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Oct
07, 2024

Oct
08, 2024

We really love Positive EV and believe that it is the best way to make money on sports betting.

- +EV is easier than arbitrage (you only need to place 1 bet instead of placing 2-3 bets at different bookmakers as quickly as possible while their odds have not changed yet)
- +EV is more profitable in the long run (because in most cases arbitrage consists of one bet on +EV and another on -EV, and you "leave" part of your potential future profit on the -EV bet in exchange for a smaller but guaranteed profit on the arbitrage right now)

If everything looks so simple and promising, then why in reality is it quite difficult to find a service that provides really profitable Positive EV signals? The reason lies in the two pillars of Positive EV's profitability: data and math. Let's explore both factors and see why you should at least try Positive EV at BetWasp.

**Positive Expected Value (+EV)** is a betting strategy that involves placing bets when bookmakers have underestimated the probability of an event happening. For example, the bookmaker has odds of +122 on heads when flipping a coin. This corresponds to a 45% implied probability.

If the odds are positive: Implied probability = 100/(Odds+100)

If the odds are negative: Implied probability = Odds/(Odds+100)

But we know that the **true probability** of heads when flipping a coin is 50%. So the bookmaker has underestimated the probability of the predicted event by 5%. This means that if you place this bet, you will have a 5% **probability advantage** over the bookie.

Probability advantage (PA) = true probability - implied probability

Let's now calculate our **expected value** for the $100 bet on this outcome.

EV = true probability*(winning amount - stake) - (1 - true probability)*stake

For our example, EV = 0.5*($222-$100)-(1-0.5)*$100=$61-$50=$11.

It turns out that, from a bet of $100 on this outcome we expect to get +$11. This is our positive expected value that represents 11% **ROI** (return on investment).

ROI = EV / stake = true probability / implied probability -1 = PA / implied probability

So, as we can see, there is a direct correlation between probability advantage (PA) and ROI. This allows us to express the EV calculation formula in a simpler form.

EV = PA * stake / implied probability

It is important to understand that you are unlikely to get this expected value after a small number of bets: you will reach this EV **cumulatively** **in the long run**, because EV is based on probability theory and therefore requires a sufficient number of bets to reach statistical significance (if we are going back to our example with a coin, you can get 9 heads out of 10 flips quite often, but with 1000 flips the distribution will be as close as possible to the true probability and will be something like 498 vs 502).

Therefore, your profit may initially fluctuate, but as the number of bets increases, it will become more stable and closer to the expected value. However, this is only true if the EV is calculated accurately, which requires determining the true probability correctly. If in our example, the true probability of heads when flipping a coin is 50% and it is an obvious fact, then how to calculate true probability when it comes to complex and uncertain events such as "total over 41.5 for Team1 in 1st half"?

Spoiler: in reality, there is no such thing as a "true" probability. If it existed, bookmakers would calculate and provide accurate odds and +EV would be impossible. In fact, bookmakers only assume the probability of a certain event (**implied probability**), and when they do it poorly, we have *a *Positive EV.

Therefore, our task here is not to calculate the probability better than the bookmakers (it's somewhere between very difficult and impossible) but to find odds where they most likely calculated the probability poorly. This is done by calculating the market average no-vig odds (most services call them "true" or "fair" for some reason, but not the "average", which they actually are) and comparing them with the bookmakers' odds (we call our average odds **Avgline**).

The quality of +EV signals almost completely depends on the quality of the average odds calculation (almost, but not completely). And the quality of average odds calculation depends on what then? Right, data and math.

*Data representativeness*.

The more bookmakers you have data from, the more reliable your average odds are (for example, calculations based on data from only 5-7 bookmakers are difficult to recognize as very reliable). The variety of bookmakers is also important (international, local, sharp, exchanges, strong in a certain sport type, etc).

*Data quality*.

