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Jul 20, 2016
Jul 20, 2016

# The maths behind Pinnacle’s “winners welcome” policy

Reports of bettors having their accounts closed or restricted to pennies by mainstream bookmakers is nothing new among profitable bettors. With Pinnacle claiming that winners are welcome, betting analyst, Joseph Buchdahl, puts our odds to the test to determine why Pinnacle not only accept winners, but also offers top-notch education to help bettors improve their performance. Read on to find out.

In the article The importance of evaluating your performance against the closing line, Dafni Serdari explained the efficient market hypothesis, according to which the odds at the moment of market closure tend to be a more accurate interpretation of the possible results.

When mistakes, or inefficiencies, in the odds are spotted, bettors will exploit them by betting, thus shifting the odds to a more efficient value. The more people bet, the more likely it is that all inefficiencies will be eliminated.

Closing odds reflect the largest amount of information about matches, and the maximum number of opinions being expressed through wagering on that information, and hence are most likely to be the most efficient.

In this article, I analyse past data to determine just how efficient Pinnacle’s closing markets are compared to the opening ones and what that means for profitable bettors.

#### Opening vs. Closing odds

One way to look for differences in market efficiency between the opening and closing odds is by means of a metric from information theory called Shannon Entropy. Named after its inventor, Claude Shannon, the father of information theory, his entropy metric measures the uncertainty associated with a random variable. The more uncertainty, the greater the entropy. The entropy, H, of a random variable X is expressed by means of the following equation:

where p is the probability of outcome i, and b is the base of the logarithm, which is typically 2. Essentially it is the negative sum of the products of all possible outcome probabilities and their logarithms.

For example, if the fair odds of Manchester United versus Liverpool were 2.00 (home), 3.50 (draw) and 4.67 (away), the entropy, H, would be given by:

– [(1/2.00)log2(1/2.00) + (1/3.50)log2(1/3.50) + (1/4.67)log2(1/4.67)] = 1.492

From a database of 132,645 global football matches stretching back to 2007, I have calculated the average entropy per match for both opening and closing Pinnacle.com betting odds for the home-draw-away betting market, with the betting margin removed.

Respectively, these are 1.457 and 1.452; hardly any difference at all. Is the idea that bettors can provide meaningful information to the market just an illusion? Could be. To find out more about the illusion of control in betting, go to Guarding against the dangers of superstition.  But what about betting odds and real results?

#### Betting odds vs. Winning results

A better way to assess the efficiency of a betting market is through the comparison of betting odds and real results. Betting odds represent probabilities of expected outcome. Results, of course, are binary – either a bet wins or it doesn’t.

Nevertheless, increase the sample size and we can study how real results compare the predictions made by the odds. For example, if 50 out of 100 teams priced at 2.00, or 25 out of 100 teams priced at 4.00, prove to be winners, this would imply those odds were 100% efficient.

Using the same soccer match dataset as above, expected outcome probabilities (i.e. odds) have been compared to observed outcome frequencies, (i.e. results), and shown in the scatter plot below. Again, Pinnacle’s margin has been removed to make the odds ‘fair’.

Two things become immediately apparent. Firstly, Pinnacle’s soccer betting odds appear to be highly efficient. In statistical terms, almost all of the variability in the observed outcome probabilities is explained by the variability in the expected probabilities.

When mistakes, or inefficiencies, in the odds are spotted, bettors exploit them by betting, thus shifting the odds to a more efficient value.

Secondly, there again seems to be little discernible difference between opening and closing odds. Indeed, the value of R-squared, a measure of the strength of the association between implied and observed probabilities is 0.996 for opening odds and 0.997 for closing odds. (R-square of 1 implies perfect correlation.)

#### Betting value in significant odds movement

Assuming that closing odds are efficient, we could investigate whether betting value existed in the opening odds where those odds were significantly longer. For example, suppose Manchester United opened at 2.50 and shortened to 2.00 by market closure.

Assuming that the closing odds were efficient, this would imply a theoretical profit expectation of 2.50/2.00 or 1.25 (25%). Such a hypothesis yields a prediction: the ratio of opening odds to closing odds should correlate strongly with observed betting yields (i.e. profits) from backing the opening odds.

For an opening/closing ratio of 1.1, we would expect to see yields of 10%; for a ratio of 1.2, 20% and so on. Again, taking the same soccer odds dataset (with Pinnacle’s margin removed), the opening/closing odds ratio for all home-draw-away outcomes (397,935 of them) has been calculated. These have then been grouped with a resolution of 1% and plotted against actual returns from betting the opening odds in the next scatter plot.

The correlation between the excepted betting yield (i..e profits) as predicted by the opening/closing odds ratio is strong and linear with the observed betting yields from opening prices, supporting the idea that closing odds must be close to the true probabilities of outcomes. We can further confirm this finding by plotting the same data to closing odds.

This time there is predictably almost no correlation. Regardless of where the opening odds started, by the time the Pinnacle market closes, there is very little scope for finding an advantage.

#### Why Pinnacle wants profitable players

This analysis of a large data set has confirmed that Pinnacle’s soccer odds are highly efficient.  It has also showed that whilst Pinnacle’s traders are pretty adept at estimating true probabilities, the size of any mistakes that they make, and by extension the advantage a bettor can achieve by spotting them, can be measured by comparing the opening and closing prices.

Most bookmakers limit and close accounts of well-informed bettors. Pinnacle uses them to create an efficient market absent of bookmaker interference.

Of course, the challenge for bettors comes in trying to figure out which odds are going to shorten sufficiently to secure a profitable advantage. Fortunately for Pinnacle customers, winners capable of such a task can do this safe in the knowledge that they will not be punished for knowing more than the traders.

While most bookmakers limit and close accounts of customers who are capable of moving prices, Pinnacle prefers to use them to create an efficient market absent of bookmaker interference. Instead of attracting and then penalising customers for betting inefficient outliers, Pinnacle rewards its winners with the best prices, highest limits and a guarantee that making a profit through skilled forecasting will not result in their custom being refused. It is precisely the efficiency of the Pinnacle odds that allows this to happen.

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