The wisdom of crowds

‘Money Without Work’ 2: Wisdom of Crowds

Part 1 of this series can be found here.

I have deliberately kept mathematical 'proof' and academic rigour of the theories of Wisdom Of Crowds and the related Efficient Market Hypothesis out of this article, writes Russell Clarke. Those who are interested can easily research further their efficacy online. For what it's worth, I believe both theories have limited real world applications, though their usefulness in sporting prediction markets is undeniable.

A brief definition of the Wisdom of the Crowd is that large groups of people are collectively smarter than individual experts at predicting outcomes. Explanations of the wisdom of the crowd are numerous but the Diversity Prediction Theorum attempts to mathematically quantify via the definition, “the squared error of the collective prediction equals the average squared error minus the prediction diversity”.

In layman’s terms, when group of predictors is large and diverse, the error is small. There are more complex layers to add to the wisdom of the crowd theories and explanations involving independence, bootstrapping and other exotically named theories, but for our purposes, we will omit the bells and whistles of academia. This is simply about, to misquote Jeremy Corbyn, “why the many are smarter than the few”. It is especially true when the crowd is diverse and independent, which is very much the situation in betting markets.

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It has been demonstrated in numerous studies that the crowd is particularly accurate in the fields of quantity estimate, general world knowledge and spatial reasoning. If we look at quantity estimate, I saw a programme on this subject where office workers were asked to guess the number of sweets in a large jar. The estimates had a huge range and yet the average was just 4 sweets from being correct! More famously, at a 1906 Plymouth Fair, 800 people were asked to guess the weight of an ox and the average was within 1% of the actual weight. I know, I need to get out more…

Related to Wisdom Of Crowds is the Efficient Market Hypothesis. The EMH in its simplest form suggests that asset prices reflect all available information (and thus, by association, it is impossible to beat the market). The latter conclusion is a stretch of the theory, particularly in sports betting.

So, what are the implications of this theory when we look at, for example, horse racing? I have evidence that in recent times a real sea-change has occurred in the racing markets and this has been caused by the increasing wisdom of the crowd. It has gone largely unnoticed as it has been gradual and marginal. However, it has been incremental and, as a result, the marketplace today is very different from that of even a few years ago.

Let me rewind to a time when starting prices were produced by the on-course betting market. A few “good men and true” would form a huddle at the 'off' of each race and compare the prices they saw offered by the bookmakers. They came to an agreement or average and that was declared as the starting price. This SP was basically the result of supply and demand in the on-course marketplace (racecourse punters and the major bookmaking offices who sent cash to the course to reduce the prices of horses that they had large liabilities on). This method was later replaced by a similar method, but one which included more on-course bookmakers.

However, the methodology is not of major importance. The SP’s were still, in theory, a result of supply and demand mechanics within the racecourse crowd. The rise and rise of betting exchanges and, crucially, their use by virtually every racecourse bookmaker means that is no longer the case. Today, the SP’s are a reflection of the betting activity on the exchanges rather than the activity on a racecourse. Suddenly, the crowd is no longer a few hundred punters on a racecourse, it is tens of thousands on an exchange. The new crowd is better informed, more diverse and greater in number. The wisdom of the crowd has increased.

If we accept the aforementioned theories at face value, the best approximation of the chance of an outcome would, in horse racing, be the Betfair Starting Price (BSP) and, in football, the Asian Handicap closing lines. That is because those markets are the largest, deepest and smartest markets for those individual sports. The participants in those marketplaces are diverse, independent and largely devoid of any 'group think'.

In both of these markets there is virtually no margin to account for and so the final prices (once every participant has eventually 'voted') can be readily converted into a percentage chance of that outcome actually happening. A BSP of 2.0 represents a 50% chance, 3.0 represents a 33% chance, 5.0 represents a 20% chance etc. Similarly, Asian Handicap Lines can be converted into % chances for football betting. Numerous empirical studies have shown both to be almost wholly accurate.

I realise I have ‘banged on’ a bit here, but, the importance of this knowledge cannot be overstated. It demonstrates the futility of trying to beat the market when it is at its most accurate. In plain English, it is arrogant in the extreme to believe you know more than the market at the closing and you will eventually find out that it pays to be humble! If you bet at BSP (Betfair Starting Price), the commission is likely to ensure you are a long-term loser (although it is a more favourable strategy than betting with bookmakers at SP with their much higher margins than the exchange commission). If you accept that logic, then it is clear that you should be betting early, when the market has less participants and is therefore less accurate.

Another use for the EMH is if you want to accurately assess systems, strategies or the records of tipsters/experts. It is a quicker and faster way to assess than simply looking at a profit/loss account, which can be wildly erroneous. So, traditionally, even those that do their research, will look at a series of results and concentrate on factors such as profit/loss, strike-rate, longest losing run, taken from a set of past results. On the surface this seems logical and sensible. However, the downside is that you will almost certainly be dealing with an inadequate sample size (again, if you need the maths, then an online check) and even if you have thousands of results, a simple Monte Carlo simulation will demonstrate the huge variance in results you could experience moving forward (more of which anon).

