This chapter is to explain my system for successful betting on football matches. The betting market on which I have successfully used my system is variable. The history of the betting market is explained in the chapter “The Betting Market”. The practice explained here was the one used for many years. However, the changes in the betting market today offer me changed possibilities, so that this system explained here is not currently used by me. The reasons for this are complex and not the subject of this article. Nevertheless, the system would still be applicable in this way today, on 10 June 2009.
So we now assume that my computer programme provides me with assessments of football matches. These assessments are provided to me in the form of probabilities on the tendency, i.e. win – draw – defeat, or also 1-X-2, or in the reciprocal value of the “fair odds”. So anyone who wants to copy the system should first start by making their own assessments in the form given, preferably without any knowledge of the betting market and the odds offered there. You can also start without these assessments. You choose the games according to your feeling. You feel that the odds are too high and bet on them. But then many statistical possibilities for checking fall flat.
Furthermore, in explaining this system, I assume that I have a selection of bookmakers with whom I have betting accounts and which are filled to the required extent. Further, all of these bookmakers offer odds on football matches taking place worldwide and daily. The odds offered are not always identical. Each bookmaker has its own signature and also different assessments. This has changed a little today, as the bookmakers often coordinate their assessments with each other. In the past, there were often very different odds, but today they are more similar. In the past, competitive aspects were perhaps in the foreground, but today everyone is afraid of making mistakes, even of cheating, and therefore they try to coexist and use common experiences.
The system you have to work with is the same system that other professional players work with. It is always the same across all games: You have to place your money on the most advantageous bets. It is also the system with which, according to popular opinion, the providers themselves earn their money. The system is basically based on placing one’s money on “bets”, on opportunities that secure a long-term profit advantage. Short-term success depends on luck, on chance. If, for example, you want to place only one bet in your life on a very ordinary fifty-fifty chance, then success depends exclusively on luck. Even if the payout odds are only, as an example, 1.85, where in theory you would be at a disadvantage, but even if the odds were 2.1 and in theory you would have an advantage. You can win or lose the bet. Fifty-fifty, that is. And if it remains the only one in your life and you even win it, then you can confidently say to every professional, every provider, every wannabe: “You do the maths nicely. I’m ahead. And that’s not going to change.”
The satisfaction you might get from such behaviour may be great, yet it is then unsuitable to build your life on it. To achieve that, one has to work for the long term. And place favourable, promising bets for the long term. I would just like to remind you once again that the poker player who calls an “all-in” is also doing nothing more than placing a bet with his money. Even if only the “small blind” is pushed into the middle, it is already a bet. The roulette player who bets 100 euros on red, or 10 euros on the 23 makes a bet. He says: “I bet red now”. The backgammon player who starts a game for money or pays in the entry money in a tournament makes a bet. “I bet that I will win the tournament” or “I bet that I will win this game.” If you buy just one ticket in the South German Class Lottery, you make a bet. “Bet that the number will be drawn? Even if it’s just the last two digits.” The person who takes out an insurance policy also makes a bet: “I bet that there will be a fire in my house some day,” or “I bet that my car will be stolen.”
It should be noted, however, that there is always an opposing side. Explained with the simplest example: if you place your 100 euros on red at roulette, then the casino is betting against you. So the casino claims: “I bet that black will come.” Except the casino has a trump card up its sleeve, because it actually says: “I bet that black comes. Or Zero.” When we play backgammon for money, there’s the opponent who says, “No, I bet that I win.” In entry money, a lot of things come together, everyone claims the same thing: “I win.” With insurance it’s a very little bit different, because you do say: “I bet that there will be a fire in my house one day,” but at the same time you say “please, please, don’t let it happen.” The insurer says, “I bet there won’t be a fire,” that stays with it.
If you bet on a football match, things don’t get much more complicated. You bet that Cologne will win, at the same moment the provider is obliged to take the other side and say, “No, they don’t.” So there are turnovers. There are always the two sides.
