Willoughby

Yes please! Need a laugh right now.

had one earlier thanks to u



Free money on Apache, shirley, as odds against in dead heat and result should stand.

Willoughby could make boiling an egg sound like splitting the atom.
I miss him on RTV as he was a source of profitability if you took the opposite view

Bit harsh howard?

He is having a pause and will come back refreshed

This one is an attempt at a  tour de force in mathematics,loper

It's one thing understanding the Maths, which isn't too hard, quite another putting it into practice. It struck me as a latter day derivative of Clive Holt's Fineform Formula. Quantify the variables with a points system to arrive at a fair price and compare the market, but using algorithms to fine tune the accuracy. Need a strong coffee before I get started tomorrow morning!

The whole thing is absolute Bull……

For once I concur with Aceform and I refuse to post the article

It’s all about stride length,a horse that has a big stride invariably beats one with a shorter stride.

Soft ground lovers and daisy cutters……grabbing the ground and skipping along on the front end….

Database…..sectional timing Zzzzzz

All of which can show you what has already happened not what will happen

I once remember James climbing under a studio table and devouring a full pizza that they had got delivered to the studio on a mundane winter evening AW meeting.

I generally found him entertaining and insightful. Is he back on the scene?

Regretably,no.
He was a  licence to print if opposing his views

Thing is these mathematicians have to keep finding liquid markets full of mug money or at least plenty of it. Then other mathematicians join in and there's very little left if anything. There's no easy way. You have to watch all the races  all the horses and lay short or back big.  There is no way to be lazy long term.

How does an algorithm predict a "not off"?

Ive been lazy long term

All me life in fact

Listening to Willoughby could at times be painful and 'awkward', such as when he was doing his brains on the American racing, or the constant sniping at jump racing when he was on a channel whose business it was to promote the sport, but generally I thought he spoke a lot of sense, and some of his 'catchphrases' are still used years later eg magic carrots / golden highway.

"Golden Highway"??
He was the fool that thought one of Johnston's 2YO's was the next coming when it had been the recipient of such circumstances at Newmarket.
It began with a V and proved to be a cash cow to those of us who thought otherwise.
I don't think the wretched creature won another race

Hard to post because of the mathematical symbols and tables.

He got that one wrong, uptheirons, but at the same course, for example, he'd made similar comments about Kingman after he had won on debut. He got that one right.

He wasn't guessing the V one, he based his views on what the clock had told him, so he was giving a genuine opinion.

He wasn't guessing about the V one

Btw, 1st time poster will be on later to remind us about Gladiatorus or whatever it was called

I also got kingman right

me and Willow were the only 2 that did

That thing was full of the best gear, widely available in Dobuy at the time

A "misguided"opinion,George.
He did his gonads punting,full stop.

He was also an arrogant pig towards RTV Staff

Busyfool 19 Jan 26 18:42 
I also got kingman right
me and Willow were the only 2 that did

Thanks for your sarcasm, I don't think Willo eulogised about 2YOs winning on debut liberally, but people evidently only remember the ones he got wrong, but he got Kingman spectacularly right.

Busyfool 19 Jan 26 18:43 
That thing was full of the best gear, widely available in Dobuy at the time

Willo might reply: don't you mean "magic carrots"?

Regarding the 'V' horse, my recollection of it was Willo was impressed by it relative to the older horse race times on the card.

But it is also my recollection that the V horse had raced hard up against the rail, whereas in the other races they did not.

I remember him coming on the forum and lecturing everyone……

Never returned….

Forum name was James Willoughby……

Iirc 'ace. he had a 'feud' with 'naps champ', which he drew a line in the sand over.

Not sure how a line drawn can be over anything

Drawing a line in the sand is a challenge, not an armistice

I didnt mind him at all, he had plenty to say and he was miles in front of the goons they have now

Ironlady hates everyone, not just Willow

I rarely hate anybody,busy.
Willo is a chancer with many lunatic ideas

Visinari did win one more race. In Oz.

