Opportunity cost is a useful concept for deciding the best way to maximize your return on investment. Even profitable players need to be aware of the potential costs of misallocating resources. Read on to learn more about applying opportunity cost to sports betting.
What is Opportunity Cost?
Imagine a high school student evaluating the merits of going to university. What tuition costs should a prospective student consider? The initial cost of tuition is an obvious expense, but it is not the only factor a student should anticipate.
In addition to the expenses that the prospective student incurs during their studies, he must also consider the salary and experience he would have gained working during this time. This is an opportunity cost for the higher education student that must be weighed against the potential benefits of a university degree.
This is an important concept in investing. A person who sets aside their money in a 1% savings account is technically a “profitable” investor, given that they will have more money at the end of the year than they did at the beginning.
However, if inflation is 3%, then in real terms the investor loses purchasing power. Since the rise in commodity prices has been greater than the return on investment (ROI) of savers, it would be better to buy the desired goods at the beginning of the year rather than save.
Opportunity Costs Applied to Sports Betting
How does this concept affect sports bettors? To look at this, we will follow four imaginary players, each of whom profit from their bets. Several (unrealistic) assumptions have been made to simplify this process:
- Players have a limited starting capital (€ 100);
- They are limited to one action (no risk diversification);
- They must wager the full amount on each bet (a betting method would be appropriate in a real scenario);
- They are capped at 100 bids per year;
- Average return on investment per bet: Player A – 0.1%, Player B – 1%, Player C – 2%, Player D – 4%.
Considering all this, this is how our players’ income looks like ( Table 1 ):
Return on investment indicates the skill level of each player. Player A makes a small profit, while Player D gets a high return on investment.
Opportunity Cost in Betting: Outrights vs. Singles
A common debate among players is whether linking funds in long-term direct bets is a good strategy or the wrong allocation of resources. This is essentially a discussion about opportunity cost.
Assuming that these skilled players have an edge in both the long-term and current markets, what is the expected return on investment required to make an annual outright rate bet the optimal choice? Let’s take a look at Table 2 :
At 100% expected return on investment, bettor A wins € 89, but even with such a high ROI, the other three players will lose by betting on a straight line versus allocating their initial funds to betting on 100 singles.
For Player D to be able to eliminate the opportunity cost of betting on single players with those € 100 over the course of the year (while otherwise the funds would be tied to the direct bet) and make a significant profit, he would need to bet with an expected return on investment of 5150%.
More skilled players must find a direct offering of incredible value to overcome the aggravating effect of placing that money in single bets.
While this may be an argument against outright betting, in this simulation our players have limited resources and should not take variance into account. Real players may see direct bets as a good way to diversify risk. Of course, not many players would pass up a bet with 100% expected return on investment.
Sports betting against the stock market
Hedge fund managers are ranked by how their performance compares to the general stock market. In simple terms, the skill level of a hedge fund manager is determined by how “skillfully” his chosen portfolio can outperform the portfolio of someone who simply buys all major stocks through an index fund.
Warren Buffett calculated that stocks are growing at an average of 6-7% per year, so we will use the higher 7% growth rate as an average. How profitable will our players be when judged the same way as hedge fund managers? Let’s take a look at Table 3 :
With an average market growth, all players are making a profit that exceeds the market, so there is no opportunity cost. However, in a fast growing market, player A suffers a small loss (opportunity cost of € 3), while the real profit of another player is significantly reduced.
In a falling market, even a losing player can outperform the stock market, while winning players perform well over traditional equity investments.
In the long run, all players will be better off betting on sports directly rather than investing, but in a one-off scenario, Player A may incur an opportunity cost during a rapidly expanding market.
Opportunity for lower odds bets
As shown above, even profitable bets can have opportunity costs. This is especially true if the player is not taking the best odds ( Table 4 ):
* See below for the calculations behind these numbers.
If each player’s initial ROI was stable by betting on Pinnacle’s margin (in this case, 2%), then applying an industry average (6%) would obviously lead to lower profits.
This is the opportunity cost of accepting lower odds, which becomes an increasingly important factor as the player becomes more profitable. Player D will incur an opportunity cost of € 191 by choosing to place bets on an industry average rather than at Pinnacle.
Using lower odds can also be unprofitable. A hypothetical gambler with an expected return on investment of 2% (€ 102) over 100 bets with a 2% margin will only return € 98 at a 6% level.
In the real world, a player reaching the level of players C and D is likely to place more bets at higher odds than here. In this case, the effect of lower ratios on profitability will be even more pronounced.
What should players benefit from the opportunity cost?
Of course, seasoned players are well aware of the importance of adopting optimal odds, and also that funds should not be tied to long-term positions that could be better used elsewhere. However, these are important concepts to remember.
Perhaps the most useful for players is the comparison with the stock market. If Warren Buffett is right (and history shows that he is), then players should outperform stock market returns by 6-7% to ensure they do not incur an opportunity cost compared to simply investing in an index fund.
In fact, profitable players are likely to find enough value rates to ensure they outperform the stock market. Another great advantage of sports betting is that there is no such thing as a falling market, so there will not be a sudden drop in a player’s funds (provided the correct betting strategy is followed), and irrational factors should not affect a player’s ability to grow their bankroll.
To break down the calculations used for the above examples, we can use the simple idea of betting heads or tails – especially in this case where the player earns 11% return on an investment of € 100.
If Bookmaker Pinnacle offered coin prices with 2% margin, this would result in a price of 1.961 for both heads and tails. On the other hand, with a standard industry margin of 6%, that translates to a price tag of 1,887.
In order to get 11% ROI after 100 bets on a coin falling by a certain side (according to innacle bookmaker’s odds), this requires the client to make a correct forecast using the calculation formula:
€ 111 / 1.961 ≈ 57 (1)
of 100 coin tosses.
Although winning the same 57 coin toss bets at a standard margin bookmaker, this results in:
€ 1 x 57 x 1.887 ≈ € 107 (2)
This means, therefore, that the client receives 4 euros less despite reaching the same winning bet amount.