Any money that is wagered on seemingly random events and, in a favourable case, can lead to a payback, constitutes a bet. Occasionally, of course, one knows it is a bad bet and makes it anyway, just for fun. But it remains a bet even if it is fun. Betting/playing with an admitted disadvantage is also more than legitimate. Only it would be convenient to know it then and to rely on the repayment of the stake in the form of adequate entertainment. If one does not win something after all, which can occasionally happen even with disadvantageous bets and above all, which is precisely what makes this form of gambling fun. The hope of winning something. The organiser of the game takes on the role: “Sure, you should have fun. But somehow the whole thing has to be financed. No one can blame me for calculating an advantage. It wouldn’t work any other way. In the end, I also win. Whether it’s with you or someone else is irrelevant for the time being.”
Well, after this long preface, I will now go into detail. The system I would like to explain here is, of course, the one I have used to bet successfully on football for a very long time. The basic ideas that need to be discussed can of course be applied to many comparable things. And it cannot be done entirely without a few mathematical considerations.
1) The system
As discussed in detail in the chapter “How a quota is created”, a quota reflects in a certain way the probability of occurrence of an event, in the form of the reciprocal value. If one has one’s own estimate of the probability of an event occurring, then the reciprocal of that probability is what I call the “fair quote”. If the price offered, the odds offered (price – odds synonymous), is above this fair odds, then in theory one has a profitable bet that is worth making.
However, since we are talking about events whose probabilities of occurrence are unknown, the quality of the assessments can only be judged in the very long term. One cannot directly check the quality of an individual assessment. The individual event occurs or does not occur. No one ever says that the individual game was well estimated. It is impossible to judge that (did I just deny God?).
And the statement “quality of assessments” applies to both sides here. You have one, the provider, your opponent, has another, now these are held against each other in the form of a bet with money staked. The outcome of the individual event is still random. In the long run, however, mathematics promises that the better will prevail in the form of overall profits.
As a small note, however, it should be mentioned here that although the outcome of the individual event remains random, the better assessment nevertheless promises more frequent success. Here is a concrete example:
We have the match Schalke – Dortmund, from 20.2. 2009 from the 1st Bundesliga. You have noted down your assessment. You claim that Schalke’s victory is 55%. The fair odds as a reciprocal result in fair odds of around 1.82. You look at a betting offer and read off that you get a 2.0. That would give you a 50% chance in the reciprocal. But this is the upper limit that the provider assumes. Since he himself calculates his betting offers with profit, he rather assumes an estimate of 45%. The difference between the estimates is large enough with 45% against 55%, so that a seemingly profitable bet results here for both sides.
The “random outcome” of the game is of course somewhat less random if one assumes the “correct” assessment. It is just that in this case it is simply not known. And, I don’t know how good your connection to the very top is, but whether everything up there runs via probabilities or via assigned fates, whether it is even set as “calculable”, only not solved by man so far, will probably remain unresolved at least for a longer while. Personally, I have assumed throughout my entire betting career (here I am again talking specifically about football betting) that my assessment is “correct”, or at least closer to the truth than that of the other person. And here, success has proven me right.
So, we are now at the point of “randomness of outcome”. And this is, depending on who was more right, not entirely random after all. If your estimate of the 55% is correct, then the event is still random, but it has a slightly greater chance compared to your opponent’s 45%…. You then have it right as often as you need it to be profitable. At odds of 2.0, it must occur at least 51 times in 100 attempts for it to be profitable.
Unfortunately, the random experiment is not repeated in this case. Instead, there is the next game, in which the competition begins anew. And even if you then bet an underdog in that game for odds of 4.0, whose probability of victory according to your estimation is 27.5%, i.e. fair odds of 3.64, you will be able to gauge success at some point. The individual game comes or does not come. One is closer here or lucky there, the other there. And so on. In the long run, the better one prevails.
You can see how complex the whole thing is by the fact that you may have been right in the first game, but the result goes against you, and in the second you are wrong, but it goes in your favour. As I said, mathematics promises you in the very long term that you will get into the order of magnitude of what you are entitled to. And the financial result is the surest, but above all the relevant, yardstick anyway.