Thanks,Cider.

yes GEORGE the days when willo and THE CAPTAIN took everything that happened in dubia transferred to uk flat racing, the other hotse was hawkwing,both never won another race between  after willo/the captain told us they,d be winning every race,boat race,fa cup final and super bowl between them

No posting of the profound article yet?

GLADITORIOUS ,they had it  winning the QUEEN ANNE by 10 lengths anything odds against was stealing money on the back of winning a hounds race in the dubia camel racing, NEVER TROUBLED THE JUDGE AGAIN

And fair play to the RP, they're still using Willo's pic from those days.

Here you go loper.

The mathematics of betting: James Willoughby on how pro punters get the numbers working in their favour
The likes of Don Johnson and Tony Bloom are betting to a vast scale - because the maths gives them an edge
author image
James Willoughby

In a recent five-part series, we profiled the people who strike fear in bookmakers; the ones who all punters aspire to be. They are the Masters of Betting – Don Johnson, Steve Lewis Hamilton, Phil Bull, Alan Potts and Tony Bloom. Here, James Willoughby explores where their edge comes from.
Not a subscriber? This is the perfect time to sign up with our introductory offer of 25% off for your first six months of a monthly subscription – just click here and enter the code MASTERSOFBETTING256 at the checkout.
The Racing Post’s Masters of Betting series showcased five influential punters with different approaches to beating the game. In every era, standout individuals like these excel not only at finding edges but also systematically exploiting them. This begs the question of where these edges come from and how masters of their craft like Tony Bloom and Don Johnson know they can be relied upon. The answer to these questions is always mathematics.
“I realised that applying mathematics and complex algorithms to sport allowed me to assess the probability of sporting events more accurately than the markets,” says Bloom.
In maths, the idea of probability has a few interpretations. The most fundamental is the long-run frequency of an event. If Bill and Ted play snooker repeatedly, the idea is that the frame score begins to converge on the true probability that each will win a future game. So, after 100 frames, if the score is 80-20 to Bill, Ted’s probability of winning a future frame is just his share of the frames won so far: 20 / (20 + 80) = 0.20.
Probabilities lie in the region between 0 and 1, but when multiplied by 100 they are the same thing as percentages – here 0.20 x 100 = 20%. The equivalent betting odds are reached using the formula (1 – p) / p where p is the decimal probability of a win. So, based on these 100 games, Ted’s odds of winning frame 101 are (1 – 0.20) / 0.20 or 4-1, so he can assume it is profitable to bet on himself if offered better odds.
Now, if we want to estimate the probabilities of each horse winning the Gold Cup, for instance, we cannot rely on the same method as with Bill and Ted’s excellent 100-frame snooker adventure; we don’t have 100 previous races all featuring the same horses under the same conditions.
To solve the problem, characteristics of each horse can be used to estimate a rating which replaces a competitor’s record of wins and losses. Various computerised methods are available for this task, including the ‘complex algorithms’ to which Bloom refers, but the Daddy of them all – and the simplest to understand – is known as the conditional logit. Let’s explain how it works.
As far back as 1986, Ruth Bolton and Randall Chapman gave birth to the ancestor of modern betting syndicates with their paper ‘Searching For Positive Returns At The Track’ in the Journal of Management Science. There had been plenty of foundational work in related areas, but the two University of Alberta researchers marshalled the maths into a coherent approach that would inspire many who read their work to make their own efforts to beat the races.
Bolton and Chapman showed how to use the conditional logit to combine winning factors about a horse (the ‘characteristics’ referred to above) using a weighting scheme learned from a database of results. The American punting genius Bill Benter read their paper and used the same mathematical machinery – albeit with clever, customised tweaks – as the first step of a process to break Hong Kong markets in the late 1980s.
Believe it or not, Benter actually described his method in a 1994 report ‘Computer Based Horse Race Handicapping and Wagering Systems'. In truth, Benter could afford to lend us all a helping hand by then and, in any case, everyone considers the conditional logit in some form or another, even if they graduate to one of Bloom’s ‘complex algorithms’ like neural network architecture or support vector machine output or gradient boosted trees.
But there is no need to descend into the opacity of these black-box methods. The conditional logit simply calculates the competitive strength of a horse by adding its virtues and subtracting its shortcomings, in just the same way we all do when assessing a race. The mathematics adds structure to the process by computing the precise weightings of each factor which best explain the results.
Consider a horse who has been off the track for 180 days since a win but gets Sean Bowen today and has the class edge implied by top weight. All these factors add or subtract from the chance of a horse compared with one of which nothing is known. The conditional logit just comes up with a rating which becomes a probability conditional on the factors possessed by the other horses in the race. (For completeness, the logit part refers to the machinery relying on the logarithm of the odds ratio – or ‘logit’ – of the horse’s chance.) 
Back to our snooker example. If we didn’t know the score between Bill and Ted in their previous 100 frames, but a panel of experts gave us marks out of ten for their potting, safety play and temperament, we could use the conditional logit to predict the match odds, using a database of matches with these same ratings and results for other players. Using this data and the characteristics of the players, the conditional logit might estimate Bill’s competitive strength as j and Ted’s competitive strength as k, then Bill wins a frame with probability j / (j + k) and Ted with probability k / (j + k).
Similarly, in a four-runner race between horses called Alpha, Beta, Charlie and Delta who had competitive strengths of a, b, c and d, Alpha’s probability of winning would then be a / (a + b + c + d) and equivalent odds thus (b + c  + d) / a to 1. (Try inventing some values – which must be positive – for a, b, c and d to convince yourself this is right.)
Let’s work through a facile example. For our success factors, let us consider the last two form figures of a horse, each encoded 1 to 4 or zero according to its finishing position. We will also give credit for any course-and-distance success. Our dataset is all British handicaps since 2010. We want to know how to price up a race strictly using these factors alone. 
Table 1 (below) contains the ratings points awarded to a horse for the presence of each factor, as calculated by the conditional logit. Constrained by the severe limitations of form figures, these values do their best to explain the results of all the races in our dataset. Study the points scheme: a horse’s last performance is more influential than its penultimate one, which aligns with common sense, while a course-and-distance win is a big deal.

