## - ROI explained

## - What influences betting odds?

## - How to calculate ROI

The primary aim for any sports gambler is ideally to end up with a larger amount of money than they initially had. It's a given that not every wager will be a win, but if we manage to secure enough wins to cover our losses, the earnings from our victories should hopefully surpass what we've lost. In simpler terms, we aspire for our overall returns to exceed our total bets. The real question then becomes, what constitutes a satisfactory return on investment in the realm of sports betting?

# What is ROI?

Delving into this question isn't exactly straightforward. While it isn't as ambiguous as the length of a piece of string, several factors need to be taken into account.

To start with, it's evident that the more bets we place, leading to a higher volume of money being staked, the potential for either significant profit or loss increases. To gauge this more effectively, it would be beneficial to have a benchmark for comparing different betting records, which vary in the number of bets and the stakes involved.

It's clear that every bettor's approach is unique. The commonly used metric for this comparison is the Return On Investment (ROI), expressed in percentage terms. Occasionally, you might come across terms like Profit Over Turnover (POT) or yield, which essentially mean the same thing.

Calculating the ROI is straightforward: it involves dividing the total returns received by the bettor by the total amount they have wagered.

For example, if a bettor has placed bets totaling INR 1,00,000 and now possesses INR 1,05,000 after accounting for all wins and losses, their ROI would be INR 1,05,000/INR 1,00,000 = 1.05 or 105%. With a net profit of INR 5,000, the profit over turnover then becomes INR 5,000/INR 1,00,000 = 0.05 or 5%.

This figure is also referred to as the yield. Connecting the two, we get: POT = ROI – 1 (or 100%). It's apparent that employing metrics like ROI or POT enables the comparison of bettors with varying betting strategies or volumes.

For instance, one bettor might risk INR 100 on every bet and, after 500 bets resulting in returns of INR 6,00,000, would demonstrate an ROI of 120% (POT = 20%). Another might wager INR 1,00,000 on each bet, and after 10,000 bets yielding returns of INR 12 crore, would exhibit the same ROI (and POT) as the former.

Though the latter has garnered a much higher absolute profit, ROI (and POT) metrics facilitate a comparison of their success levels, attributable either to skill or fortune.

# Length of betting history

Is an ROI of 120% consistently as commendable as another instance of 120% ROI? The answer is no, for two primary reasons.

Sports bettors have the opportunity to replace bias with skill. The first reason pertains to the length of the betting history, not in terms of time but as the total number of bets placed. All betting activities, similar to coin flips, are governed by probability laws. If a coin is flipped 10 times resulting in six heads, would we deduce that the coin is biased towards heads?

Highly unlikely. Conversely, if it's flipped 1,000 times with 600 instances of heads, only someone in denial would believe the coin isn't biased. A longer record increases the likelihood that a deviation from expected outcomes stems from factors beyond mere chance.

In the case of coin flips, a biased coin is to blame; for sports bettors, this deviation can be attributed to skill.

To further illustrate, consider two betting records where all odds are 2.00 (implying a 50% chance of winning), deemed fair and devoid of any bookmaker margin. Both bettors have achieved a 105% return (or a 5% yield).

The only difference lies in the volume of bets: the first has placed 250 bets, while the second has placed 2,500. The diagram below showcases the potential outcomes each bettor might encounter due to luck (chance), assuming neither possesses any skill.

The first bettor's range of outcomes (250 bets) is depicted by the blue curve, with their actual 5% yield marked by a vertical black line. Observing the blue curve's areas to the left and right of this line represents the chances of achieving a yield lower or higher than 5% (105% ROI) due to luck. The right side corresponds to about a 21.5% probability of the bettor outperforming their actual results if fortune had been more favorable. This likelihood is too significant to conclusively attribute their success to skill.

Conversely, the second bettor's possibilities with 2,500 bets are represented by the orange curve. Despite achieving a 5% yield (105% ROI) like the first, the odds of surpassing this performance are much slimmer, less than 1%.

Sure, one might still argue their success is down to sheer luck, but it's a harder case to make compared to the first bettor. For the second bettor, it's more plausible to believe other factors, aside from luck, are at play.

Assuming no foul play, the most logical explanation would be skill.

This brings us to our initial factor in evaluating the quality of an ROI. In the given example, although both ROIs are identical, the second bettor's is considered superior as it's more justifiable to attribute their success to skill rather than luck.

As the saying goes, luck eventually runs out; only skill can consistently pave the way for future gains.