So my system was that I simply used my computer to create estimates for all the leagues I covered and then compared them with the odds on offer. You can read about how my computer did this in the chapter “My football programme”. That I nevertheless continued to be influenced by intuition is quite natural. This intuition flowed into the following variations:
If a game was (is) clearly indicated, I can of course look for reasons for it. It is guaranteed not always a “mistake” made by the provider, the opponent. The mistake can always be on my side as well. If many bookmakers agree on an assessment for a match, special caution is required. Then it is advisable to adjust your own assessment. Occasionally, you can simply skip this or that game altogether. You certainly haven’t lost anything from that. In the worst case, you have only given away a potential profit. But that alone does not “cost” money. But who says that one would have had an advantage?
Then, of course, there were leagues in which I “felt comfortable”. Somehow you notice that the assessments are right and everything works out. In other leagues, you tend to have worse results and prefer to leave the games out altogether. Of course, there were teams that you “liked”. Either you had good reason to believe that this or that team was underestimated or the team was often shown, you played them and they won. Then, of course, one had gradually developed more confidence in that team and preferred to play it. But if one day the computer indicated that one should bet against this team, one had a good reason not to follow this suggestion. “Nah, I’m not betting against them.”
Another control option, of course, is always the amount of the bets. If a game is very clearly indicated or one is very convinced of the assessment, then one can bet the game higher. Another, which seems less reliable to you, you can then, instead of leaving it out, just play it smaller.
But how do you play the games in the first place? I will explain that in the next section.
a. Advantage of combination betting
As mentioned earlier, many providers had combination bets anyway. That is, you had to combine several games if you wanted to place a bet at all. These providers did this, on the one hand, to protect themselves from errors in the odds, and on the other hand, to take advantage of a mathematical law. However, I doubt that they did this consciously. The mathematical law that they used (unknowingly) was that the combination of events increases the advantage for the one who has the advantage on his side. Since, of course, every provider was convinced that his odds were the right ones and that he had an advantage in practically every game that was bet on, it could be assumed that this advantage would increase with a combination.
This mathematical law requires a little explanation As in other cases, this fact is best explained by example. In order to keep the example nice and clear, I will once again use the good old coin toss and also assume that the distribution of chances is actually 50-50 for heads or tails. If a provider were to offer odds of 1.90 on a coin toss, he would have a clear advantage. 2.0 would be the fair odds (1/0.5, the inverse, as usual). Instead of 2.0, however, he only pays 1.90. With 100 attempts with the distribution 50 times tails and 50 times heads, he would collect 100 * 100 euros for a stake of 100 euros, since the bettor would have to deposit the money. However, he would have to pay something back in 50 cases. The payout would be 100 * 1.90 for each of the 50 cases, i.e. 190 euros per hit. The player hits 50 times, so he only gets back 9500 euros for his 10,000 euros. That makes a loss of 500 euros on a turnover of 10,000, which is 5%.
But now let’s assume you always bet a combination of 2 coin tosses in a row. As we have learned, not only does the probability of occurrence multiply (since the events are independent) but one may also multiply the odds together to calculate the payout. The provider has not changed his offer for the second roll of the dice either. One always gets 1.90. So the probability of occurrence for “two heads in a row” would be quickly calculated as 0.5 * 0.5 = 0.25 or 25%. The wage that one receives for the occurrence of head – head in succession would also be easy to calculate. One gets 1.90 * 1.90 = 3.61 as a quota.
Now we do 100 times two coin tosses in a row. Ideally, the event “heads – heads” would occur 25 times. That means you would win 25 times and lose the other 75 times. With the 25 wins, one would get back 100 euros * 3.61 each, i.e. 361 euros. That would be the case in 25 cases, so you would get back 25 * 361 = 9025 euros for the 10,000 euros you bet.