The data should not contain incorrect odds. This is very important for arbitrage, but critical for +EV. In arbitrage, if there is an odds error, you will obviously see it before placing a bet and simply skip this signal as wrong. But if you have a +EV signal that is based on average odds that are partially calculated on incorrect bookmakers odds, then there is no way you will know or check this!

The main reason for incorrect odds is a low odds update frequency. Here means not the data refresh frequency in the user interface, but the frequency with which the service retrieves bookmaker odds. For example, one real +EV service updates odds in live events every 40 seconds. But during this time, the odds in tennis or basketball can be updated several times, so this service will calculate the average odds at least partly on outdated data which will make some +EV signals false.

But the user cannot distinguish a correct +EV signal from a false one here and now, he will discover a significant amount of false signals only in the long run, because he will not get the expected profit from these signals.

*No-vig odds calculation*.

All bookmakers odds contain a no-vig probability ("true" probability calculated by them) plus a margin (what percentage of turnover the bookmaker plans to receive as his profit). It is because of the margin factored into the odds ordinary gamblers always lose money in the long run.

Implied probability = no vig probability + margin

Since the margin of each bookmaker is very different, it is incorrect to compare odds that include margin between different bookmakers. That is why we need to first calculate the margin and cut it from the odds, get the no-vig probabilities and only then proceed to calculating the average market odds. In this way, we will consider as +EV those bookmaker odds that, even with a margin, exceed the market average no-vig odds. Each +EV service has its own formula for cutting the margin and its correctness directly affects the reliability of the average odds calculation (it's not enough to simply calculate the total margin on opposite outcomes and divide it between them).

*Average odds calculation formula*.

As we have already mentioned, the quality of +EV signals almost completely depends on the quality of the average odds calculation. Since each service has its own average calculation formula, you see different +EV signals (and get a different profitability) in different services, even if they operate on the same dataset. Approaches to calculating the average can vary from the easiest and least accurate arithmetic average to the most complex and usually most accurate weighted average using artificial intelligence.

So, we have a sufficiently reliable average market probability (no-vig "true" probability), what next? Obviously, we compare it with the implied bookmakers probability. And here it is important which indicator we use to identify and evaluate the bet as +EV. It means, when you see a signal that the bet is 5% Positive EV, what exactly is that 5%? Most services use ROI for this, but we use PA (probability advantage). To understand why, let's go back to the formulas.

PA = true probability - implied probability

ROI = true probability / implied probability - 1

In mathematical terms, PA is an absolute parameter, while ROI is relative. Based on this, we can make the following conclusions.

**PA**should be used as the primary parameter to identify +EV bets.**ROI**should be used as an additional parameter to evaluate an already identified +EV bets.

As we have already mentioned, there is a direct correlation between PA and ROI.

PA = ROI / implied probability

Why then do most services use ROI as the main parameter? Simply because it is more familiar and clear for the user. But such simplification is not always good and can lead to missing reliable +EV bets and focusing on risky ones, let's look at some examples.

Odds | Implied Probability | "True" probability | PA | ROI |

-233 | 70% | 75% | 5% | 7.14% |

138 | 42% | 46.5% | 4.5% | 10.7% |

355 | 16% | 20% | 4% | 25% |

This is a clear example of why the strategy of identifying +EV bets by ROI is unreliable. ROI is volatile for different odds ranges. Also, ROI is not informative enough for some odds ranges and for cases where there is a significant difference between the true probability and implied probability. ROI often "underestimates" reliable +EV bets and "overestimates" risky ones.

In summary, we should not determine whether a bet is +EV using ROI (for this we use PA). ROI (or its indirect expression as EV) is used as an additional parameter to evaluate the efficiency of the overall +EV strategy in the long run (it is not informative enough when it comes to a single +EV bet).

- BetWasp has data from 40+ different bookmakers.
- BetWasp scans the odds for most bookmakers every 1-3 seconds in Live events and 5-30 seconds in Prematch events.
- BetWasp has a proprietary complex formula for calculating no-vig average odds based on machine learning using an impressive amount of historical data for modeling and analysis.

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