The way this works is this: when assessing a future race, and a horse has won its last two races and is a course-and-distance winner, its competitive strength is 23 + 15 + 15 = 53pts, while a horse unplaced on its last two races gets only 20pts (not zero because this group still produces a small percentage of winners). After performing the same calculation for every horse in a race, the probability of a horse winning based on these limited criteria is just its score divided by the sum of all scores, including its own. Table 2 (below) works through a calculation for a sample race.

It could not be much simpler. To recap: the form figures and course-and-distance-winner status is converted to a score, then the probability of a win is just the fraction of the total score of all horses (here 200). So, for the horse named Alpha, a total of 31pts from second place on its penultimate start and third place last time out can easily be calculated from the weightings of these factors in Table 1. When this is expressed as a fraction of the total score of all horses, the resulting probability of a win is 31/200 = 0.155, which is shown in the column second from the right.
The corresponding odds are shown for information purposes; notice that the spread of odds for this imaginary race is far less than might be encountered in a real one. Why? We are considering nothing but a scanty few facts about a horse, whereas the market takes a lot more into consideration.
If we wanted to specify a model which was much more sophisticated, form figures would not do. Instead, our factors might include form and speed ratings, jockey ratings, weight carried, draw advantage and number of recent runs. Now, the conditional logit would assemble a much more formidable betting tool by learning from our past database of results how to weight each factor independent of all others, making sure that no factor was double-counted – the pitfall known as ‘collinearity’.
The conditional logit is the scientific way to do trends analysis: the more useful data we have on the horses in the race, the more our calculated probabilities become accurate, the more they diverge from one another and, crucially, the SP too. Now we have a betting machine, and a reason to form a powerful organisation to bring its influence on the betting market, in a similar way Bloom has done.
Behind the scenes of the conditional logit, some powerful maths is at work, although the complexity is less than undergraduate level. Even if you don’t understand it fully, off-the-shelf software for all the common programming languages will do the job for you, or you can ask ChatGPT to write it.
How Benter extracted inside information from the odds
Bill Benter knew the power of the conditional logit, but he realised there was one vital second step necessary before the whole thing would fly well enough to defeat betting markets.
Each of the factors that the conditional logit uses explains a proportion of the variance in the results of all races. But, when you first assemble a model and let it loose, it will not have the power to defeat the market because a component of the odds comes from inside information which you cannot beat with data. It turns out that, thanks to a clever trick, you can use inside information to your advantage without even knowing what it is.
Table 3 (below) shows Benter’s method in action. If you blend your model odds with the SP in just the right proportion, factors in the SP which are not in your model will be incorporated into a new improved probability estimate.