That would be a loss of 975 euros or almost 10%. And again, this is not witchcraft. It is the multiplication as an arithmetic operation that makes this happen. In both cases, in both events, you have a disadvantage with the bet. This disadvantage multiplies, as do the probability of occurrence and the odds. The disadvantage becomes greater because it multiplies.
But that is of course also a question of perspective. For it is still unclear who actually has the advantage. My programme showed me the games with an advantage. My programme was quite good so far that it could give me reasonably realistic figures. So I gratefully accepted the offer of having to combine. With providers who had no compulsion to combine, I was also happy to combine voluntarily. The providers thought they had an (even greater, if conscious) advantage, and I was also convinced that I had an advantage. So the end result had to provide the answer. And this proved me right, at least to the extent that I could pay the rent permanently and regularly and fill the fridge. Oh yes, and it was also warm in my flat, even in winter.
Conclusion: combining several games is to the advantage of the person who would also have the advantage in the single game.
b. The system bets
To win in the long run, however, apart from the good games, which were determined by comparing the fair odds and the odds offered, it is also necessary to combine the games and to have an adequate turnover, which will then (hopefully) bring the advantages one has to bear in a sufficient, preferably of course in an optimal way.
System bets are presented in detail in the chapter “The Betting Market”. Here only so much: A system bet forms the complete number of possible combination bets of this selection in the specified number from a number of selected games. So a 4 out of 13 is a bet in which all possible 4 combinations of 13 games are played, a 3 out of 11 is a bet in which all possible 3 combinations of 11 games are played.
So the problem is on the one hand the combination, on the other hand the amount of turnover. In addition, one must consider that the provider will become aware of one and take protective measures.
There are at least three points to consider regarding the problem of composition. The first point is the advantage one assumes the selected game offers. The second point is the reliability of the forecast one has made oneself. I always had enough reason to at least check whether my computer was more likely to “go wrong” in this game and more likely to be right in that game. Thirdly, the amount of the odds is an influencing factor that is not insignificant.
For various reasons, I prefer to bet on system bets almost all the time. The coincidence here, in conceptual terms, is that my system was system betting. What advantages this offers I would like to explain below, point by point.
i. The attention aspect
The system bets thus offered me the chance to “accommodate” all the selected games with each provider. Because often enough it was a high number. In fact, often enough it was almost the only way to get any money at all on all those games. If you imagine that with a betting offer of often well over 100 games on a weekend, I had already selected 20 games per provider, then the problem becomes obvious quite quickly. How else should one get money on the games than with a system bet?
Of course, the 20 games selected were not always different for each provider. That was also quite intentional on my part. A game could appear in my selection at several providers for several reasons: First, because I thought the game was good and simply liked to have more money on it. Then there is the consideration that providers are often tired of only being played on their weak points. This means that many (would-be) professionals only and exclusively play top rates. One bookmaker pays 1.80 on a game, the other 1.85 and the third 1.90. That is the maximum. Then the man inevitably gets a lot of turnover on the game. He gets annoyed by this at some point. He also despises the players who do it. “Yes, a great system you have. Always play maximum courses and trust that those will be mistakes then already. Anyone can do that.”
I too played these games then, it’s not like that. But: the same provider had odds of 2.10 on another game that was also interesting for me, for example. And on this game, he knew and I knew too, there was a 2.20 at another bookmaker. Then I played the 2.10 anyway. Then my bets didn’t “bother” him as much because I wasn’t classified as a pure “maximum player”. And that, of course, affected all providers. So I was quite happy to play other games, with any provider, on which the provider did not pay the maximum. An insidious deception. But effective. I got bans much less often.
In addition, the system bets are simply less conspicuous. A player who picks 20 or even more games looks more like an entertainment player. I never stopped dictating bets on the phone. How and why should I have any advantage? So the (perhaps naïve) thought goes.
