Introduction

The placing of restrictions on winning punters by bookmakers isn’t a new phenomenon. With bookmakers acting as principal in taking bets from punters, and thus exposed to potential losses by taking bets at fixed odds, it isn’t surprising that bookmakers take steps to limit such losses, either by placing limits on the amounts wagered or closing the accounts of those punters perceived to be consistently profitable.

What has changed in recent years is the proportion of bets placed on-line and the introduction of betting exchanges. On-line betting enables restrictions on punters to be placed more easily, whilst exchanges i) enable punters to arbitrage bookmaker odds, ii) give bookmakers market information that in previous times would have been gleaned by taking bets from informed punters, iii) provide competition and margin pressure for bookmakers and iv) decrease bookmaker flexibility in being able to take trading positions for or against horses because of the risk of arbitrage via the exchanges.

In the light of these changes to the market place it would be surprising if restrictions were not more prevalent than in the past, although bookmakers do argue that a relatively small proportion of punters are restricted and those that complain are ‘a vocal minority’ (Coral representative Simon Clare speaking on The Morning Line, 22^nd March 2014). Since information about restrictions isn’t published by bookmakers, the true extent of restrictions placed is unknown. As the plural of anecdote is not data, the fact that the majority of people I know that bet on horses are restricted in some way by bookmakers is hard to use in an argument, so I will leave that for social media commentators and first look at bookmaker restrictions in the context of different types of punter.

Punter Categories

Arbitrageurs/Anomaly Players

If bookmaker prices are out of line with exchange prices these players will attempt to extract an arbitrage profit by laying their bets back via exchanges. The extent to which bets are laid back is not fully known, but it would be surprising if a significant proportion were not hedged. Pricewise in the Racing Post is the highest profile example of bookmakers placing restrictions on clients. Given Pricewise’s popularity it is hardly surprising restrictions are placed on those attempting to get on at advertised prices. In addition some bets can be placed that favour the punter over the bookmaker – commonly known as each-way thieving, including each-way doubles, and rule 4 deductions with odds-on horses withdrawn. It is difficult to have much sympathy with complaints about restrictions from arbitrageurs/anomaly players.

SP Predictors

Bets are placed at fixed odds with the expectation that SP will be shorter. Arbitrage isn’t possible at the time the bet is placed, this is about identifying mispricing in odds setting. Given the time and effort put into making tissues by the bookmaking firms, and the information available in exchange prices, consistently being able to beat SP without being privy to inside information requires skill, time and effort, and, in my view, is a rare commodity, and the population of SP predictors is overly represented by those with access to inside information.

The placing of restrictions on SP predictors by bookmakers is therefore a defensive reaction to the risks of being on the wrong side of inside information. There is a negative consequence to this, in that it is likely that these restrictions, erring on the side of caution, could well catch more punters than those with access to information, including punters with no skill, and thus reduce overall bookmaker profitability. The consequence of this is that racing, partly funded by bookmaker profits through the Levy, receives a lower level of funding than would otherwise be the case. So why would bookmakers, in business to make money, have a policy in place that acted to reduce their overall profitability? The answer lies in considering risk aversion. Does a bookmaker wish to make an almost certain profit of £100m, or have a 95% chance of making a profit of £105m and a 5% chance of making a profit of £90m? The probability weighted return from the latter scenario is £104.25m, yet the consequences of posting a £90m profit for the employees of the business would be severe. It is not difficult to imagine policies being put in place at bookmakers that meant the probability of making an almost certain £100m were maximised.

So is it possible to put policies in place that will reduce the 5% chance in the example above to a lower percentage, and as a consequence reduce the extent to which bookmakers felt the need to place restrictions on SP predictors? In my view this is about integrity. Quoting from the BHA’s website on Integrity Services: One of the key responsibilities for Racing’s regulator is to protect the integrity of the sport on and off the racecourse. Millions of pounds are bet each year on British racing, and for the sport to flourish and for racegoers and punters to be attracted to the sport, racing has to be, and seen to be, clean and fair.