In Table 3, we are using 80% of the SP and 20% of the model odds, although this is just for demonstration purposes. The blended odds of this new ‘augmented model’ are a weighted average (technically, the geometric not arithmetic mean is correct because we are averaging ratios) of the two separate odds. On average, the blended odds will contain some factors not included in the model (such as inside information) and some factors which are not in the SP (such as your striding analysis or jockey ratings, for instance).
How well does Benter’s tweak – which comes from the idea of model aggregation in statistics – actually work? Judge for yourself. Table 4 (below) contains the results of the 67,992 British handicap races in our sample for the highest-rated horse by 1) the model, 2) the SP (i.e. the favourite) and 3) the augmented two-step model, blending the SP with the seemingly naive model derived from placings described above. This time, however, the weighting scheme is not the arbitrary 80% - 20% but the result of a back test.

Table 4 shows the effectiveness of Benter’s trick. The fundamental model in the first row loses money (5% at Betfair SP) because the model’s approach of using finishing positions is naive; the second row shows that 27.8% of SP favourites and joint favourites succeeded for a loss of 3% at Betfair SP; the third row shows the huge advantage of Benter’s two-step approach: with the recency bias towards horses with eye-catching form figures removed, Strike Rate (SR) goes up from 27.8% to 29.0%, Impact Value (IV) goes up from 2.36 to 2.45 and Return on Investment (ROI) approaches parity. (Remember, this is not the performance of the horse the augmented model thinks is the best value, only the one it thinks should be favourite.)
The data in Table 4 shows a profound truth to the modeller. Eye-catching form figures next to a horse’s name has to be a form of price anchoring! In other words, both punters with no private information and paid experts in the media are too heavily influenced by recency, especially when it is represented coarsely by 1s next to a horse’s name. When the influence of recent form is discounted from market odds – the weighting scheme here might be 90% SP and 10% the negative of model odds – horses with 1s next to their name have their prices pushed out and the augmented model’s ‘favourite’ does significantly better than the market choice.
Yet different settings and different fundamental models will produce different insights, each of which is informative about markets at that time and place. But the power of the betting market is profound at all times and needs a lot more respect than it is given in racing broadcasts. Nowadays, the smart racing expert should be a lot less interested in pushing their own subjective opinion and a lot more motivated by explaining market odds near the off time of a race. One brilliant judge is not going to defeat the aggregated opinion of smart thinking and inside information in a liquid market long term, but there is a lot to learn and pass on. 
Executive summary
Betting syndicates and advanced punters who rely on mathematical models have to be able to specify a probability distribution over the runners which is more accurate than the prices available to bet. This is achieved by comparing the factors about a horse with those of its opponents, weighting each factor according to its value.
The most fundamental way to do this at scale is via the conditional logit. Under different names – stochastic utility, multinomial regression – this technique has been used for decades, but smart thinkers like Bill Benter adapted it to absorb the ‘private information’ implicit in the prices of highly liquid yet inefficient markets such as those in Hong Kong at the end of the 1980s.
As you can see, even a naive model which systematically loses money can be useful when combined with pricing information. It informs a discounting scheme. As long as the fundamental model points consistently towards either profit or loss, it can be harnessed to increase accuracy.
The maths needed to beat the market is well established. And there are plenty of other techniques available to modern horse racing modellers too. While the Masters of Betting each have a distinct edge which you and I do not understand, their true genius is the long-term, systematic application of methodology at scale. For this, they truly deserve our awe.

As you are agood egg loper.