Sure, you will object, you can remain inconspicuous for a few weeks or months. But you become conspicuous when you ask for payouts. And repeatedly. Because one has simply won. Of course, that was an aspect at some point. And that’s how gambling bans came about from time to time. Nevertheless, my way of playing was less conspicuous and many things were perhaps attributed to my excessive luck. And who knows? Maybe it was true?
ii. The advantages in the games
Of course, there were always games in my selection that offered a great advantage. And some of them were definitely the “premium bets”, the preferred games. Games that simply “tasted” good to me, that I then also definitely wanted to play more expensively than others. Others offered smaller advantages, had higher odds or were simply not as interesting, appealed to me less. A lower turnover had to be played there. So, some games expensive, some small. That was the goal.
And you could also achieve that optimally with the system bets. I could play 4 or 5 system bets. And in each of them there were two or three games that I had identified as particularly good. In addition, of course, there was even the possibility of playing these games with other providers (even if not for the highest price!) in further system bets. It was unobtrusive and effective. More turnover on some games, less on others. I will explain how to calculate all this.
iii. The turnover
The turnover, which you have to make at least to be able to feed on it, must of course be of a certain order of magnitude. Since I never made more than 5% profit on the turnover, even with the system bets, I had to make a turnover of 50,000 DM per weekend. That was quite a normal figure. However, since I played with different providers, even this was not so noticeable. At one 3000 DM, at the other 5000 DM. Everything was within reason.
Of course, we knew many people personally and had a relaxed relationship. The motto was: “How much am I allowed to play on this bet? “Yes, well, 3 out of 6 á 100 DM, that’s fine.” “All right, thank you. But of course you don’t have to accept anything if you don’t like it.” So it became a personal but fair duel. Both sides had the opportunity to learn. What’s more, my argument was always: “Even if you have a minus so far and maybe there were a few quota mistakes. Who knows if this weekend the odds aren’t all just right and the advantage is on your side?” And it’s hard to give in to that. Especially since the providers are usually vain and believe in their assessments. But among the vain, I am the king….
iv. High quotas
There has always been the problem of how to “accommodate” very high odds in betting. The one problem here is that you would like to play them if displayed and selected. The only way to do that was still system bets. Either because it was compulsory anyway, or because you played everything else in systems anyway. Then there was always a maximum payout per bet. And because of the high odds, there was the problem that the theoretical maximum payout could easily be exceeded. Especially if there were more than one high odds among them. My computer, stupid as it is, naturally made no distinction. The odds of 12.0 were too high for it, it simply showed it to me, because the fair odds were 9.76.
But there was a solution to this problem: I played a 3 out of 10 with certain 10 games, but small. And then I made another 3 out of 11 with the same 10 games. The eleventh game was then the game with the high odds. If there were more than one, I just played several 3 out of 11s and changed the last game in each case, leaving the others the same. So I had a “normal” and desirable turnover on the other 10 games and a smaller turnover on the high odds, which was appropriate for these games. And the maximum payout (per bet) was not in danger.
v. Comparison of system and combination bets
In principle, I recommend betting in systems to every player. One should also not disregard subjective factors. And one subjective factor is the size of the entertainment offered. So, in principle, I recommend that you familiarise yourself once with the calculation procedures of system bets and then apply what you have learned in practice. I have made this recommendation very often, but feel that most have avoided it because of a lack of understanding.
The reasoning is quite simple and obvious: one plays a combination bet, even the small or pure entertainment player. He chooses six of the nine Bundesliga matches and combines them in one bet, stake 5 or 10 euros. This is legitimate, provides entertainment and is simply fun. Of course, I have often enough heard the “sad losers” tell me about the tragic case when they got five of the six games right. And of all things, the one doesn’t come! I also had to tell them often enough that the chance of getting one of six wrong is six times as great as the chance of getting them all right. Because: you don’t know yet which of the six won’t come. There are six possibilities.
In this case, my regret is limited, but I have always had to praise their obviously great football sense, because it is in any case a good achievement to guess five games correctly. At the same time, however, I had to say that in a way it was their own fault. After all, there are system bets.
My recommendation is therefore in principle: system bets. The argument I often heard, but which, without wanting to offend anyone, was obviously only meant to conceal a lack of understanding, was: “I only play with very small stakes.
