The primary task of any sports bettor is to (hopefully) finish with more money than they started with. None of us will win every bet, but provided we win enough to cover the losing bets, our profits from the winners should (hopefully) be greater than the stakes lost on the losers. To put it another way, our overall return will (hopefully) be greater than the total amount we have bet. The question is: what is a good return?
What is ROI?
Answering this is not so straightforward. It’s not as vague as asking how long a piece of string is, but there are a number of points to consider.
Firstly, it’s clear that the more bets we have had, and hence the greater volume of money staked, the greater the absolute profit (or loss for that matter) might be. It would be useful to have some standard measure to compare different betting histories with different numbers of bets and different stakes.
Clearly, no two bettors are the same. The typical metric used is what’s known as the Return On Investment (or ROI), expressed as a percentage. Sometimes you might also see this called the Profit Over Turnover (POT) or yield. These are all essentially equivalent.
The ROI is calculated simply by dividing the total money returned to the bettor by the total they have staked.
If a bettor had staked $1,000 over a series of bets and now had $1,050 after all the wins and losses were totted up, their ROI would be $1,050/$1,000 = 1.05 or 105%. Since the net profit is $50, the profit over turnover is then simply $50/$1,000 = 0.05 or 5%.
This is also known as the yield. Relating the two, we have: POT = ROI – 1 (or 100%). It should be obvious that using such metrics as ROI or POT allows different bettors with different staking preferences or numbers of bets to be compared.
One bettor might bet $1 on every stake, and after 500 bets and a return of $600 would be showing an ROI of 120% (POT = 20%). Another bettor might stake $1,000 on every bet, and after 10,000 of them and a return of $12 million would be showing the same ROI (and POT) as the first bettor.
Obviously the second one has made far more absolute profit, but the ROI (and POT) allow us to compare their level of success (due to skill or luck) in their performances.
Length of betting history
Is an ROI of 120% always as good as another ROI of 120%? The answer is no, and there are two reasons why.
Sports bettors can replace bias with skill
The first is the length of betting history, not in time but expressed as the number of bets. All betting, like coin tosses, are subject to the laws of probability. If we tossed a coin 10 times and see six heads, would we conclude the coin was biased towards heads?
Almost certainly not. By contrast, if we tossed it a 1,000 times and witnessed 600 heads, only a fool would still believe the coin was unbiased. The longer the record, the more likely it is that a deviation from the expected outcome is due to something other than chance.
For coin tosses, that will be a biased coin; for sports bettors, we can replace bias with skill.
To illustrate this further, consider two betting histories, where all the betting odds are 2.00 and are fair (with no bookmaker’s margin), implying a 50% win probability, and where both bettors have returned 105% (or a yield of 5%).
The only difference is the length. The first bettor has placed 250 bets, the second 2,500. The diagram below illustrates the ranges of possible outcomes each bettor could experience simply because of good or bad luck (chance), assuming neither have any skill.
The range of possibility for the first bettor (250 bets) is represented by the blue curve. Their actual yield (5%) is shown by means of the vertical black line. Look at the areas under the blue curve to the left and right of the black line.
Their sizes are equivalent to the probabilities of actually achieving less than or more than a 5% yield (105% ROI).
The area to the right is about 21.5% of the total area under the blue curve, meaning there’s a 21.5% chance this bettor could have done better than they actually did simply if they’d been luckier. It’s arguably too much to be able to say this bettor is skilled.
The range of possibility for the second bettor with 2,500 bets is shown by the orange curve. Again, we know they’ve achieved a 5% yield (105% ROI), but this time, the likelihood of doing better is far smaller, indeed less than 1%.
Sure, we could still try to argue they’ve been really lucky, but it’s much harder to do so than for the first bettor. Instead, for the second bettor, it becomes easier to argue that something else other than luck is influencing the actual outcome.
Assuming the bettor is not cheating, the most obvious explanation is skill.
So we now have our first factor when determining how good an ROI is. In this example, both ROIs are the same, but that of the second bettor is better because it is easier for us to argue that it’s a consequence of skill and not luck.
Luck, as we all know, runs out in the end; only skill is sustainable in leading to future profits.
All other things being equal, where two bettors have the same yield, the better one is the one with a longer record.
Influence of the betting odds
Of course, all other things are rarely equal, and the most obvious difference between bettors with different betting preferences is in the betting odds. We can compare two bettors betting at different odds in the same way as we did with the different lengths of their betting records.
