Football bets or bets on events with indeterminable probabilities

Before I go into this really complex topic in more detail, I would first like to recapitulate what we have seen so far:
In other words, one tries to achieve the greatest possible equity for all the money one stakes. In the best case, which is indispensable for professional players or aspiring professional players, the bets or money stakes should be placed with positive equity.
What makes the equity positive is also clear in principle: the probability of occurrence must be in favourable proportion to the payout ratio. The fair odds or the correct payout odds are calculated as the inverse of the probability of occurrence. So if you want to bet on a 40% event (W-ness = 0.4), you would have to get a payout ratio of at least 1/0.4 = 2.5. Above 2.5 the bet becomes profitable, it is then also called a “value-bet”. If the probability of occurrence is e.g. 90 % (=0.9), the payout ratio must be at least 1/0.9 = 1.111.

Furthermore, in all the examples so far, I have endeavoured to show that even with an apparently obvious distribution of chances, this is nevertheless not guaranteed (there is no LaPlace experiment; even with the often-cited coin toss, the distribution of chances is not guaranteed to be 50/50; with dice, it is not guaranteed to be 1/6, 1/6. …; even in roulette it is not guaranteed to be exactly 1/37 for each number; even in the lottery I would find objections, although especially there it is repeatedly pointed out that the organiser or his inspector “have satisfied themselves of the proper condition of the device”).

Instead of the wording “it is not safe…. ” one should actually even say: “it is certainly not…. “. Because the pure LaPlace experiment does not exist, as shown elsewhere (e.g. chapter “Murphy’s law”). But at this point I may refer to the book by Rudolf Taschner. The book is entitled “Number, Time, Chance”. In it he also deals with this problem. And his considerations are quite worthy of attention. So he has made the following consideration: The roulette wheel or the dice are specially constructed so that it becomes a purely random experiment. It is precisely the intention to achieve this. And an effort is even made to ensure that the equal distribution is as reliable and exact as possible.

And that is absolutely correct. In the case of dice, so-called “precision dice” were specially produced. Precisely because it was presumably discovered that a normal dice with holes for the eyes has a shifted centre of gravity. At the Backgammon World Championship, each participant had to buy a few registered precision dice before the tournament. One then came to the game with these dice, each with his and these were shuffled and then selected in turn. Or the roulette wheels are maintained daily.

Thus, we can assume a very good approximation in all these examples. In particular, the examples are also suitable for working out the basic principle using still relatively simple calculation examples. You could also call this: The tools of the trade.

But what happens when the probabilities of occurrence seem to become completely indeterminable? How can one even begin to determine the probabilities of occurrence for a football match as 1 – X – 2, win , draw, defeat?

And here are actually two methods that I have personally developed. And I still believe that they are unique. But before I explain them in a little more detail, I would like to try to make the basic approach a little more understandable:

If someone were to succeed in distributing the 100% on any sporting event in the future among the various outcomes in such a way that they come as close as possible to reality, then you would at least have an approach to competing on the betting market with this system.
So if you wanted to enter the game, I would advise setting the probabilities, calculated to 100%, for the upcoming Bundesliga matchday (as a first approach). I am writing these lines on 02.07.2008 and have just today received the match schedule for the coming season. So I’ll ask my computer how it estimates the games.

Here are the results of the calculation:
Pairing Percentages Fair odds BM odds Goal expectations.
Home Ausw 1 X 2
1 FC Bayern HSV 56.60% 27.87% 15.52% 1.77 3.59 6.44 1.65 3.20 5.25 1.41 0.59
2 Schalke 04 Hannover 60.91% 21.77% 17.32% 1.64 4.59 5.77 1.55 4.00 4.75 1.99 0.96
3 Wolfsburg FC Cologne 62.05% 20.44% 17.51% 1.61 4.89 5.71 1.55 4.25 4.75 2.16 1.06
4 Leverkusen Dortmund 57.03% 21.63% 21.34% 1.75 4.62 4.68 1.65 4.00 4.00 2.06 1.19
5 Frankfurt Hertha 39.88% 28.11% 32.01% 2.51 3.56 3.12 2.30 3.15 2.80 1.33 1.17
6 Karlsruhe Bochum 44.02% 25.97% 30.01% 2.27 3.85 3.33 2.10 3.40 3.00 1.57 1.25
7 Cottbus Hoffenheim 37.07% 27.76% 35.17% 2.70 3.60 2.84 2.45 3.20 2.60 1.32 1.28
8 Bielefeld Bremen 20.62% 23.24% 56.14% 4.85 4.30 1.78 4.25 3.70 1.70 1.04 1.86
9 Gladbach Stuttgart 33.50% 23.66% 42.84% 2.98 4.23 2.33 2.70 3.70 2.15 1.56 1.78

