishing Speed % where a horse will run its fastest times. A front-running horse will do best at the bottom of this range, while a hold-up horse will do best at the top of the range, but there is a sweet spot between them which fits the profile of the average horse, if such a concept has meaning.

When we look at those Musidora Finishing Split %s, we don’t see a horse who stole the race from the front because Snowfall’s Last 3f (%) highlighted in the final column is the highest in the race. It could still be that she was ‘flattered’ by the winning margin, however, because we still need to remember she started the sprint for home ahead of her rivals. Moreover, a sprint finish does not suit every horse.

Picking out some Dante Festival talking points

Wednesday

Sky Bet Race To The Ebor Jorvik Handicap (1m 4f)

We won’t go too deep at this entry-level stage, but hopefully the theory expounded above enables the reader to start going through some sectionals data to see if the numbers either confirm their impressions or throw new light on a race.

The above was the first race of the meeting. Ilaraab swept through from off the pace and won going away. The sectional percentages here show it was a relatively fast finish, so we can normalise the result by thinking of the finish as not being ‘stretched out’ enough by the early pace. As most would agree merely from a visual analysis, Ilaraab is a progressive horse who was value for more than the winning margin of three lengths. He must be a prospective Group-race winner, especially as he can clearly cope with a steady pace which tends to be a barrier to horses progressing from more stronger-run handicaps.

Duke of York Clipper Logistics Stakes (Group 2, 6f)

This is a far more subtle example and highlights that there is no ultimate truth to a result. Understandably, many were raving about the performance of the lightly raced Starman after his neck win over Nahaarr in the Duke of York Stakes. If you read the close-up comments in the Racing Post (but not on this esteemed website), it is clear that at least one race-reader wants you to believe that Starman was the best horse in this race by dint of the fact he was ‘holding’ Nahaarr, last year’s Ayr Gold Cup winner, in the final strides.

But this ignores what happened earlier. The sectionals show that Nahaarr was forced to accelerate well above his cruising speed to reach that challenging position; his F4 and F5 furlongs were faster than anything the winner produced.

It could be that, just as the race-readers are implying, there is something inherently superior to Nahaarr in Starman’s make-up. Perhaps he was idling and could have pulled out extra.

Just wait a minute. Imagine if the two horses had occupied each other’s positions three furlongs out. Would Starman really have accelerated past Nahaarr had the latter been given the same 0.29sec start at the beginning of the sectional? Nahaarr has won over seven furlongs and thrived in the white-hot heat of a handicap; moreover, he reached a higher speed in the race than Starman.

Surely this is the point in comparing them? Starman might have scored the goal, but he had the easier chance. Nahaarr is a horse who is ideally suited by some give in the ground, and this may shape his fate, but he deserved a lot of credit for this effort, as the sectionals show.

Thursday

Al Basti Equiworld Dante Stakes (Group 2, 1m 2f 56yd)

It may not have been a truly vintage renewal of the Dante in terms of figures, but it was an interesting race which featured some good young horses in the making. The first three took a long time to wear down Roman Empire after Hollie Doyle dashed him for home. You can argue that Hurricane Lane and High Definition will do better over further, with the latter coming from a poor position and running the highest Last 3f (%) in the race. Gear Up should be sharper for the run too.

An interesting horse to flag up here is Pythagoras. Sectional upgrades don’t just exist to flag up ‘unlucky’ losers, and this colt was not the best horse in the field at all, but he did suffer a very uneven ride and he is lengths better than his finishing position. As this was his best effort yet on figures, it is worth spending a little time on him.

It is clear that connections are a little vexed over what will turn out to be the Galileo colt’s best trip. He takes a keen hold, and in anchoring him Paul Hanagan found himself at the back of the field. Presumably, this was a reaction to his effort in the Blue Riband Trial at Epsom, where he had raced close up early and appeared not to get home. Either way, you can see from the sectionals that he quickened as well as any horse when set down in the straight, staying over towards the far side on a wing too.

Understandably, Pythagoras did not see out the trip given that he ran so unevenly, but he did show some standout talent which was hidden in the hottest part of the race. We will leave his best trip and tactics to his trainer Richard Fahey, who will know the horse best. It could be that he should be remembered for the autumn when soft going comes around.

Friday

Oaks Farm Stables Fillies’ Stakes (7f 192yd)

Oh my goodness. When a horse wins a race where the slowest finisher runs a Last 3f (%) of 106% - and the winner clears right away in the closing stages - you know you have seen something.

The Ed Walker-trained Primo Bacio, a three-year-old filly who has plenty of improvement to make physically before it can be said that she is mature, finished off here in 11.15sec and 11.63sec for a final quarter of 34.07sec – all these marks being the best at the meeting. This wasn’t fast ground, either, remember.

Neither was Primo Bacio’s final time of 1min 38.07 slow. So, if you assume she behaves like the ‘average’ horse in being able to run a faster time when paced more evenly – in accordance with our fundamental law of sectional times – then there is no doubt whatsoever she is of Group 1 standard.

But, just one second. Before we drape her in the winner’s blanket for the Group 1 Coronation Stakes at Royal Ascot, it is worth discussing more fully what we touched on earlier: how safe it is to make these projections?

Primo Bacio is a fast horse. There is no doubt over that. She cruised into it here and ran away like a mustang. Not surprisingly, given this capacity, she owns a quick action and a good deal of natural speed. The question is: can she actually run a much faster time if going off faster - that is, following a stronger pace?

Here there is some doubt. When Primo Bacio meets a stronger pace, her last-three-furlong speed will decline naturally. In order for her to run a faster time overall, the trade-off between early and late pace needs to be such that if she goes a second faster early, she runs less than a second slower late.

This exchange tends to be fruitful when a horse who had won a slowly run race has an excess of stamina for the trip. But Primo Bacio isn’t this type of horse at all – her action says that, as does her pedigree (she is out of a mare suited by seven furlongs and by Awtaad, a very smart miler).

The point here is to highlight that when we make projections from sectionals, they are only projections. Just like the Expected Goals model sometimes wrongly assumes that all players and teams have average ability to finish chances (because, after all, most do), different types of races bring out different qualities in horses, and not all horses behave the same way.

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