The Racing Post’s Masters of Betting series showcased five influential punters with different approaches to beating the game. In every era, standout individuals like these excel not only at finding edges but also systematically exploiting them. This begs the question of where these edges come from and how masters of their craft like Tony Bloom and Don Johnson know they can be relied upon. The answer to these questions is always mathematics.

“I realised that applying mathematics and complex algorithms to sport allowed me to assess the probability of sporting events more accurately than the markets,” says Bloom.

In maths, the idea of probability has a few interpretations. The most fundamental is the long-run frequency of an event. If Bill and Ted play snooker repeatedly, the idea is that the frame score begins to converge on the true probability that each will win a future game. So, after 100 frames, if the score is 80-20 to Bill, Ted’s probability of winning a future frame is just his share of the frames won so far: 20 / (20 + 80) = 0.20.

Probabilities lie in the region between 0 and 1, but when multiplied by 100 they are the same thing as percentages – here 0.20 x 100 = 20%. The equivalent betting odds are reached using the formula (1 – p) / p where p is the decimal probability of a win. So, based on these 100 games, Ted’s odds of winning frame 101 are (1 – 0.20) / 0.20 or 4-1, so he can assume it is profitable to bet on himself if offered better odds.

Now, if we want to estimate the probabilities of each horse winning the Gold Cup, for instance, we cannot rely on the same method as with Bill and Ted’s excellent 100-frame snooker adventure; we don’t have 100 previous races all featuring the same horses under the same conditions.

To solve the problem, characteristics of each horse can be used to estimate a rating which replaces a competitor’s record of wins and losses. Various computerised methods are available for this task, including the ‘complex algorithms’ to which Bloom refers, but the Daddy of them all – and the simplest to understand – is known as the conditional logit. Let’s explain how it works.

As far back as 1986, Ruth Bolton and Randall Chapman gave birth to the ancestor of modern betting syndicates with their paper ‘Searching For Positive Returns At The Track’ in the Journal of Management Science. There had been plenty of foundational work in related areas, but the two University of Alberta researchers marshalled the maths into a coherent approach that would inspire many who read their work to make their own efforts to beat the races.

Bolton and Chapman showed how to use the conditional logit to combine winning factors about a horse (the ‘characteristics’ referred to above) using a weighting scheme learned from a database of results. The American punting genius Bill Benter read their paper and used the same mathematical machinery – albeit with clever, customised tweaks – as the first step of a process to break Hong Kong markets in the late 1980s.

Believe it or not, Benter actually described his method in a 1994 report ‘Computer Based Horse Race Handicapping and Wagering Systems'. In truth, Benter could afford to lend us all a helping hand by then and, in any case, everyone considers the conditional logit in some form or another, even if they graduate to one of Bloom’s ‘complex algorithms’ like neural network architecture or support vector machine output or gradient boosted trees.

But there is no need to descend into the opacity of these black-box methods. The conditional logit simply calculates the competitive strength of a horse by adding its virtues and subtracting its shortcomings, in just the same way we all do when assessing a race. The mathematics adds structure to the process by computing the precise weightings of each factor which best explain the results.

Consider a horse who has been off the track for 180 days since a win but gets Sean Bowen today and has the class edge implied by top weight. All these factors add or subtract from the chance of a horse compared with one of which nothing is known. The conditional logit just comes up with a rating which becomes a probability conditional on the factors possessed by the other horses in the race. (For completeness, the logit part refers to the machinery relying on the logarithm of the odds ratio – or ‘logit’ – of the horse’s chance.) 

Back to our snooker example. If we didn’t know the score between Bill and Ted in their previous 100 frames, but a panel of experts gave us marks out of ten for their potting, safety play and temperament, we could use the conditional logit to predict the match odds, using a database of matches with these same ratings and results for other players. Using this data and the characteristics of the players, the conditional logit might estimate Bill’s competitive strength as j and Ted’s competitive strength as k, then Bill wins a frame with probability j / (j + k) and Ted with probability k / (j + k).

Similarly, in a four-runner race between horses called Alpha, Beta, Charlie and Delta who had competitive strengths of a, b, c and d, Alpha’s probability of winning would then be a / (a + b + c + d) and equivalent odds thus (b + c  + d) / a to 1. (Try inventing some values – which must be positive – for a, b, c and d to convince yourself this is right.)