In my view the integrity in British racing would be improved if the BHA’s Integrity Services group were charged with the collection and timely dissemination of the following information: spell/gallop records – it would be immediately obvious if a horse hadn’t had sight of the gallops for a while, or its preparation routine had changed so that it had undertaken an increase in work; horse weights – enabling changes and progression over the season to be tracked; veterinary records – wind operations, setbacks, treatments and the like would be known; jockey riding instructions –so that intentions, and changes in intention relative to usual instructions were known. Note that in many racing jurisdictions some or all of this information is already available to the public.

The consequence of publishing this information is that bookmakers would have more confidence in making prices in the face of reduced information asymmetry. They would be less exposed to the risks of insiders taking advantage of overly generous prices to those in the know. The need to place less reliance on betting restrictions as a source of risk control follows. In the recent Barney Curley inspired betting coup, it is difficult to imagine the horses involved receiving the same preparation as they had received for previous races, and publication of the above information would likely have highlighted this.

SP Players

The final category of punter is those that are successful betting at SP. This category is likely to still include insiders, however I’d expect them to form a lower proportion than the SP predictors group. At first sight it would seem obvious that restricting winning punters would increase bookmaker profits. Higher bookmaker profits mean a higher Levy, ergo restricting winning punters is good for racing. However the tricky bit here is the identification of winning punters. The returns from betting on horses are inherently noisy since the processes involved are probabilistic, not deterministic. So a good restrictions policy must be able to separate winning punters from those that have no skill and were simply in receipt of a lucky run. Why is this? Because the no skill punter is the bookmakers (and skilled punters) friend, likely in the future to contribute to the bookmakers (and skilled punters) profits. Restricting him at the top of a winning run is bad for business and bad for racing. So how easy is it to identify winning punters? In the absence of information about the algorithms used by bookmakers, an experiment is described below in which bookmaker restrictions were modelled.

Modelling Bookmaker Restrictions

No Skilled Players Model

A sequence of 250 ten runner races was set up with 50,000 individuals betting on the outcome of each race. Bets were placed by punters in proportion to fixed bookmaker odds (3/1, 4/1, 5/1, 11/2, 9/1, 14/1, 16/1, 25/1, 33/1, 40/1), with the odds for each race kept constant. The result for each race and the selection of each punter in each race was made randomly, with the race result probability in proportion to odds. This is a stylised representation of betting over the course of a year across the country. No punters were assumed to possess skill. Because of the over-round the majority of punters lost money by the end of the 250 race sequence. I make the assumption that bookmakers believe certain punters possess skill, and wish to restrict them from betting. We know this isn’t the case, with chance the only driver of returns. Since the only information the bookmakers can use is historic returns, an algorithm is set up that identifies so-called skilled punters who have, over the preceding 20 races, at least 1 successful bet in 3 and have a return of at least 75% on stakes over those 20 races. I have no knowledge of the actual algorithms used to restrict punters, but have chosen values with the knowledge that statistical tests of significance increase in power as i) the number of observations increases, ii) the size of the difference away from the null is increased and iii) the volatility of the effect is reduced. The algorithm described meets all three criteria, albeit with an arbitrary choice of values. The experiment described above is adjusted so that from race 20 onwards if a punter meets the restriction algorithm he is restricted from placing any further bets in subsequent races. At the end of the 250 races 7.2% of punters were restricted. This proportion is consistent with what we’re told about restrictions being applied to a minority of punters, vocal or otherwise. Table 1 below shows the effect on total stakes, punters and bookmaker profitability with the unrestricted case based as 100.