Asian Handicap bettors or US point spread bettors will typically bet at odds of around 2.000.
By contrast, win-only horse racing specialists may have records where the average odds are 10.000 or higher. Intuitively, what do you think we will see? Let’s have a look.
The two bettors in the figure below now both have records of 2,500 bets. The range of possible performances as defined by probability theory is again shown by means of the blue curve (odds = 10.000) and orange curve (odds = 2.000).
Look again at the relative areas under the curves to the left and right of the yield = 5% line.
Betting at longer odds can deliver bigger positive returns
Despite the records being of equal length, it is much more probable that a yield of 5% can happen simply by chance (with no skill) for the bettor betting at odds of 10. This happens simply because lower-probability events are more greatly influenced by good and bad luck.
Betting at longer odds can deliver bigger positive returns (and yields) just by being lucky, but the flipside is that bad luck will deliver the opposite, as the figure above illustrates.
In fact, for the bettor betting at odds of 10.000 to match the small likelihood of making a 5% yield (or better) of the bettor betting odds of 2.000, they would need to increase their betting record to about 22,000 bets!
We now have our second factor when determining how good an ROI is. All other things being equal, where two bettors have the same yield, the better one is the one who has achieved it with the shorter odds.
The conclusion from this is that superior yields (ROIs) are to be expected from bettors who bet on longer odds, assuming they are equivalently skilled to shorter-odds bettors. The yields may be larger in magnitude, but they are not necessarily a greater evidence of skill.
Unless we take into account the betting odds (and the betting history lengths), comparing yields for two different bettors to find evidence of skill is really not a fair comparison.
Likelihood as a measure of betting skill
So let’s return to our original question: what makes a good ROI? We know now that the quality of an ROI (or yield) is influenced by both the length of the betting history and the size of the betting odds.
When analysing both of these factors, we did this by considering the likelihood of seeing a particular outcome within a range of all possible outcomes.
Arguably, then, comparing likelihoods is a better way to compare two bettors’ performances than simply ROI alone, since the likelihood of a particular outcome is a meaningful measure of the underlying skill of the bettor.
Doing so then allows us to get a better idea of what ROIs might be expected from bettors using different odds.
I’ve done this in the two charts below, considering three possible levels: a 10% likelihood that outcomes happen by chance; a 1% likelihood; and a 0.1% likelihood.
As previously explained, the smaller the likelihood something can happen purely by chance (luck), the more confident we can be in believing chance is not the only thing influencing the outcome.
It is important to understand, however, that these likelihood figures are NOT equivalent to 90%, 99%, and 99.9% probability that the bettor is skilled. This is purely a qualitative, not quantitative, relationship.
The first chart covers a typical odds range for the majority of sports betting markets, ones typically favoured by many sports bettors.
For example, we can see that a bettor with outcomes that have only a 1% probability of arising by chance (red line), their expected yield from odds of 1.5 would be about 5% (ROI = 105%).
A similarly skilled bettor betting at odds of 3.000 would have an expected yield of over 10%.
Extending these relationships out to much longer odds is illustrated in the second chart (below), covering markets with many more runners, for example win-only markets in golf and horse racing.
The same bettor betting at odds of 20.000 would be expected to show a yield of over 35% (ROI = 135%).
The conclusion from this is that if a bettor betting at such long odds is not showing such large yields, they are not as skilled as the one betting at shorter odds and will be sitting on an odds-yield curve below the red one.
To put this another way, it’s about 10 times more likely that a bettor will show a yield of 15% from odds of 5.000 than an equivalent yield from odds of 3.000, and another 10 times more likely still to show it from odds of 14.000.
Conclusion
Not all ROIs are the same in betting. Just because one bettor has an ROI twice as large as that of another does not necessarily make them a more skilled bettor. Bigger yields are to be expected from not only shorter betting histories, but also betting at longer odds.
A bigger yield might feel nice in the short term, but ultimately the defining factor influencing the sustainability of profitability will be the skill level of the bettor.
Hopefully, by exploring the concept of likelihood a little more in this article, you will have gained a better understanding for what makes a good ROI.
For those wishing to explore the mathematics behind these ideas, Joseph Buchdhal's latest book Monte Carlo or Bust: Simple Simulations for Aspiring Sports Bettors might be what you are looking for. Sign up with Pinnacle for outstanding odds with low margins.
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