Let’s work through a facile example. For our success factors, let us consider the last two form figures of a horse, each encoded 1 to 4 or zero according to its finishing position. We will also give credit for any course-and-distance success. Our dataset is all British handicaps since 2010. We want to know how to price up a race strictly using these factors alone. 

Table 1 (below) contains the ratings points awarded to a horse for the presence of each factor, as calculated by the conditional logit. Constrained by the severe limitations of form figures, these values do their best to explain the results of all the races in our dataset. Study the points scheme: a horse’s last performance is more influential than its penultimate one, which aligns with common sense, while a course-and-distance win is a big deal.


The way this works is this: when assessing a future race, and a horse has won its last two races and is a course-and-distance winner, its competitive strength is 23 + 15 + 15 = 53pts, while a horse unplaced on its last two races gets only 20pts (not zero because this group still produces a small percentage of winners). After performing the same calculation for every horse in a race, the probability of a horse winning based on these limited criteria is just its score divided by the sum of all scores, including its own. Table 2 (below) works through a calculation for a sample race.


It could not be much simpler. To recap: the form figures and course-and-distance-winner status is converted to a score, then the probability of a win is just the fraction of the total score of all horses (here 200). So, for the horse named Alpha, a total of 31pts from second place on its penultimate start and third place last time out can easily be calculated from the weightings of these factors in Table 1. When this is expressed as a fraction of the total score of all horses, the resulting probability of a win is 31/200 = 0.155, which is shown in the column second from the right.

The corresponding odds are shown for information purposes; notice that the spread of odds for this imaginary race is far less than might be encountered in a real one. Why? We are considering nothing but a scanty few facts about a horse, whereas the market takes a lot more into consideration.

If we wanted to specify a model which was much more sophisticated, form figures would not do. Instead, our factors might include form and speed ratings, jockey ratings, weight carried, draw advantage and number of recent runs. Now, the conditional logit would assemble a much more formidable betting tool by learning from our past database of results how to weight each factor independent of all others, making sure that no factor was double-counted – the pitfall known as ‘collinearity’.

The conditional logit is the scientific way to do trends analysis: the more useful data we have on the horses in the race, the more our calculated probabilities become accurate, the more they diverge from one another and, crucially, the SP too. Now we have a betting machine, and a reason to form a powerful organisation to bring its influence on the betting market, in a similar way Bloom has done.

Behind the scenes of the conditional logit, some powerful maths is at work, although the complexity is less than undergraduate level. Even if you don’t understand it fully, off-the-shelf software for all the common programming languages will do the job for you, or you can ask ChatGPT to write it.

How Benter extracted inside information from the odds

Bill Benter knew the power of the conditional logit, but he realised there was one vital second step necessary before the whole thing would fly well enough to defeat betting markets.

Each of the factors that the conditional logit uses explains a proportion of the variance in the results of all races. But, when you first assemble a model and let it loose, it will not have the power to defeat the market because a component of the odds comes from inside information which you cannot beat with data. It turns out that, thanks to a clever trick, you can use inside information to your advantage without even knowing what it is.

Table 3 (below) shows Benter’s method in action. If you blend your model odds with the SP in just the right proportion, factors in the SP which are not in your model will be incorporated into a new improved probability estimate.


In Table 3, we are using 80% of the SP and 20% of the model odds, although this is just for demonstration purposes. The blended odds of this new ‘augmented model’ are a weighted average (technically, the geometric not arithmetic mean is correct because we are averaging ratios) of the two separate odds. On average, the blended odds will contain some factors not included in the model (such as inside information) and some factors which are not in the SP (such as your striding analysis or jockey ratings, for instance).

How well does Benter’s tweak – which comes from the idea of model aggregation in statistics – actually work? Judge for yourself. Table 4 (below) contains the results of the 67,992 British handicap races in our sample for the highest-rated horse by 1) the model, 2) the SP (i.e. the favourite) and 3) the augmented two-step model, blending the SP with the seemingly naive model derived from placings described above. This time, however, the weighting scheme is not the arbitrary 80% - 20% but the result of a back test.


