## - How to test the credibility of a tipster's record?

## - Method 1: Study the closing prices

## - Method 2: The Wald–Wolfowitz runs test for randomness

For those interested in utilizing tipsters to identify bets with a positive expectation, two critical inquiries arise: Is the tipster's success due to skill or luck? And, is their performance history authentic? Our previous explorations have delved into evaluating a tipster's prowess and scrutinizing betting records for signs of skill surpassing luck. Our current focus shifts to gauging the authenticity of such records. Continue reading to discover more.

Our past investigations have centered on assessing a tipster's competence and scrutinizing betting records for signs of skill outweighing luck. However, upon obtaining what appears to be a trustworthy record from a tipster, how can you ascertain its value for your investment? Let's delve into this query.

# How to test the credibility of a tipster's record? The t-test revisited

In earlier discussions, I highlighted the utility of the t-test in searching for signs of forecasting ability, examining if profits from betting could occur by chance. The lower this probability, the higher the chance that skill, rather than luck, is at play. Yet, when a betting record seems implausible, it may suggest manipulation.

Reviewing the performance of an online soccer tipster focused on over/under and match odds, known for “quality tips, great odds and BIG winnings,” from August 2013 to October 2014, before his predictions were tracked by a reputable tipster monitoring service (which was later discontinued due to allegations of misconduct), he provided 296 tips. These had an expected win rate of 50% and average odds of 2.04, with 220 being successful, translating to a 74% win rate and a 151% return on investment. The profit chart presents as follows:

With a t-score of 9.3, the likelihood of such profit arising by chance is nearly one in a million trillion. The improbability of this scenario, combined with a profit trend bordering on the implausible, should raise concerns. However, this does not conclusively indicate dishonesty. The tipster might still possess unmatched forecasting talent. So, how can we verify this?

# Method 1: Study the closing prices

Mirio Mella has previously discussed the relevance of market shifts. As bets are placed, prices adjust, reflecting the collective opinion and news about teams or players. The more interest there is, the more likely the odds will decrease. Dafni Serdari further emphasizes the importance of the closing price.

“The odds available just before a match starts are termed the closing line and incorporate all statistics, news, betting activities, and market sentiment. This closing line should represent the market's most efficient point, hence offering the most accurate estimation of the actual probability.”

Consistently outperforming the closing price is a hallmark of sharp bettors. They introduce valuable information into the market, evidenced by their ability to decrease the odds. When they consistently surpass the closing price by more than the margin, it indicates a positive expectation, distinguishing successful from unsuccessful bettors, or sharps from squares.

In a comprehensive analysis of opening and closing prices, it was shown conclusively that the extent to which you beat the closing price predicts your profit expectation well. For instance, betting at an odds of 2.20 on a team that ends at 2.00 suggests a 10% edge (minus the margin).

Does “7x7Bets”, our “quality tipster”, consistently outperform the closing price? With a profit expectation of 51%, we'd anticipate odds of 2.00 to contract by 51% plus the margin to around 1.30. Reviewing the tipster's last 20 tips in our sample reveals:

8 prices shorten (average 6.7%, largest 19.5%)

7 prices lengthen (average (3.5%, largest 7.1%)

5 stay the same

Average movement was a 1.5% shortening

Typical margin is 2%

This movement does not significantly deviate from what would be expected by chance. “7x7Bets” is not systematically affecting our market, failing even to cover the margin. Clearly, while he was advising tips, we were not influenced by his recommendations.

# Method 2: The Wald–Wolfowitz runs test for randomness

Another method for assessing the reliability of a tipster’s betting history is the Wald–Wolfowitz run test for randomness. Named after statisticians Abraham Wald and Jacob Wolfowitz, who identified survivorship bias, this test checks if a sequence of binary data is random.

Irrespective of any potential signal from the tipster’s skill, the sequence of wins and losses should mirror the inherent randomness of the history, as each bet is independent of the last. A tipster offering even-money bets without predictive skill would resemble a coin flip sequence. A tipster boasting a 74% win rate would equate to a biased coin favoring heads over tails at a 74:26 ratio. We'd expect three times more heads than tails, yet the sequence distribution should remain random.

Consider the following sequence of wins and losses:

**W W L L W L W W W W L W W L L L L L W W**

This sequence includes 11 wins, 9 losses, and 9 runs observed (Ro), where a run is a consecutive sequence of wins or losses (counting singular instances). To determine if this sequence is random, we compare the expected number of runs from 11 wins and 9 losses against what is observed. The larger the discrepancy, the less likely the sequence is random. The expected number of runs (Re), assuming randomness, is calculated as follows:

Where W and L represent the number of wins and losses respectively. The distribution of potential runs roughly follows a normal curve with a standard deviation (σ), determined by:

The test statistic (Z) is then calculated:

Subsequently, this is converted into a probability (the p-value) that the observed and expected run difference could occur by chance. In Excel, the NORMSDIST function can be used, as I did with my own runs test calculator. A smaller p-value suggests a higher chance to reject the hypothesis of randomness and independence in the win-loss sequence, typically at p-value = 5% (Z = 1.96) or at 1% (Z = 2.58).

For the given sequence, Re = 10.9, Z = 0.88, and the p-value = 38%, leading us to conclude that the sequence is random.

The assumption for a successful runs test is that each bet's outcome probability remains consistent (similar to a coin flip). Although this may not always hold true, especially with varying odds, it generally should not be significantly breached where odds are closely matched.

This is most applicable to Asian handicaps and point spreads where odds are roughly around 2.00. For “7x7Bets”, 96% of his tips had win probabilities between 40% and 60%, with 78% falling between 45% and 55%. What does a run test indicate about his record?

Number of tips (n) = 296

Winners (W) = 220

Losers (L) = 76

Observed runs (Ro) = 135

Expected runs (Re) = 114

Z = 3.21

P-value = 0.1%

These findings confidently allow us to discard the randomness hypothesis. The deviation from expected runs for a tipster with a 74% win rate and average odds near 2.00 is too significant. A detailed examination explains the randomness test's failure: an abundance of shorter runs contrasted with a scarcity of longer ones.

[The anticipated number of runs with at least x wins is roughly nqpx where p = win expectation (74%) and q = 1 – p (26%)].

For instance, there were 67 instances of at least 2 consecutive wins against an expected 56. Conversely, only 2 runs of at least 8 consecutive wins were recorded, whereas 7 were expected.

# Fooled by randomness

If this tip history isn’t random, what is it? The simplest answer is manipulation. The excessive number of shorter winning streaks suggests that losing outcomes were frequently inserted to interrupt longer winning sequences. Why?

We're prone to a cognitive bias known as the clustering illusion, mistakenly attributing significance to inevitable sequences or clusters in random distributions. Thus, when asked to generate random binary sequences, most people will alternate between W and L more frequently than random distribution would suggest, especially if one outcome seems to recur too frequently.

It appears “7x7Bets” considered prolonged winning streaks as unnatural, though, in reality, with a sequence of 296 tips and a 74% win expectation, we should expect to see at least one 15-win streak. His longest was 11, with another at 9 and two at 7.

# Too good to be true?

If a tipster’s record seems implausibly perfect, it likely is. Prior to committing, scrutinize it for signs of surpassing closing odds and for randomness in win-loss sequences. Absence of these indicators suggests you should retain your funds.

In the case of “7x7Bets”, further closing price analysis for his latest tips reveals he continues to have no impact on our market. Moreover, he's been found altering past tip histories, likely aiming to make his record appear less improbable. A subsequent Wald–Wolfowitz runs test could ascertain whether randomness still eludes him. If so, ensure you're not misled.

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