No Skilled Players Model            Unrestricted                       Restricted

Stakes                                                               100                                              94.2

Bookmaker Profit                                        100                                              92.3

Punters                                                            100                                              92.8

Winning Punters (%)                                32.4%                                            35.1%

Table 1: No Skilled Players Model summary statistics

The information in Table 1 shows the restriction algorithm generates a substantial number of false positives. As a result the overall number of players is reduced and bookmaker profits are reduced, leading to reduced funding for racing. Of course the experiment is designed to generate this exact false positive result. However it does enable comparison with a model in which some proportion of players are skilled. This is covered in the next section.

Skilled Players Model

What happens if a proportion of players are introduced that have skill? How many skilled punters does the algorithm detect, and what is the effect on overall bookmaker profitability now that skilled punters are part of the model?  Skilled players are assumed to have an edge of 7% (that is the probability of their picks being successful is increased by this amount) and comprise 10% of the overall universe of punters. Table 2 below contains the results.

Skilled Players Model             Unrestricted                            Restricted

Stakes                                                            100                                                       94.0

Bookmaker Profit                                    100                                                        92.0

Punters                                                        100                                                        92.5

Winning Punters (%)                           34.0%                                                     36.7%

Skilled Punters detected                    10.4%                                                   10.4%

Table 2: Skilled Players Model summary statistics

At the end of the 250 races 7.5% of punters were restricted. Only 10.4% of the skilled punters were detected, and the number of false positives identified is significant. The similarity between tables 1 and 2 is striking. The algorithm does a poor job of identifying skilled players. No doubt the algorithm outlined above is too simplistic, and the risk managers working for bookmakers will have designed sophisticated algorithms that are able to separate skilled players from the rest more successfully than the one suggested here. The body of literature surrounding the identification of signal (skilled punters) in the presence of noise (no skill punters) is substantial, and I’m sure this literature has been mined extensively by bookmakers in the pursuit of the best algorithms. However the data sets are noisy due to the nature of punting returns, and no matter how sophisticated the algorithms, the data sets themselves will set a limit on the ability to identify skilled punters. A natural reaction, particularly for those in charge of risk models, would be to err on the side of caution, which has the consequence of increasing the proportion of false positives, and restricting too many punters. Whilst it would seem irrational to act in a manner that reduces profitability, when risk considerations are taken into account for those in charge of risk models, the placing of restrictions on too many, rather than too few punters is a significant possibility. This has negative implications for the funding of British racing.

No Skill and Skilled Players Models Compared

A comparison of the No Skill and Skilled Player Models above demonstrate the difficulty in identifying skilled punters. Poorly defined account restriction models have the potential to harm British racing by placing restrictions on too many punters, leading to lower levels of funding for British racing than would otherwise be the case. In the experiments above, the restriction algorithm leads to a slow steady decline in the number of punters in the simulation. Is it a co-incidence many within British racing point to a slow steady decline in betting on British racing? Is it possible that account restrictions are a contributory factor?

In an earlier section I proposed that the BHA’s Integrity Services team take responsibility for the collection and dissemination of additional information that would benefit bookmakers in price setting. I further propose this team is given oversight of the account restriction algorithms used by bookmakers to restrict punters. Bookmakers would be expected to demonstrate the algorithms used minimised false positive detection rates. This additional responsibility would dovetail with the existing relationship that exists between the BHA and bookmakers, with the BHA writing on its website as follows: In recent years we have established a good working relationship with all of the established bookmakers and their umbrella association (Association of British Bookmakers). The betting industry, like the BHA, wants racing to be clean and willingly share information whenever they see suspicious betting activity.

Summary

Account restrictions are considered in terms of the types of bet placed. In the case of arbitrage and anomaly bets the placing of account restrictions seem a perfectly reasonable response on the part of bookmakers acting to protect their business. It would be difficult to argue restrictions placed upon this type of punter harms British racing. For account restrictions put in place to try and identify SP predictors (in my judgement comprising principally insiders) these restrictions are a direct consequence of the paucity of information supplied to punters. These restrictions are likely to harm the funding of British racing, but the culprit is the lack of information rather than the rational response of bookmakers desirous of minimising their exposure to a source of downside risk. An increase in the amount of information provided to punters as part of the BHA Integrity Services team is proposed, as well as being given oversight of the account restriction algorithms used by bookmakers, who will be expected to demonstrate they minimise false positive detection rates due to the risk of incorrectly specified algorithms resulting in a lower level of funding for British racing than would otherwise be the case.