Using our appreciation of the accuracy of the markets, we can gain a quicker and more accurate guide to how a strategy will perform in the future and in the longer-term. We can ignore profit/loss figures and instead concentrate on how the selections (winners and losers) perform against the market. There are a few criteria you could apply but a very simple method is demonstrated below:

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Two figures you require are the price at which the selection is advised (or a morning price) and the eventual BSP. Then it becomes a simple comparison. If a horse is advised at 10/1 (11.0 digital odds) and the bsp is 7.0, then that would be assessed as +4 (11-7). Similarly, a horse advised at 8/1 (9.0) and the bsp is 9.0 would be assessed as 0 (9-9) and a horse advised at 12/1 (13.0) that has an eventual bsp of 18.0 would be -5 (13-18).

After as few as fifty bets you would get a good reading of the number of selections that are positive as opposed to negative, and, the running total would give an indication of the magnitude of the long-term profits/losses that are likely. The actual results and profits/loss are largely irrelevant as they may just reflect either a favourable or unfavourable run of winners/losers. You can be sure, however, that if you continue to beat the "closing line” you have unearthed a source of long-term profit.

- RC

Next week: Part 3: Bookmakers - Sharps and Softs

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14 replies
  1. Janves
    Janves says:

    Hello Russell,

    thank you very much for your good post.

    I do have a few thoughts/questions about this topic.
    I am familiar with Wisdom of the crowd and completely agree with you, it is something you cannot ignore and it is also one of the reasons why looking for a golden goose in terms of everlasting betting system is impossible as market will always, after time, adjust to it and correct itself.
    You mentioned betting at early prices is more favourable for obvious reasons, as if you’re right, you got on the value train. One thing, in my eyes, and here I would like to hear your opinion, is betting in the markets, where the amount of money involved is smaller, can give you slight advantage (or lesser disadvantage) against the crowd. For example Tuesday evening AW racing will see most of the money involved in the last 5-10 minutes before the off unlike any race on the festival meeting, where there is money right from the opening.
    I have read a loads on this topic but one post by a tennis tipster called Nishikori is very interesting. He has over 3000 tips on Pickio with a ROI of 9% betting only on ATP/WTA which is imo very good. He made a research to his numbers and find out, betting at Pinnacle closing line would have still shown almost 6% yield, which, based on the theory of the Wisdom of the crowd should not be possible. Over these 3000 bets, was he lucky (mathematically practically 0% chance) and his Pinnacle closing line will regress to the mean in the future or is this because he is good at picking the bets, where the market does not have it right and over time he is adjusting his data he chooses his picks so he he is still one step ahead (eg he does develop his systems and improving them over time instead of just using the same one for a whole time)?

    Thank you Russell

    • Russell
      Russell says:

      Hi Janves,

      Thanks for the comment and I will have a look at the link you sent.

      I am aware of Nishikori and I think he was challenged to a bet by somebody regarding the ROI on the next batch of bets (I can’t readily remember the number). I think Nishikori won the bet, albeit at a reduced ROI. He was then challenged again, but they couldn’t agree on the ROI level (I think around 4%). I believe an analysis of his bets did show that he made the vast majority of his profits on bets where he beat the closing line. I don’t know if his selection method is “fixed” or “evolving”.

      Regarding your point re size of markets….yes, the smaller the market, the less efficient it is likely to be.

      • davewood53
        davewood53 says:

        Thanks for your input on restrictions. I’ve only experienced a few as I’m not a high volume bettor and it intrigued me to be restricted by Betfair (not the exchange obviously) when they were the only losing account in my profile (and I don’t arb). They invited me to use the exchange instead but the commission would in general have compromised my Roi, which is always based on assessment of relative value of early price, though these, especially overnight, have become harder to come by -especially to any kind of decent wager on the exchange. What amused, if that’s the right word, was when I found PP had done the same. Then I wondered which was the dog and which the tail? I just closed the accounts.
        I’m no Mathematician but I will now deploy your comparative strategy regarding early prices and BSP to my bets as an additional column in my records. I’m intrigued as a guide to why certain angles I have used have seemed to run their course over time. Thanks; I find your anecdotal writing style refreshingly easy to follow and look forward to the follow-ups.

        • Russell
          Russell says:

          Hi Dave,

          Thanks for taking the time to comment.

          Regarding why “certain angles….seem to run their course over time”, the answer will either be that the market has started to account for the angle (in which case you would see reduced prices over time), or, the angle was perhaps ‘overfitted’ to the data and so the results were false and unlikely to be replicated in real time. The latter explanation is usually the more likely and a subject for another article entirely!

