People often wonder how much success in betting depends on luck and how much depends on skill. Read on to find out how the closing line can be used to test your own betting skills.
One approach to assessing forecasting skills is to compare a player’s actual profit with what might have happened by chance. The downside to this approach is the time (or rather the number of bets) it can take before we can form more specific opinions.
The sports line of BC Pinnacle is the last available odds before the market closes and is often used as a measure of success for players. If the odds you are betting on are higher than the closing prices, then you are an experienced player.
A better can place, say, 2,500 bets before he can be confident that such a performance is probably not just luck. But if he makes five bets a day, it will take him over a year. Unfortunately, the range of possibilities due to randomness is large, and it takes a long time for the law of large numbers to take effect.
Fortunately, there is an alternative approach. There is compelling evidence that the margin with which you beat the close is a reliable predictor of your profitability.
By beating the close by 10%, you should expect to profit over 10% turnover in the long term, assuming that the close accurately represents the “true” odds of athletic performance. These odds are considered effective.
Of course, there are profitable players who have not managed to beat the closing line, who therefore can argue against this hypothesis. For them, then there must be two possibilities: either they are wrong, or they are lucky, and in general both will regress to some mean value. In addition, the hypothesis of an effective closing line is not entirely correct, and there are lines that are systematically identified by such players who failed to reach the “true” prices.
In this article, we want to look at how we could theoretically use the close line to test a player’s skill, given that the effective close line hypothesis is correct. After all, Marko Bloom, trading director at Pinnacle, said that the closing line is, on average, very, very accurate, and his traders are trying to reach the most efficient line with whatever information they have at their disposal. To achieve our goals, let’s take his word for it.
Analysis of real rates
Chart 1 shows a real bettor’s profitable betting history of 1214 bets over an 11-week period at the beginning of 2019, with an average odds of 2.065 and a return on turnover of 5.73%:
The blue line is the actual performance, the red line is the expected performance. Obviously, the actual profit turned out to be overestimated compared to expectations. How did we calculate the expected profit?
In his betting history, the player carefully recorded all the odds at which he placed his bets, and all the closing prices for those bets. As mentioned earlier, the ratio of these two prices provides us with a reliable estimate of the expected player advantage. Of course, both prices contain the bookmaker’s margin. We need to remove it from the close in order to calculate an estimate of the “fair” “true” price, assuming full price efficiency at the close of the market.
The first bet in a series, for example, was made at odds of 2.13. At the closing line, it was already 1.85. After the bookmaker’s margin was removed, the “true” closing price was 1.89. Therefore, the expected advantage that the player had was 2.13 / 1.89 = 12.8%. This means that for every 100 such bets that can be placed, a profit of 12.8 units can be expected.
The average retained advantage was 2.19%, which translates to an expected return versus 2.19% turnover. The average “fair” closing price was 2.024.
Could the closing line be superior by accident?
To investigate how and why a trader can “break” the close in this way, we must start by assessing the likelihood that it will happen by accident. To do this, we examined a sample of 162,672 bets on football matches with the opening and closing odds from the Pinnacle bookmaker. Based on this sample, 35.7% of the opening odds on home and away matches (with averages and medians of 3.443 and 2.75, respectively) theoretically had a profitable edge over their “fair” closing prices. The average ratio of the opening price to the “fair” closing price for this sample was 0.969%, which means the expected level of rate losses on turnover of -3.1%
If we had randomly identified 1214 rates from this sample, we would have expected the average ratio to be 0.969. Of course, we don’t always get 0.969, just like we don’t always get 10 heads and 10 tails when we flip a coin 20 times. How likely would it be to randomly sample 1,000, which implies a break-even expectation?
We can answer this question if we know the standard deviation in the ratio of the opening price to the “fair” closing price. In this sample, it was 0.114 (or 11.4%), which means that approximately two-thirds of the individual coefficients are between 0.855 and 1.083, as defined by the normal distribution.
With this information, we can estimate what the standard deviation of the average price ratio for a sample of 1214 bids will be. The standard deviation in an average betting metric such as yield, or in this case, the open to close ratio, is inversely proportional to the square root of the number of bets. Therefore, the standard deviation of the average price ratio here can be calculated by dividing 0.114 by the square root of 1214. We get the number 0.0033.
In other words, for a sample of 1214 bets with odds like ours, about two-thirds of the values will be between 0.966 and 0.972. We can now calculate the probability that the average open / fair price of 1,000 in a sample of 1,214 bets will happen by chance, given the expected value of 0.969. The answer is actually 0% (actually about 1 in 100 million trillion to be more precise). Given that 1.000 is over nine standard deviations from 0.969, this result is unlikely to come as a surprise to anyone familiar with the normal distribution statistics.
How to identify a qualified player?