For now, these are the results without adjustments to the teamnews.
Before a season, the teamnews are of course of a different nature than during the season. Before the season, it is necessary to reclassify the teams on the basis of the last season, on the basis of transfers, on the basis of coaching changes, the atmosphere, the money invested and some other assessments.
All these things are reset at the beginning of a season. However, at the moment, these are the best results I can get. So these would be competitive in the market, in my opinion, given the current state of knowledge. Here, as you can see, the probabilities of occurrence for 1 – X – 2 are prefixed. These form the basis for the overall concept. The 3 values per game add up to 1 (100%). The 3 following values, i.e. the “fair odds”, are the reciprocal values of the probabilities. And the ones after that, i.e. the BM odds, would be the odds that a conventional bookmaker could well realistically pay. They are the odds “with profit”. So the values are always a certain amount below the fair odds, so that the bookmaker can also make a profit if the forecasts are good.

The last two columns are the core of the first part of my concept. They represent the number of goals I expect per team in that match. Of course, a game cannot end 1.41 : 0.59, as the first one did. But calculated over 100 games, the computer claims, Bayern would score about 141 goals and HSV 59. So Bayern are favourites, that’s clear, the effect will of course be felt in the goals.

And these goal expectations were originally translated into probabilities with a simulation on this basis. However, one day I managed to replace this simulation with a function. The function works more reliably, because the simulation is of course subject to fluctuations. So even if I run it 1000 times, as we have seen before in other random experiments, there would once be 1435 goals for Bayern and, for example, only 579 for HSV or, in another one, 1392 for Bayern and 612 for HSV. That could not be avoided. And the resulting probabilities (in this case, based on the simulation, they would correctly be called “relative frequencies”) would also look different. The fair course for Bavaria would be 1.77 in one simulation, perhaps 1.74 in another and 1.80 in the third.

Very well, the function replaces the simulation. The results are reliable and the mapping is 1:1. The function maps the results as well as possible.

All right, so I have years of experience with this and a software product that calculates these numbers. However, anyone could also or should first make rough estimates to start betting. So at first it would be enough to write down estimated values of, let’s say for example, 50% – 30% – 20%. You gradually get used to it. And you try to do this independently of the market, i.e. of already known odds, match day by match day. From this, you get the fair odds through inverse value formation. In the end, my second, self-developed but mathematically flawless concept serves to check the numbers. But I will present this to you later (see chapter “Approaching the problem of checking forecasts”).

Let me come back to the initial situation: After the fair odds have been set, one can first place theoretical bets. Of course, honesty towards yourself is essential. You write down the bets that you think you would have to place. To do this, note the provider with whom you would have placed the bet at the given time (i.e. the theoretical bet). Then note down all the games of the same type, provider, odds, the stake per game should then be one unit. And after the weekend, after knowing the results, the bets are settled. And week by week, provider by provider you get a final result. After a few weeks/months, a trend will then certainly be visible.

b) Checking the quality of the bets:

Alright, so the foundation stone for my current bread and butter was laid. And checking the quality of my bets is done like this: Do I still have money or do I have none left? Are all the bills paid? So you check every day if you still have money. Counting money every day. Is there any left, has it increased or decreased?

By the way, there is another problem:
Over time, you win or lose a lot of bets. That goes without saying. According to the structure of the Asian betting system, in which the handicap compensates for the difference in playing strength, it is even theoretically the case that any participant who only places his bets at random should already have won 50% of his bets. So 50% is the expected number of winning and losing bets. The loss that then theoretically occurs is due to the insufficient payout ratio. So on average, the random player bets at odds of, let’s say, 1.95. And if he actually wins 50 out of 100 players, ,each á 100 Euros, as expected, then a loss of 5095 Euros – 50100 Euros = -250 Euros remains, i.e. a loss of 2.5%.

So the problem now is this: You win and lose games. Everyone else wins or loses games as well. How do I check whether my bet was good? Yes, you can count the money. But isn’t there another method? You watch a match or get a match report. Yes, you see that your own team was even better, should have won, more chances to score, more possession, more corners. But according to the odds, they were favourites. Another game, you had the underdog, the team was inferior and lost. But: wasn’t the course of the game simply appropriate to the assessment of the game? But then again the question: whose assessment? Since I played it, there was a deviation from the “market assessment”. So was my assessment correct or that of the market?

If I assign a team a 65% chance of winning and yet, based on the market assessment, I play the opposing team. So the market estimates the game (in ignorance) at 70%. Me, 65%. I see the game. Surely I can’t expect my team to be the better one now? No, they should be clearly inferior according to my assessment. But just a little less clearly. In the end, you win or lose the game. And you’re not a bit smarter. The only difference is that the good player won that little bit more often than the average player and that little bit more often than the bad player. So you have to count money again. Unfortunately, you really do run out of options.

So I set out on a quest to actually check the quality of assessments in the very long term. And this on a mathematical basis. There is a mathematically quite flawless way to do this. And that leads on to the next chapter.