      • Janves
        Janves says:

        Thank you for your reply. Yes, I have read about the wager. In that article I posted the link to, he divided his bets by EV into four groups, which proved more you beat the BSP, more profitable seem the bets be. Following on that, it does seem that it is not as much important how often, but how much on average you beat the BSP

  2. Kevin Penney
    Kevin Penney says:

    I’m sorry Russell but this makes no sense as a general theorem if we accept that 97% of the crowd lose in the long run. There are many factors that determine the thinking of the crowd and it doesn’t necessarily amount to collective wisdom even when the market has settled. There are many systems and approaches that are profitable to BSP, although I do accept that where you have the time then yes, of course, get involved at early prices. The caveat is be prepared, if you have any pretensions to being a winner, to have your accounts restricted by the bookies. Unfortunately you can’t move that activity to the exchanges because at most meetings the liquidity is non existent the night before.

    • Janves
      Janves says:

      It makes perfect sense. That 97% majority are losers because of the bookies margin/exchange commission. If you discount for that, random picks would see you break even over time. You need to see the bigger picture. That BSP is on AVERAGE the best indicator of the probability, not on individual basis. That is a fact. And yes, there are many systems and approaches which are profitable at BSP, but these will almost certainly disappear over period of time as markets adjust (how long it will take depends on how obvious the angle is) while new angles will appear.
      If it was correct, bookies would only stake restrict or banned winners and that is not the case. You do not even have to be a winner to have your account restricted. Bookies will restrict your stakes or completely ban you just for regularly beating BSP even when losing. And my experience is that it takes them very little time.

    • Russell
      Russell says:

      Hi Kevin,

      Thanks for the comment.

      The efficiency of the market isn’t really a point of contention. The 97% of punters that lose, do so because of the market’s efficiency.

      You are quite correct about bookmaker restrictions!

  3. Martin Colwell
    Martin Colwell says:

    You can make money from betting but it is hard. You need to find value. I have done so via golf and horse racing and continue to do so. I have read Wisdom of the Crowds and so appreciate the theory. it does make sense as a concept, even when applied to betting.
    However i wonder how much betting markets in certain sports are controlled by bookmakers? They are able to control prices and dump money onto Betfair that does not provide value for punters. I appreciate the concept of volume driving prices up and down (the wisdom of crowds) in a market, but the drops in prices are more about bookmakers taking advantage of that fact rather than purely volume driven.
    In horse racing runners trained by John Gosden provide less value on average than those trained by Mick Appleby for instance, regardless of the class of race they are looking at. And that is not all down to the form of the horse but also that average Joe punter is drawn to Gosden and Dettori, rather than those less well known. So the bookmakers take advantage.

    Hence where value can be found by zagging when others zig.

    i did enjoy the article and the challenge it provides to the thinking of the punter and so thanks for that.

    • Matt Bisogno
      Matt Bisogno says:

      More on this in the next episode, Martin. It’s called Sharps and Softs, and looks at different types of bookmakers…

  4. richard firth
    richard firth says:

    How about against the crowd, Alan Potts, Why not just try to pick winners, I pick winners from odds on to 140-1
    Nobody pretends it’s easy but just form and instinct has stood me well and it’s much better fun, I will be using the profile stuff with draw and also paying attention to trainers debut horses added to my form study I cant wait .
    Are the people top of page two metre’s apart ?

    • Russell
      Russell says:

      Hi Richard,

      Thank you for the comments.

      Against The Crowd by Alan Potts is an excellent book and highlights that you need to find angles that are not taken into account by the crowd. As I’m sure Dave Renham will testify, the draw was one such angle a few years ago but the market adapted and prices fell. Dave now has to drill much deeper into draw statistics to find areas that the crowd have yet to identify. His use of these stats on Geegeez is excellent in doing this. It seems you have recognised this….

  5. Tony
    Tony says:

    Russel this is my Flat Hcaps model based on new data it hasn’t seen before 2017-2019 trained on data from 2012-2016
    This my network prediction vs the actual stk rate as you can see its fairly close but around the 20% and above I start getting an edge is this the area is the area I should be concentrating on? Any advice would be appreciated .Thanks Tony

    NN % Noq Now Act %
    3 2,208.00 103 4.66%
    4 4,944.00 231 4.67%
    5 3,382.00 189 5.59%
    6 3,388.00 202 5.96%
    7 3,842.00 268 6.98%
    8 3,907.00 272 6.96%
    9 4,254.00 344 8.09%
    10 4,208.00 403 9.58%
    11 4,236.00 396 9.35%
    12 4,058.00 410 10.10%
    13 3,704.00 433 11.69%
    14 3,252.00 402 12.36%
    15 2,917.00 388 13.30%
    16 4,341.00 649 14.95%
    17 1,521.00 260 17.09%
    18 1,251.00 238 19.02%
    19 944 214 22.67%
    20 770 162 21.04%
    21 591 133 22.50%
    22 478 135 28.24%
    23 385 89 23.12%
    24 287 61 21.25%
    25 227 70 30.84%
    26 159 55 34.59%
    27 119 43 36.13%
    28 121 42 34.71%
    29 75 28 37.33%
    32 145 40 27.59%
    34 80 31 38.75%
    36 55 24 43.64%
    38 27 14 51.85%
    40 20 10 50.00%
    45 32 15 46.88%
    50 11 6 54.55%
    55 9 4 44.44%

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