The conclusion from this analysis is clear. If a player were to show an average bet price to a “fair” closing price ratio of 1.000 when the expectation is 0.969 in a sample of 1214 bets, this could not be due to luck. Instead, the explanation must be causal; the most obvious is the experience of the bettor and the bookmaker responding to this experienced player. If this is not an explanation, we still need another causal explanation; we repeat, this cannot be just luck.
Let’s go back to our real player and his performance. First, we must acknowledge that the average ratios, 2.065, are significantly different from the average quotes in our analyzed sample, 3.443. How does this change the calculation?
The larger the coefficient, the more likely it will move. Again, this is not a surprising observation. If we move the 80% / 20% offer by only 5%, to 75% / 25%, the quotes for the favorite will move from 1.25 to 1.333, and for the underdog – from 5.0 to 4.0. In fact, the standard deviation of the opening / closing ratio is proportional to the logarithm of the odds. A factor of 1.25 usually had a standard deviation of about 0.043, while a factor of 5.0 had a value of about 0.14.
Likewise, the average ratio of the open price to the “fair” close price changes with the average odds, falling approximately linearly as the odds increase. Odds of 1.25 show an average ratio of around 0.99, while odds of 5.0 show a figure of around 0.95.
A player’s average probability of 2.06 will have a standard deviation of about 0.079. Dividing this standard deviation by the square root of 1214 gives us 0.0022, so again the ratio of 1.000 is about nine standard deviations from the expected 0.98.
Finally, we must remember that the player here not only met the “fair” closing price on average, but outstripped him by 2.19%. What are the chances of doing this when the expectation is 2.0%? Approximately one followed by 75 zeros, or about 18.5 standard deviations. This player was moving the line and so the bookmaker quickly recognized him as someone with better knowledge than the rest of the market at the moment they bet on the published odds.
It is worth briefly reminding readers that there has been an earlier attempt to model how often a player would theoretically have to hit the “fair” closing price to have any profitable expected value at all. The figure that came out then was about 70%. Our player beat the “fair” closing price 73.5% of the time (beating the published closing price 84.2% of the time).
Close line value versus P&L
Let’s go back to the player’s actual profit / loss (P / L) from the above example. Using the traditional approach to significance testing, this representation can probably happen by chance about once in every 200 players. On this basis, it is likely that there is more than luck involved, but if we had a sample of 200 players and this would be the best result, we could not really rule out the possibility that the others did not have any skill. generally.
The Chart 2 below compares the two approaches for a 2.00 bet, illustrating how much faster the Closing Line Price (CLV) methodology provides meaningful information to a player about his chances of becoming a long-term winner with the expected an advantage of 2%. The Y-axis is logarithmic, measuring the probability that an expected / actual profit on turnover of 2% will happen by chance for the CLV and P / L methods, respectively.
Compared to the CLV method, the use of actual P&L is hardly even recorded. Even after 1000 bets, there is only one in 10 chance that luck could bring a 2% profit, where the expectation is 2% loss. Statisticians testing hypotheses won’t blink an eye. If such players showed an expected return of 2% based on how they “break” fair closing prices, then only 50 of them would provide confidence that this will happen about 10,000 times.
Of course, you can reasonably point out that the gains and losses are real, and closing the lines just gives us an idea of what to expect. According to this indicator, our player made very good bets with a yield of about 6%. However, the key point here is that it takes much longer to separate randomness from causality with P&L than it takes to close the line value.
Provided that the end-line value hypothesis is correct (which may not be entirely true), it provides a much more reliable indicator of a player’s skill than a simple betting history. Perhaps “breaking” the “fair” closing line tells us much more about the long-term expectations for this player. It is also possible that two-thirds of our player’s actual profitability from the 1214 bets presented in this article were due to luck. In the long term, we can expect them to regress back to 2.19%.
We know that those profitable players who fail to “break” the closing line may say, “Doesn’t my betting history just prove that the effective closing line hypothesis is not valid for the purpose of assessing expected profitability?” Yes, it is possible, but there are two points to consider.
First, if a player breaks the closing line the way our player did in this article, we have to explain it. This cannot be explained by chance, as the numbers have proved. The obvious answer is that such players are experienced and qualified, and the bookmaker knows it.
Therefore, if one profitable player can move the lines, why not another do the same? If such a player is unable to offer reasonable and testable explanations, the likelihood that they were simply lucky should remain. Remember that you may have a record for the profitability of betting, but if you are the best of a million tracked players, what does that really mean?
Secondly, given this information, the close line acts as a gauge, allowing the player to very quickly measure their expected performance. Since even small deviations from expectations are extremely unlikely for samples such as 50x bets, the bettor will be able to very quickly determine if the market thinks he has lost his advantage. This is an unrealistic situation with profit / loss analysis alone.
Until the bookmakers show us the profit / loss data compared to the closing line value, we will never know for sure how reliable the CLV indicator is. But in the end, Marco Blum told us that the professionals are moving the lines, and it’s hard to disagree with that. This way, if you are careful enough to keep track of your bets, keep closing prices in check and you can very quickly determine if your bookmaker and market thinks you are a winner.