Table 4 shows the effectiveness of Benter’s trick. The fundamental model in the first

Table 4 shows the effectiveness of Benter’s trick. The fundamental model in the first row loses money (5% at Betfair SP) because the model’s approach of using finishing positions is naive; the second row shows that 27.8% of SP favourites and joint favourites succeeded for a loss of 3% at Betfair SP; the third row shows the huge advantage of Benter’s two-step approach: with the recency bias towards horses with eye-catching form figures removed, Strike Rate (SR) goes up from 27.8% to 29.0%, Impact Value (IV) goes up from 2.36 to 2.45 and Return on Investment (ROI) approaches parity. (Remember, this is not the performance of the horse the augmented model thinks is the best value, only the one it thinks should be favourite.)

The data in Table 4 shows a profound truth to the modeller. Eye-catching form figures next to a horse’s name has to be a form of price anchoring! In other words, both punters with no private information and paid experts in the media are too heavily influenced by recency, especially when it is represented coarsely by 1s next to a horse’s name. When the influence of recent form is discounted from market odds – the weighting scheme here might be 90% SP and 10% the negative of model odds – horses with 1s next to their name have their prices pushed out and the augmented model’s ‘favourite’ does significantly better than the market choice.

Yet different settings and different fundamental models will produce different insights, each of which is informative about markets at that time and place. But the power of the betting market is profound at all times and needs a lot more respect than it is given in racing broadcasts. Nowadays, the smart racing expert should be a lot less interested in pushing their own subjective opinion and a lot more motivated by explaining market odds near the off time of a race. One brilliant judge is not going to defeat the aggregated opinion of smart thinking and inside information in a liquid market long term, but there is a lot to learn and pass on. 

Executive summary

Betting syndicates and advanced punters who rely on mathematical models have to be able to specify a probability distribution over the runners which is more accurate than the prices available to bet. This is achieved by comparing the factors about a horse with those of its opponents, weighting each factor according to its value.

The most fundamental way to do this at scale is via the conditional logit. Under different names – stochastic utility, multinomial regression – this technique has been used for decades, but smart thinkers like Bill Benter adapted it to absorb the ‘private information’ implicit in the prices of highly liquid yet inefficient markets such as those in Hong Kong at the end of the 1980s.

As you can see, even a naive model which systematically loses money can be useful when combined with pricing information. It informs a discounting scheme. As long as the fundamental model points consistently towards either profit or loss, it can be harnessed to increase accuracy.

The maths needed to beat the market is well established. And there are plenty of other techniques available to modern horse racing modellers too. While the Masters of Betting each have a distinct edge which you and I do not understand, their true genius is the long-term, systematic application of methodology at scale. For this, they truly deserve our awe.

Racing Post+ Ultimate subscribers can read our Masters of Betting series here:

Meet the former jockey who took $15m off Atlantic City - and is now one of the world's biggest racing punters

How a dodgy bank loan led to nearly 40 years as a pro punter - proving old-school methods still have their place

When science met punting: the godfather of modern-day betting and his golden rules that remain valid to this day 

'I was down £11,000 but you can't let that alter what you do' - meet one of the giants of on-course betting 

Poker genius, visionary football chairman and pioneering data-led punter - the many (profitable) faces of Tony Bloom


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Published on 19 January 2026
inMasters of Betting

Last updated 12:29, 19 January 2026

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He would empty the Emirates Stadium when Arsenal were at home

Where's Mr Campbell when you need him?

Thank you Saxon and UTI, you are both very kind. Sad when one can't afford the RP's charges.

I did a deal with the RP,loper.

I have read Brother Willoughby's tablets of stone.

I assume he has had every betting avenue closed to him because he now has the game by the short and curlies.

Has he thought of offering his perfected system to the proletariat? I would be very keen to subscribe.

Where do I join?

He has lost every angle he thought that he developed,loper.
Without Willo we could never have Layed Gladitorious at Evens at Royal Ascot.
Please bring him back