I counter that most providers also accept system bets with very small stakes. So if you only want to “risk” 10 euros on these six games, you still play them as 3 out of 6, with a basic stake of 50 cents per row. There are 20 rows, * 50 cents, makes 10 euros.
The effect you achieve is explained like this: the possible maximum payout, if all six games come up, is of course much lower than with the full combination. But you also have a few advantages on your side. You also get payouts with three, four or five correct numbers. You don’t have to despair if a game is hopelessly against you. You can always get something back when the others come. Subjectively speaking, this also offers a higher entertainment value.
Another aspect deserves mention: you can play games that kick off at the same time. Then the difference is somewhat smaller. So you play the Saturday games of the Bundesliga, either you win or you lose. Full combos must all be right, with system bets a few right ones are enough.
But if you play a system bet with games with different kick-off times, then the difference becomes noticeable. With a system bet, one wrong game can still do no harm. If, for example, you have combined the evening matches (in the system), you can still expect them with excitement, perhaps even more excitement. If you have played a full combination and one game is wrong, then you have lost. The suspense, the entertainment on the remaining games of the combination goes towards zero. Only if you place another bet. But then you have even made more turnover than your budget allows, possibly against your will but still forced because of the entertainment.
In my practice, this aspect also played a role. I often played system bets with games from different days. If the first games were favourable, one is happy and looks forward to the coming games. That is the subjective factor. Objectively, however, it also makes sense to play that way. Because if the games went unfavourably, let’s say those of Friday and Saturday, then I had no or only low stakes on the Sunday games. But I wanted to play the games. That meant I had to replay them, then in smaller systems, of course.
vi. Long-term assessment of betting quality
Another aspect is the assessment of betting quality. If you always play full combos, there may be one hit that distorts the statistics because it happens by chance. If it is even a second one in a short time, you can be completely misled. In the same way, a long dry spell can make you despair, even though you are actually a good bettor (“Only one game wrong again. Such bad luck, always the same.”).
If you make system bets, you can still control the amount you bet. You don’t have to become a professional (want to) and bet thousands, but can check the quality of your own tips with small bets. You have regular payouts. And that provides a quite reliable method to check the quality. And if it should still be negative after a few months, you can either blame it on bad luck or simply try to bet better, to use the experience. This does not mean that you are at a disadvantage or that you simply can’t do it and should stop. Keep going, keep at it and be ready to learn. The “willing to learn” also applies to me, of course. You always have to expect or accept that people either have a better assessment or a better method.
In principle, however, the situation is like this: all bets in which you actually have an advantage are recommended to bet money on. Theoretically, of course, the more the better, but there are also money management questions that advise you what percentage of your capital you should/could/must bet on which advantage. Contrary to other recommendations, it also does not depend on the odds whether you make a single, combination or system bet with a game. There is an advantage everywhere, if well chosen. Then the only question is how much turnover you want on it and how you place the money. To understand this a little better, I have another real “treat” for you, namely….
vii. A bit of mathematics
You can calculate a lot of things on this, many even very concretely. A few details about turnover can be found in the chapter “Turnover”. There you will also find, for example, that there is a formula with which you can calculate, given a certain advantage and a certain budget, how much money you should bet on a certain game.
Here, however, we will only deal with how to calculate how to achieve the recommended turnover in system bets. To do this, I will first ask a provocative question: How much money do you have “placed” on each individual game that is in a 3 out of 8 bet of 20 euros?
Of course, you can look at all the individual lines that you have placed with the 3 out of 8 and count them. We remember: with a 3 out of 8 with the game numbers 1,2,3,4,5,6,7,8 the first row would be with the games 1,2,3, the second with the games 1,2,4 and so on (example in the chapter “The betting market”). If we now look for game 5, i.e. the question, how much money did I bet on game 5, then we can count off all those where there is a 5. A 3 out of 8 is 56 rows, because 8 over 3 = (876) / (3*2) = 8 * 7 = 56. On recounting, you would surely find that there are a total of 21 rows where there is a 5. But isn’t there a reasonable consideration for this first followed by an equally simple calculation?
