Theory of Probability and Sports Betting

This article is written especially for those who do not have a technical mind warehouse or poorly studied at the university (or at school) and not able to understand the physical meaning of the mathematical and probabilistic laws and how they are reflected in real life. Therefore, no complicated formulas or abstruse scientific definitions, you will not see here. We will try to tell you everything clear and simple language and explain to the illustrative examples. RESULT OF SPORTS EVENTS - Random variables This means that the result of the events on which you place a bet in the first place, not known in advance (if, of course, is not match-fixing, but even in these cases, the "misfire"), and secondly, at each event, there is a possibility its occurrence. The simplest and most understandable illustration of a random event - a perfect toss a coin, the coin is such that does not have any physical defects, that is, for example, it is not bent, not leaky and not ground off from any edge. For this coin is known beforehand that without the use of sleight of hand and other tricks she drops one of the parties, "heads" or "tails" with a probability of 50% or 0.5, that is, c equal chances. In coin with obvious physical defects also have a certain probability of loss of each party, but, in contrast to the perfect coin, they are not known in advance, but may be determined experimentally. Why the theory of probability can not be bypassed At gamblers There is a myth that the theory of probability in sports betting is not working, as the result of a sporting event affects too many accidents, including a lot depends on the human factor. But it's the same as if to assume that gravity does not act on the plane, since it allows him to fly, despite the weight of several hundred tons. And at the same time the plane did not flap its wings like a bird. What is the result of a sporting event depends on many contingencies, only it says that we can not advance and know exactly the probability of this outcome. Just as, for example, we can not determine the probability of loss of coins with defects, which throw up in a wind tunnel with the ever-changing strength and direction of the wind. But this does not mean that the theory of probability in such cases does not work. Probability and mathematical laws are actually the same fundamental laws of nature, like gravity. Just manifestations law of universal gravitation in real life the most obvious, and hardly anyone in their right mind would ever think to check it, for example, jumped from the roof and trying to take off, waving his hands, even knowing that the aircraft being in the thousands times heavier fly can. The laws of probability theory does not have the same clarity available, but that they do not stop working just as inevitably, no matter what your attitude toward them or understanding. HOW DOES THE THEORY OF PROBABILITY IN PRACTICE Probability of an event can be simplistically considered how often it happens. But there is an important nuance. For example, the probability of one of the parties a perfect coin 50% or 1/2 = 0.5, meaning that on average, each of the parties should fall once the two throws. But in fact, you can toss a coin ten times, and everything will fall ten times, for example, the "eagle." This nuance is called "dispersion", and that he often misleads many players, even those who, like, consider themselves familiar with the principles of probability theory. In fact, the value of probability (it is called the expectation) is the frequency with which the event will occur in an infinite number of attempts. The fewer tests (in our example, throws a coin), the more (in percentage terms) the actual outcome may deviate from expectation. This is the variance, that is a clear influence of chance on the outcome of this particular test. But also at variance has its limits, for example, if you throw ten "heads" of the ten shots the perfect coin, though very rare, but nevertheless probable event, see a hundred "eagles" after a hundred shots already, in principle, impossible. The number of deletions "eagles" after a hundred shots perfect, emphasize once again, the coins may range from about 40 to 60. After 1000 shots - from 440 to 560. And so on. Substantial output beyond this will only mean that our coin is not really ideal, for example, she has shifted the center of gravity. Theory of Probability and betting odds How it relates to sports betting? The most direct way! At sports events, on which you place a bet: the victory of one of the teams, a draw or Thoth, also has its own probability, or the frequency with which it should take place under constant conditions. But, unlike the perfect coin, this probability is not known in advance to anyone, even the bookmakers. One thing is clear: none of the events in the sport does not happen 100% probability, even as we have noted above, match-fixing. This means that any bet may lose, that is, "100% sure thing" win-win betting or does not exist. This is the first and most important thing that you need to remember about the theory of probability in sports betting. So, the real probability of a sporting event no one knows, even the bookie. Simplistically we can say that the most probability he estimates, giving factor for this event. And this estimate is approximately equal to the value of 1 / ratio (theoretically more involved here and the bookmaker margin, but to keep things simple, we will ignore it). That is, the ratio of 2 corresponds exactly to the