When all is said and done, among two bettors with equivalent yields, the one with an extensive betting record is deemed superior.

# Influence of the betting odds

Certainly, in the realm of sports betting, not all variables remain constant, with the odds offered on bets standing out as a notable factor that differentiates one bettor's strategy from another's. Let's explore this by comparing two bettors who engage in betting at different odds, akin to our examination of their betting history lengths.

Bettors who specialize in Asian Handicap or US point spread typically engage with odds around 2.000.

Conversely, specialists in win-only horse racing may find their average betting odds soaring to 10.000 or even beyond. Intuitively, we might wonder about the implications of such differences in odds. Let's delve into this.

Consider two bettors presented below, both with a betting history spanning 2,500 wagers. Probability theory helps us visualize their potential performance outcomes through the blue curve (odds = 10.000) and the orange curve (odds = 2.000).

Examining the areas under these curves relative to the yield = 5% line highlights a key insight.

Betting at higher odds can indeed result in more significant positive returns. Despite having identical bet counts, achieving a 5% yield by chance alone is far more likely for the bettor wagering at odds of 10, a phenomenon attributed to the higher impact of luck on lower-probability events.

Engaging in bets at these higher odds could yield greater returns (and yields) purely through fortune. However, the opposite scenario, influenced by misfortune, is equally plausible, as depicted above.

Remarkably, for the bettor engaged at odds of 10.000 to emulate the slim likelihood of realizing a 5% yield (or superior) akin to their counterpart betting at odds of 2.000, their betting history would need to extend to approximately 22,000 bets!

This introduces a second crucial consideration in assessing the merit of an ROI. All else being equal, the more commendable achievement is that of a bettor who attains a given yield at lower odds.

This leads to the inference that superior yields (ROIs) are anticipated from bettors engaged at longer odds, provided their skill levels match those betting at shorter odds. While these yields may be more substantial, they don't necessarily signify a higher degree of skill.

Without considering both the betting odds and the length of betting history, drawing comparisons between the yields of two distinct bettors to discern evidence of skill becomes an inequitable endeavor.

# Likelihood as a measure of betting skill

Returning to our initial inquiry, what constitutes a commendable ROI? It's evident that the quality of an ROI (or yield) is influenced by both the betting history's length and the betting odds' magnitude.

In our analysis, we approached this by evaluating the likelihood of witnessing a specific outcome within the full spectrum of possible outcomes.

Hence, comparing these likelihoods offers a more refined method for assessing the performances of two bettors than simply looking at ROI alone. This is because the likelihood of a particular outcome serves as a meaningful indicator of the bettor's underlying skill.

This enables a clearer understanding of the ROIs one might expect from bettors operating at various odds.

The two charts below, considering likelihood levels of 10%, 1%, and 0.1% happening by chance, help illustrate this point.

It's crucial, however, to note that these likelihood percentages do not directly translate to a 90%, 99%, or 99.9% certainty of the bettor's skill. This is a qualitative, rather than quantitative, correlation.

The first chart encompasses odds typically encountered across a broad range of sports betting markets, favored by many bettors.

For instance, a bettor whose outcomes manifest with only a 1% chance likelihood (depicted by the red line), is expected to yield about 5% (ROI = 105%) from odds of 1.5.

A bettor of similar skill engaging at odds of 3.000 is projected to achieve a yield exceeding 10%.

Extending this analysis to significantly longer odds, as shown in the second chart, caters to markets featuring a larger pool of competitors, such as win-only bets in golf and horse racing.

Here, the same bettor, when betting at odds of 20.000, would likely exhibit a yield surpassing 35% (ROI = 135%).

This suggests that a bettor not demonstrating such substantial yields at these extended odds lacks the skill level of their counterpart betting at shorter odds, indicated by their position below the red odds-yield curve.

To contextualize, it's roughly tenfold more likely for a bettor to achieve a 15% yield from odds of 5.000 than an equivalent yield from odds of 3.000, with this likelihood increasing tenfold again for odds of 14.000.

# Conclusion

The landscape of betting ROIs is nuanced. A bettor boasting an ROI double that of another does not necessarily equate to superior skill. Higher yields can indeed stem from not only shorter betting histories but also engagements at longer odds.

While a substantial yield may offer immediate gratification, the true determinant of sustainable profitability is the bettor's skill level.

Through this exploration into the concept of likelihood, the aim is to provide a deeper comprehension of what signifies a commendable ROI in sports betting.

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