In 2014 Pinnacle tested the Wisdom of the Crowd hypothesis by inviting people to guess the number of chocolate balls in a video. By the end of the test, the average guess was just 1.4% higher than the actual figure, despite only 1 person out of the 608 entries guessing correctly.
[Although] the results of sporting events cannot be known a priori, yet even under these conditions the crowd does generally provide an accurate assessment of the respective probabilities of the outcomes.
Of course, sporting outcomes are binary by nature: they either happen or they don’t. However, it is the flow of money via which the opinions of bettors are expressed that is used by bookmakers to judge the respective outcome probabilities, by means of the odds. It is true that herds are prone to expressing systematic biased judgement when faced with uncertainty, leading to a collectively less wise opinion.
However, typically we find that the more liquid (or popular) the betting market, the better the collective wisdom. The greater the number of independently acting players expressing a range of diverse views about a sporting event there are, the more likely it is that a crowd will be wise and the betting odds accurate.
The wisdom of Pinnacle bettors
I have previously examined just how accurate Pinnacle’s 1X2 soccer match betting odds are, and by extension how wise their market is, by means of comparing expected outcome probabilities (defined by the odds) to actual outcome percentages. This analysis demonstrated that Pinnacle’s betting odds, on average, are highly efficient – that is to say, accurate.
The greater the number of independently acting players expressing a range of diverse views about a sporting event there are, the more likely it is that a crowd will be wise and the betting odds accurate.
For example, teams fairly priced at 2.00 (i.e. once Pinnacle’s margin has been removed) typically win about 50% of the time. Teams priced at 4.00 win 25% of the time, and so on. Whilst such an observation is not conclusive proof of market efficiency, it is consistent with it.
Of course, not all bookmakers offer the same price for a team. For example, Pinnacle offered a price of 2.22 for Liverpool to beat Tottenham in their game played 11th February 2017. This varied between 2.15 and 2.33 with other bookmakers. How do we know which price was more accurate?
Testing Pinnacle’s wisdom against other bookmakers
One way we could test relative price efficiency of Pinnacle versus other bookmakers is to formulate the following hypothesis and accompanying test:
1) Assume Pinnacle’s odds (with their margin removed) provide an exact measure of the true outcome probabilities.
2) Consequently, the ratio of another bookmaker’s odds to Pinnacle’s odds provides a measure of expected value or expected return.
3) Analyse actual returns across a range of expected values.
For example, with the margin removed, Pinnacle’s estimated fair price for Liverpool to beat Tottenham was about 2.25, implying roughly a 44% outcome probability. Consequently, if our hypothesis is correct, the best market price of 2.33 would offer an expected return of about 1.035 or profit of +3.5% (2.33/2.25).
On the other hand, betting at the market low of 2.15 would entail an expected return of 0.956 or loss of -4.4% (2.15/2.25). If we then find that all bets with an expected profit of +3.5% (or loss of -4.4%) collectively return a profit of 3.5% (or loss of 4.4%), we would conclude that our hypothesis is correct, that is to say Pinnacle’s odds, on average, are efficient, accurate or wise.
So, how wise is Pinnacle’s soccer match betting markets? I’ve analysed a sample of 35,570 league matches played throughout Europe since the start of the 2012/13 season, yielding 106,710 possible outcomes from the home/draw/away market.
For each, the expected value (or return) is calculated by the ratio of the odds from one of four leading bookmakers to that of Pinnacle’s price with their margin removed, yielding 426,840 expected returns. Actual returns are then calculated for 0.01 intervals in expected return (for example 0.98, 0.99, 1.00, 1.01 etc) before a 5-point running average is used to smooth the variance in the data. Data is plotted in a scatter graph below, with very low and very high-expected returns removed for which there are understandably far fewer contributing data points.
The correlation between expected and observed returns is very strong and essentially 1:1. That is to say, when the expected return over a sample of matches is 90%, we actually return about 90% (or a loss of 10%). When the expected return is 105%, we actually return about 105% (or a profit of 5%)
Market folly or manipulation
Let’s now reverse the process. This time, let’s assume that our other bookmakers’ odds (with their margins removed) provide an accurate measure of true outcome probabilities. How do actual returns, this time betting Pinnacle’s odds, compare to those expected by the hypothesis? Take a look.
Now, correlation between expected and actual returns is completely absent. If a fair price is 2.00, whether Pinnacle offers 1.8 or 2.1 makes no difference: we lose about 2% regardless (which is roughly the size of Pinnacle’s soccer match betting market margin). The implication is that the odds from the four other bookmakers used in this analysis do not, on average, provide any meaningful measure of the true outcome probabilities relative to Pinnacle’s. It’s Pinnacle’s price, which provides the accurate measure.
What pricing model does your bookmaker use?
Presumably, there are two possible explanations for such a finding. Perhaps other bookmakers don’t know how to set prices properly. Evidently, that is not a credible conclusion, given the longevity of success of these bookmakers. Alternatively, we could speculate that bookmakers are intentionally shifting prices away from market efficiency in favour of pursuing interests of their business models.
Pinnacle’s pricing model utilises crowd wisdom and accepts sharp players to tighten them. Other bookmakers from Europe and the UK prefer to encourage a steady flow of squares via promotional offers, a wider variety of low-liquidity markets and the regular availability of best market prices (if not the lowest margins). With respect to the last of those, a casual perusal of any odds comparison will reveal numerous matches where bookmakers are significantly out of line with Pinnacle’s market, and in the extreme offer loss-leading value to the player.
In my analysis sample, such positive expectation was available in 4.1% of the betting propositions. Naturally, this would account for why so many of these alternative brands, in contrast to Pinnacle, rely on account closures to mitigate the threat of players taking systematic advantage of these loss-leading prices either through value betting or arbitrage. It will also come as no surprise to learn that whilst Pinnacle openly accepts arbitrage players, other brands do not, and that typically the bookmaker on the negative expectation side of the arbitrage, from the perspective of the punter, is Pinnacle.
This is not to say Pinnacle’s betting market is perfectly efficient; just that inefficiencies are harder to find and exploit. However, those sharp enough to find them can do so safe in the knowledge that their custom will always be welcome. It helps, indeed, to build the wise betting market that sets Pinnacle apart from its competitors.