# Mathematical strategies and sports betting

05.10.2021

Today we will talk about the connection between betting and mathematics, we will discuss what is the difference between sports betting and classic gambling. We will also consider some mathematical models of the game. As always, everything will be illustrated with examples and taught in as much detail as possible, it will definitely not be boring.

## Introduction

Many newcomers to the topic of betting are sure that sports betting is a kind of gambling. They believe that in the bookmaker's office you just need to guess whose victory is. And this is tantamount to guessing the color that will appear on the roulette wheel next time. After all, both there and there the result is the same - getting a win if the forecast was correct.

This is only partly true, but in its essence, betting is not gambling. Correct betting is directly related to mathematics, especially with its section probability theory and mathematical statistics. But there is also entertaining betting, in which the player guesses the winner. And such bets are pure gambling.

## Why correct betting is not equal to gambling

Roulette is the simplest game of chances, so let's analyze gambling using its example. In roulette (as in other gambling games), all probabilities are always static. The chance of getting black or red (as well as half of the field or even-odd) is always 48.65%.

Both black and red sectors on a field of 18, and a total of 37 sectors - 36 colored and zero, which is not refers to any color (as well as half or even-odd number). It is when the ball hits zero that the casino wins, this is their margin, which is also static and is at the level of 2.7%.

The same happens if you place bets on a dozen or a series of numbers, but there the chances are already lower - one in three, or rather 32.43% (12 out of 37). But on the other hand, the gain is proportionally tripled. Multiply 32.43% by three - 97.3%, and again the house's margin is 2.7%. In bets on six, four, three, two or one number, everything is exactly the same. The player always knows the calculated probability, the margin is fixed, so the casino is always in the black by the same 2.7% at a distance.

Sports betting is different. Even the bookmaker himself does not know for sure the probabilities of the outcomes of sporting events. He calculates them with the help of the most modern equipment and entire analytical departments, but still, no one is able to take into account all the factors in sports.

The estimate of the probability of BC is embedded in its coefficients, we have already discussed this issue more than once in previous materials. The 2.00 coefficient is approximately equal to the 50% probability, the 3.00 coefficient is 33.3%, the 4.00 coefficient is 25%, and so on.

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This is the key difference between betting and gambling - in the absence of clear betting probabilities. And this is what helps professional bettors make money at a distance in the bookmaker's office. In roulette, the bettor bets on a known probability (50%) with odds of 18 to 37. This is a priori negative mathematical expectation, and he will always be in the red at a decent distance of 1000 repetitions and above.

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In sports betting, a player can find outcomes that the bookmaker underestimated, and bet on a 2.00 odds with a 55-60% probability, or 3.00 with a 40% probability, and so on. This is the whole essence of value betting, which we have also talked about more than once. And this is the only way to profit from the bookmaker's office.

In general, if the bettor guesses the outcomes without taking into account the odds, he is guaranteed to be in the red. If a bettor compares his estimate of the probability and the estimate of the bookmaker, bets only on profitable mathematical outcomes, then a plus at a distance is inevitable.

In roulette and other gambling games, this method simply does not exist, there are static probabilities, a static negative expectation from - for margin. Therefore, you can be in the black only on short periods, and over a long distance the bettor will inevitably get a drain, because he will lose 2.7% on each spin of the bankroll.

## The connection between betting and mathematics

In correct betting, mathematics is literally everywhere. You constantly need to count something, taking into account every little thing - every hundredth of the coefficient, every 0.1% of the margin, every profit unit, every percent deviation from the average, even every ruble - everything is of great importance at a distance, with a large number of repetitions.

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All this is unnecessary if you place your bets once a week with beer. But if a bettor plans to make 1000 or more bets per year, he will have to make friends with mathematics.

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Today we have already touched upon the question of how the odds set by the bookmaker are related and the calculation of probabilities. What other aspects of betting is there math? At least the player makes calculations:

1. Bookmaker's margin;
2. The probabilities of an outcome, which itself consists of many calculations, which will be discussed in the next section;
3. Expectations and volume of the bet value;
4. The size of the bet when playing by non-standard system;
5. Overlapping rates, if the strategy requires it;
6. Own rates, results, profitability indicators of bet strategies.

And many other calculations. For example, calculating bonus wagering, developing new bet strategies, planning a budget for the next period, and much more. And if a bettor sells his predictions or subscriptions, then the number of calculations increases significantly.