probability 1/2 = 50%. Contact formula 1 / probability (expressed in the format from 0 to 1), respectively, will give us a minimum break-even rate ratio for a given probability. A ratio of about 1.10 reflects the probability of 1 / 1.10 = 90.9%. What can be described in words, as an event that should occur, on average 9 times out of 10. But do not forget about the dispersion! At a short distance from the specified event likely to happen 20 times out of 20 (that often enters into euphoria inexperienced players catch a similar successful series, which makes them believe that they have discovered the "magic grail"). And two times in a row could not happen three times or even four times in a row, although the latter will happen rarely, but still will, from time to time. And we can calculate how often this will happen. In an unfortunate opportunity to play four consecutive bets with a coefficient of 1.10 also has its own probability. If we assume that the bookmaker ratio roughly corresponds to the real probability of the event (that "on set" several rates will be far from the truth), then the probability of an unsuccessful series of N lost bets in a row can be calculated by the formula: (1 - 1 / ratio) in degree N. For four consecutive losses ratio 1.10 obtain the probability of (1 - 1 / 1.10) to the power of 4 = 0.0000683 or curved, 1 time out of 14 000. Again, note the variance! This does not mean that you can safely "slip" 13 999 times, and "get" exactly 14 000th. No, exactly the same chance of such misfortune can happen to you as essentially later than 14 000th times, and immediately on the first try, but also more than once on some of the segments of 14 000 tests. And it does not depend on how much you believe in this rate. Another common misconception is that many players believe: after losing one, and even more than a few bets in a row, the probability of winning the next rate increase. And why use progressive betting strategies, such as the Dogon. Alas, it is not so. In fact, the probability of winning your bet does not depend on how much time you have lost before. The same after you throw a few "heads" in a row, the probability to throw in the next roll of the "tails" in a perfect coin does not change and remains the same 50%. It is also necessary to remember. Statistical significance As you probably already understand, it is impossible to make reliable conclusions about whether profitable bets on the race or not, after only 10 attempts. And even after the 100 still can not. Because of the dispersion of your real results at a distance can be very different from that shown in this short stretch, to the point that to be in the end, negative, despite the first 10 or 100 bets with profit. Number of bids you want to do before to evaluate the quality of your game is called statistically significant sample size. The minimum number of it depends on the used coefficients. The higher the coefficient - the greater the dispersion, the need to make more bets, to understand where they have zavedut. For roughly equally likely events (rates around 2) you need to do at least 500, preferably 1000 bets before the first serious conclusions. Wow? What do you think! Statistics such a thing. Now you should be clear that various kinds of "Kapper" (predictions sellers), showing as proof of their success short series of multiple bets, in fact, do not prove anything. MARGIN, or why sports betting, as opposed to the casino, you can earn Perfect, "a spherical bookmaker in a vacuum", makes a margin. Margin - is a small "supplement" to the probability that makes the loss ratio for the player, if this probability is known in advance and accurately. In the example of an ideal coin for the probability of 50% on the "eagle" and "tails" break-even point will correspond to the coefficients for 2 on that and the other. If we put 100 rubles, still on that "eagle" or "tails", in 50% of cases, we will win $ 100 * 2 = 200 rubles, and in 50% of cases - play for $ 100. Total 50% * 100 * 2 (our winnings) -50% * 100 (our losses) will give us zero - we will stay even. But again, what? That's right, the variance. This is true for a very large number of times (ideally - infinite), that professional players called "distance". That is, in the distance we will remain at their, and, for example, after 10 bets on these rolls on such factors (Repetition is the mother of learning!), Our results can vary in a very wide range, from a loss of 1,000 rubles to win the same in 1000. But you have to assess the profitability or unprofitability of its rate is at a distance, if you seriously and are going for a long time to make betting on sports, and do not expect to catch a successful band ( "positive dispersion of emissions"), take the money and never return to the rates in bookmakers. The sad truth is that a known equally probable events (eg, virtual games) you in any bookmaker will not see a factor of 2: he will always be lower, just on the size of the margin. That is about 1.97 in the most advanced bookmakers like Pinnacle, and up to 1.80, and even lower in the most greedy bookmakers. It is easy to find, putting the equiprobable events at a rate below 2, we get a loss in the distance. It unites the bookmakers with casino, where, for example, on the roulette there is always a sector of "zero", which plays the role of margins. After payment of even money bets at roulette (red / black, odd / ODD) also goes by a factor of 2, but because of the "zero" probability of actually slightly below 50%. Since the "paid" 36 numbers on the wheel, and "zero" - 37 th, this difference, "the casino margin" at roulette, is exactly equal to 1/37. At a distance it guarantees a profit for the casino, and for the players - a loss. This fact leads to one more popular among players myth: many people believe that because of the margin of bookmakers have a steady income at a distance, betting on sports, in principle, impossible. But there is one major difference bookmaker from the casino, which radically changes the situation. If casino games all the probabilities are known in advance, the real probabilities of the sports events (not to be confused with the virtual "horses" and other betting games disguised as machine guns), as you already know, is not known to anyone, including the bookmakers! Therefore it is quite real, furthermore, regularly occur a situation where bookmakers give higher ratios for two events whose real probability is around 50%. What (you already know how to find it) means profit on the distance to the player making such bets! And Margin here is of no importance. If one of the two equally likely events given above factor 2, the margin size affects only the magnitude of the coefficient on the opposite outcome. It will be the lower, the higher the margin of the bookmaker, but we have what difference, we're not going to bet on the opposite event, is not it ?! Another indication that the margin is not an obstacle for earnings on rates is the existence of "forks". But indirect evidence that betting analytics is not without sin when assessing the probabilities of events and exhibiting them coefficients, this line of motion when, at times, the favorite in the match with changes to just the opposite over time. Most often this is due to the fact that customers bookmaker too much put on one of the events. But foolish as to believe that excessive amounts of bets players alter the probability of this event! Of course not, in fact, that only means that analysts initially misjudged him. And in general, contrary to popular belief, the primary purpose of a bookmaker is not solution of the problem as close as possible to reality, to determine the probability of each event. Much more important for the bookmaker correctly predict the proportion of betting players that, regardless of the outcome of the match to get a uniform profit from all outcomes. Finally, if the margin is ensured bookmakers profits in the same way as it does for the casino, would we have heard about the mass cases of reduction of the limit rates or even completely block the accounts of successful players, as well as other tricks, especially for unscrupulous bookmakers to avoid paying the winnings ? How often do you cut interest rates limits the players at the casino? If only we are not talking about the obviously fraudulent activities, then never. But bookmakers repression against players thrive all the time, and is easier to call the bookmakers who do not repair any obstacles to those who have won, in fact, those currently in the entire global network of only two: Pinnacle and Sbobet. All other online bookmakers all the forces will try to show the door you as soon as you manage to start winning, and some bookmakers you can get a "black mark", even being in the red, just because your style of betting might seem employees of the office of potentially winning ! WHEN THE MARGIN has a significant impact Despite all the above, there are cases where the margin is still a significant barrier. And it is much-loved by the majority of casino players express. Let's see what happens with the expectation of our rates, if we take them to express. Suppose we put on equally probable events on the coefficient of 1.98 (the minimum margin on the market) and will collect five such rapid rates. Factor in this Express will equal 30.43. The actual probability of winning 3.125%. And what is the break-even rate for such a possibility? 1 / 0.03125 = 32! It would seem that for a single rate of break-even point we are only in the ratio of 0.02, and in five fingers express the difference has increased by more than half the unit! This shows that the influence of the margin in the expression is enhanced, in general, it is multiplied by the number of events to express. Estimating the probability of sporting events It was shown above that the secret to success in sports betting is not contrary to mathematics or probability theory and formulated quite simple at first glance: it is necessary to choose the rate at which the bookmaker factor incorrectly estimates the probability of the event, making it profitable for the player. In the example of equally probable events have to choose one of them, which is given to the above factor of 2. It is best with some margin (for example, from 2.10 and up) at the bookmaker, to take into account the effect of estimation error and reduce the potential damage from a local variance. But the difficulty is that the methods of objective assessment of the likelihood of sporting events does not exist. We can not take any objective (ie not dependent on someone else's opinion) data, such as statistics, enter them into some sort of program that on the basis of these data will give certainly true probability of an upcoming event, at least approximately. An important role in assessing the probability of a sporting event always plays a view assessing which forms the basis of own impressions about the game athletes, or based on any other premises. Many people confuse the probability of occurrence of an event in the future and its frequency in the matches already held.