Introduction

Tune in to Racing UK or ATR and the chances are the focus will be on picking the winner of the next race. The Racing Post has pages of form and commentary distilled into selections, naps and tips, typically resulting in one selection per race being made. Tipsters tables contain one selection per race,  Tom Segal’s Pricewise column in the Racing Post usually recommends one and occasionally two selections in a handful of Saturday races. For any gambler the key measure of success is the amount of money made or lost over a reasonable time period, and implicit in the various pieces of advice on offer is that one selection per race is the way to achieve gambling success. It seems obvious – there can only be one winner, I just need to find it! One of the consequences of making one selection per race is that you are maximising the chances of sustaining a long losing run. The volatility of your profits/losses are also maximised, as is the path dependency of your trading strategy. None of these are attractive characteristics.  Apart from the effect on your bank balance, losing runs can lead to self-doubt as methodology and existence of a trading edge are questioned, yet the length of the losing run  may be just noise, in line with what you might expect given the size of your trading edge. So what sort of losing runs might you expect given different degrees of edge over the market?  In this blog post Monte Carlo Simulation (MC) is used to compare losing runs given different degrees of trading edge and at different odds.

Methodology

A ten runner race is set up with a set of book odds where the book sums to a 7% over-round. A rating is attached to each horse, and the true odds of each horse winning is defined to be a function of the book odds and its rating. The function works so that highly rated horses have lower true odds than the book odds and vice versa for lowly rated horses. One of the parameters in the function is the degree to which the ratings have an edge over the market. The greater the edge the more the book odds are adjusted. The approach is Bayesian in nature.  The ratings used are arbitrary – they express in numerical form the the likelihood of a particular horse winning – the results presented here are not specific to the use of rating systems. Implicit in any bet placed by a gambler in a probabilistic setting is a set of underlying decisions based upon preferences or rankings that can be thought of as a set of ratings, even if they aren’t expressed as such.

Monte Carlo methods are used to run the race 30,000 times (defined as one simulation, this is equivalent to betting on 15 races a week for 40 years) using the true odds, as defined earlier, to determine the probability of each horse winning. If the winner coincides with the horse that is also top rated, the gambler wins. The book odds associated with the top rated selection and the level of edge are kept constant per simulation run. The process is repeated so that simulations are run at 4 different book odds and 4 levels of edge, to give 16 simulations in total. The book odds chosen are evens, 3/1, 6/1 and 9/1 and the levels of edge chosen to correspond to differing levels of Return on Capital (RoC) of 10%, 5% , 0% (break-even) and -7%.  The latter case represents someone with no edge whose losses over time equal the book over-round.

Relationship Between Edge,  Book Odds and True Odds

Table 1 below gives the relationship between the odds at which you back and the true odds for given levels of edge. So backing at 6/1 with a 10% edge represents true odds of 5.3/1. At a 5% edge backing a 3/1 shot represents true odds of 2.8/1, and backing an even money shot with a 10% edge has true odds of 4/5. The difference between book and true odds is small and sets the context for the analysis that follows. Whilst not the subject of this blog post, tables such as this can be used to give trigger levels at which bets become interesting for a given level of perceived trading edge.