## Mathematical strategies in sports betting

One of the main approaches to sports betting is mathematical. It involves creating a working betting strategy based on mathematics. Most players get this approach a little bit wrong. On betting sites and publics, you can regularly read forecasts with "analytics" in the spirit of:

1. These teams have played past matches on TB (2.5), so the probability of “total over” is quite high;
2. The team has scored two goals in three of the last five matches, so the probability of their two goals today is 60%;
3. The team won four out of five head-to-head meetings, and for sure they will win today.

What's wrong with these examples? For a start, ephemeral definitions such as “probably” or “pretty high”, as in examples №1 and №3, are inappropriate in betting. In example№2, the bettor tries to deduce a clear probability, but he does it over a distance of five matches, which is negligible. The fact that the team scored ITB (1.5) goals in three of the last five games does not mean anything at all. No probability can be deduced from this, only a tendency, and even then, rather illusory.

If a team had scored two or more goals in 600 games out of the last thousand, this would be a clear indicator of probability around 60%. But the problem is that it will take a couple of decades for an average team to play a thousand matches, and during this time, not only the team, but also football itself will change beyond recognition.

The distance in a season or two can be considered more or less indicative. if we are talking about football. But here, too, there are some nuances, because very often teams are seriously updated in the offseason - veterans have finished their careers, a strong player has come, coaches are changing, there may be motivational or financial problems.

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Accordingly, in the markets of football goals, it is generally unrealistic to deduce any probabilities, at least in such a primitive way. There are two ways out of this situation: the first is to use more complex mathematical models in these markets, for example, modus, median, Bayesian distribution. The second is to look for more productive markets in which the distance is filled faster - points in basketball and tennis, statistics of players and teams, averages for entire leagues.

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## An example of developing an adequate statistical strategy

In individual sports, things are better - the same person plays there all the time. Yes, it comes in different forms, different moods, different climatic conditions and financial motivation, but still it is one. In the same tennis, a lot of indicators are taken into account, according to them the required distance is filled quite quickly.

For example, a young Russian tennis player Andrei Rublev:

He recently played his 269th match. He won 169 of them, but it is still impossible to speak with confidence about his solid percentage of victories of 62.8%, because the distance has not been formed. The situation with the sets is already much more indicative, because Andrey played them 685.

But in tennis there are even smaller segments. So, there are almost seven thousand games on Rublev's account, and he has played more than forty thousand points in his career! And this is already an indicator. Moreover, there is something to work with here. We can refine these statistics under certain conditions, for example, points won in the last year against players from the TOP-100.

Here we also see a decent number of points won back and we can confidently say that at this stage of his career Andrey wins 53% of all points and 55.7% of all games.

And this can be used to build a mathematical strategy. Again, we look at the bookmaker's coefficients and compare. If the victory in Rublev's game is estimated at more than 1.80, we can safely take it, since this is a statistically confirmed value bet. The same scheme can be used to work with any sports and markets, the main thing is that there is a decent distance for them.

## Mathematical strategy "deviation from the mean"

Averages are also quite important, but they only work over long periods. For example, in basketball, a team can score 100 in one match and 150 the next. Does the 125 average give us anything? No. But over the course of the entire season (82 matches), it will level out and come to a more or less adequate value. And in 3-5 seasons it will become as accurate as possible.

This can be used to build mathematical strategies of a different type. Namely - the search for strong deviations from the average and the rate of return to them. This strategy can be used both within one match and within an entire season, which will be much more accurate.

1. An example of using a bet in a match: the average performance of a basketball team is 120 points per game. In the first half, they scored only 40 points. In this situation, there is a high probability that they will get the missing points in the second half, and it is worth betting on their current ITB. Even if they don't get to 120, the 85-90 points per match that is currently being offered is well above 50%.

1. An example of using a bet in the season: a team has very high xG (expected goals), but due to low implementation it scores little and regularly loses points. By Xpoints, it should be much higher in the standings. The use cases are to catch high totals in subsequent matches, hoping that the goals will finally come. Or look for happiness in the long-term markets, betting that this team will end the season much higher than it is now.

This is just the tip of the iceberg, everything that fits into one material. The topic of sports betting can be developed endlessly, which we will do in our training section “Articles”. Read it and your understanding of correct betting will grow tremendously. The probability is 99.9%.