Betting tipsters often promise
high strike rates that will win you a fortune. Although the promise of big
profits is alluring, how can you tell the difference between a profitable
tipster and a salesman. Read on to find out the two factors you need to evaluate
before you decide which expert picks to trust.
In a previous article, we explained how luck
influences betting and whether profit is always a sign of skilful betting.
Using a series of coin tosses as an example, we used a binomial calculator to
calculate the probability of making a profit after ten consecutive wagers.
The binomial distribution is well suited
to 5050 propositions like point spread or Asian handicap markets,
where the odds for each side are close to even money, or a little shorter after
the bookmaker applies his betting margin. Often, however, bettors bet on
all sorts of different prices with all sorts of different stakes, for example
1X2 markets in soccer or match betting in tennis.
In such circumstances, we can rely on what is known
as the tdistribution and the student’s ttest for statistical
significance, which uses it. In this article, I explain how to use the
tdistribution to gauge the performance of a betting tipster.
The length of a tipster’s record
The tdistribution is very similar to the
bellshaped normal distribution and for numbers of wagers above about
30, is to all intents and purposes the same thing. The ttest investigates the
likelihood that a profit from a series of wagers could have happened by chance.
A return of 120% from 100 wagers at odds of 10.00
or longer is most likely to be a consequence of luck. Same returns from betting
oddson prices is an indication of skill.
The smaller the likelihood, the more probable it is
that something else, like the bettor’s skill, is explaining their
profitability. The ttest simply compares the bettor’s observed return to a
theoretical expectation (assuming chance only) defined by the market they’re
betting in.
Usually this would be a loss equivalent to the
bookmaker’s margin, or break even if the bettor is taking the trouble to find
best prices using an odds comparison tool. The resulting tscore is then
analysed to determine whether the difference is statistically significant.
It should be intuitively obvious that the larger
the profitability the bigger the tscore and more statistically significant the
betting history, in other words, the more likely it is that skill has played a
part. The tscore is directly proportional to a bettor’s excess average return
over expectation.
Similarly, the longer the history (for an
equivalent return) the more likely it is that something other than chance is at
work. Consider, for example, two bettors with a 120% return on investment. The
first achieved it from 10 wagers, the second from a 1,000. Who is more likely
to be the skilled bettor?
If in doubt, think of tossing coins again. Landing six plus heads out of 10 tosses is obviously far more likely than landing 600 plus from 1,000 assuming only chance. Were one to land 600 or more heads, one might reasonably suspect the coin to be biased.
If in doubt, think of tossing coins again. Landing six plus heads out of 10 tosses is obviously far more likely than landing 600 plus from 1,000 assuming only chance. Were one to land 600 or more heads, one might reasonably suspect the coin to be biased.
Similarly, we are more likely to conclude that a
bettor with a long record of profitability is demonstrating skill. The tscore
is in fact proportional to the square root of the number of wagers.
Long vs. short odds
Less intuitive is the influence of the betting
odds. In fact, a 120% return on investment from betting odds around 1.25 will
be a much better indicator of skill than an equivalent profitability from
betting odds around 5.00. Betting on lower probability outcomes (longer odds)
is inherently riskier (assuming equivalent stakes) because it is more at the
mercy of random variability.
To put it another way, returns are more volatile.
19 or 21 winners at odds of 5.00 will give returns of 95% or 105% respectively.
In contrast, 79 or 81 winners at odds of 1.25 will show 98.75% or 101.25%
profit over turnover. Betting longer odds implies taking more risk to get more
reward.
We can see the influence of the betting odds by
means of the standard deviation in profits and losses of the betting
history. For level staking, the standard deviation can be approximated by the
following expression.
Where o represents the average
odds for the betting history and r is the bettor’s actual return. The standard
deviation in profits and losses betting at odds of 5.00 is more than eight
times larger than when betting at odds of 1.25. Assuming that expected
returns (based on luck only) are 100% (or break even), the tscore is given by
the following equation:
Where n is the number of wagers.
Consequently, the tscore for equivalent returns and length of betting history
will be more than eight times smaller betting at odds of 5.00 compared to 1.25.
It should be clear that superior yields achieved
through betting longer odds, as is typical in markets like horse racing, are
not necessarily a sign of better forecasting talent. The same amount of luck
will deliver much bigger percentage returns.
Hence, comparisons of betting histories that
consider only percentage returns, as is common when ranking tipsters, are
fundamentally misleading. By taking into consideration the betting odds, the
tscore provides a measure of the quality of the riskadjusted return in excess
of expectation.
Calculating chance
The final step is to convert the tscore into a
probability (the pvalue) that a history of profitability could arise by chance
only. Those with Microsoft Excel can make use of the TDIST function. This
takes the form TDIST (t, degrees of freedom, tails), where t is the tscore
whilst degrees of freedom is the number of independent pieces of data and is
equivalent to the number of wagers minus one.
The tails argument can be either one (for the onetailed
ttest) or two (for the 2tailed ttest). Since we’re really only interested in
whether a profit is statistically significant, the former is preferred in this
case. Alternatively, one can make use of an online calculator where
these values can be inputted.
The table below shows some examples of tscores and
their corresponding pvalues for betting histories of 100 wagers and a return
on investment of 120%.
Odds

tscore

pvalue

1.5

3.33

0.06%

1.75

2.46

0.78%

2

2.04

2.19%

2.5

1.60

5.63%

3

1.36

8.83%

4

1.09

13.89%

5

0.94

17.56%

10

0.62

26.98%

25

0.37

35.45%

50

0.26

39.72%

Evidently, the average odds at which someone bets
has a big influence on whether their profitability can be considered lucky or
skilful. A return of 120% from 100 wagers at odd of 10.00 or longer should
clearly be considered largely a consequence of luck.
By contrast, if a bettor was to show the same
return betting oddson prices, it is far more likely that the profitability has
arisen because of their skill. Consequently, when comparing betting histories,
for example from tipsters, it is not enough just to analyse their percentage
returns, but also the length of their records and the odds at which they were
achieved.