Table 1: Book odds and true odds for differing levels of edge

Relationship Between Edge, Book Odds and Losing Run Length

Table 2 below gives the maximum losing run that from each simulation. The longest losing run experienced from betting at constant odds of evens with a 10% edge was 14 races, at 9/1 with a 10% edge 80 races. The reason it is often a long wait between drinks for top rated selections is the size of the trading edge compared with the odds at which horses are backed. Since the number in Table 2 represent the extreme case of the simulation, the length of losing run that occurs 5% of the time  is reported in Table 3.  Note how the length of losing run changes little with edge. If you typically bet at 6/1 and think you have a 5% edge, and you are on your 17th losing wager, there are no obvious signs from Tables 2 and 3 that you are experiencing anything other than a losing run that occurs one time in twenty. If Pricewise has a 10% edge and gives 3 selections a week all at 9/1, these results suggest that at worst  he could go half a year without a selecting a winner. Note that in practice gamblers will be betting wherever value is perceived regardless of book odds, and the fixing of odds across all simulations is artificial. However it would be straightforward to weight the results to reflect the proportion of bets you typically placed at various odds.

In finance one criteria used to judge the quality of returns delivered by investment managers is the Sharpe Ratio. This penalises returns by the volatility of the return stream. Inspection of table 3 shows that the highest Sharpe Ratio would come from betting even money shots. To emphasise, there is no suggestion that betting even money represents greater value than betting at bigger odds. The simulations are set up so the Return on Capital achieved are the same, and the value inherent in the even money shot is the same as in the 6/1 shot. However the path to terminal wealth followed by betting at evens is inherently less volatile than betting at bigger odds.

Table 2: Book odds and maximum losing runs  for differing levels of edge

Table 3: Book odds and 95% probability losing runs

Relationship Between Edge, Book Odds and Time to Last Cumulative Loss

The results presented so far are unaffected by staking plans. In Table 4 below the number given represents the last race in the simulation at which cumulative profits are negative. This gives a sense of the number of races for the signal inherent in the edge to outweigh the noise. For level stakes betting at 6/1 with a 10% edge , profitability is always positive from the 2,324th race. Note the substantial step up in the wait for cumulative profitability when betting at 6/1 compared with 9/1 at the 5% edge level, and when betting at 3/1 compared with 6/1 at the 10% edge level.  The results highlight the increased path dependency inherent in betting at higher odds. The range of possible outcomes is such that it can take much longer to move into positive cumulative profitability.

Note that employing staking plans such as The Kelly Criterion would potentially improve this level staking result so that the month numbers were lower, particularly for the higher odds results presented, however since the cumulative profits/losses will have meandered around zero the effect on the broad thrust of the conclusion reached is likely to be small.

Table 4: Book odds and number of races and last breake-ven race

Conclusions

If you choose to bet on the horse that represents your top pick in a race, and you adopt this as a betting approach over many races, you are maximising the total profits you can expect to accrue over time. However this approach has costs associated with it. Whilst maximising expected total profits, you are also maximising both the volatility of your trading profits and exposure to path dependency.

Losing run length is primarily driven by the odds at which you back horses. It is difficult to identify that you have lost your edge in the middle of a losing run because losing run length is primarily driven by the odds at which you bet rather than the size of your betting edge. What may appear to be a loss of ability could merely be an unlucky run that is merely noise.  The reason it is often a long wait between drinks for top rated selections is the size of the trading edge compared with the odds at which horses are backed.

Betting at shorter prices minimises trading profit volatility, path dependency and reduces losing run length. Splitting your stake across more than one selection in a race will (subject to your edge being similar across all runners in a race) increase the probability that your edge will be reflected in your trading profits. These profits will not be as large as if you had made one winning selection, however what you make will be made far more often.  Betting on a number of horses in a race effectively creates one shorter priced aggregate bet. This has a number of attractive features – it reduces losing run length, reduces trading profit volatility and reduces exposure to path dependency. The cost of this approach is that over the long run total profits will be less than betting on one selection only. The trade-off between the two approaches is interesting. Given the associated drawbacks, it is surprising the one selection per race approach appears to be so little questioned and so popular.