There is. I’m sure you’ve figured it out by now, but I’ll go ahead and utter the phrase that is always sufficient for me to illustrate: “A game that is in a 3 out of 8 is in all 2 out of 7 bets.” I have reduced both values by 1. And it really does stand there. I take all the other 7 games and put them together as 2 out of 7. That’s 7 over 2, or 7*6 / 2 = 21 combinations. And then I could add the game 5 I’m looking for to each of these combinations of two. Then I would have made three-person combinations out of the two-person combinations and the game would always be there. At the same time, there are all the possibilities to put the game in. So we would have found an answer to the question above: If we play a game in a 3 out of 8 á 20 euros, then we have indeed put in 56 * 20 euros = 1120 euros in total. But on each individual game we have bet (only) 21 * 20 = 420 euros.
We can use another procedure to check this. This procedure works like this: We continued to play these 3 out of 8 á 20 euros. One game takes place before the others. This game has unfortunately “gone to shit”. It is lost. The other games begin. But what bet do we have now?
The answer is actually relatively simple. Our 3 out of 8 has become a 3 out of 7 after losing the first game. One game is wrong, all the combos where the game was in are lost. But we still have a bet. The other games can still come and still give us a good payout. We are left with a 3 out of 7. We calculate a 3 out of 7 á 20 in the same way as always. There are still 7 over 3 or (765) / (3*2) rows “alive”. That is 7 * 5 = 35 rows. We used to have a 3 out of 8 with 56 rows. Now we have another 3 out of 7, which is 35 rows. This obviously means that we have lost 21 rows. That 21 again…
But it’s true. And in Pascal’s triangle, in a way, we have gone one step backwards. Take a look. The 56 is made up of a 35 and a 21. I’d like to, but I can’t do witchcraft, again and still not.
Let’s take a very concrete example. And even if it remains fictitious, it offers us all forms of accounting methods and possibilities. So I place a fictitious bet on the Saturday Bundesliga matches of 21 February 2009. Here is the list of these matches with the fair odds as calculated by my computer for the upcoming match day:
|Deutschland, 1. Bundesliga||1||X||2|
|8||21/2/09||15:30||FC Bayern||–||FC Köln||1.46||5.62||7.24|
If you want to give yourself a little treat, take the reciprocal of all the fair odds on a match and add up these three values. The result must always be 100%. Now I will include a fictitious list of offers here with the already selected tips on the advantage games:
|Deutschland, 1. Bundesliga||1||X||2|
|8||21/2/09||15:30||FC Bayern||–||FC Köln||8.50|
So we are to play Schalke to win, Werder Bremen win, Gladbach win, Frankfurt, Wolfsburg, Bielefeld, Hoffenheim, Cologne and Leverkusen also all to win. But the draws really don’t offer themselves at the moment in the Bundesliga. The odds you get are all clearly below fair odds. However, since this is fictitious, the odds I have assumed do not exist on the betting market, at least certainly not all of them with one provider.
So we play a 3 out of 9. 3 out of 9 are 9 over 3 = (987) / (32) = 34*7 = 84 rows. We also risk 20 euros each for this. So the total stake is 1680 euros. I also definitely made this fictitious bet before the end of the games. But who believes me?
We now know a few things: each game is in all 2 out of 8 bets. That’s 8 over 2 = (8*7) / 2 = 4 *7 = 28 rows. 28 * 20 euros = 560 euros. So we have now bet every game with 560 euros. Even Cologne, who never win in Munich, you dreamer! And I would also advise playing a 3 out of 8 without Cologne and a 3 out of 9 with Cologne. as explained above.
We’ll stick with the 3 out of 9 for today. The following diagram shows all possible payouts. If we get game 1, game 2, game 3 right, we get back the multiplication of the three odds in units, at the back the value is given in Euros. So if only exactly these three games were correct, we would also only get back 235 euros. If we got these three games right and also game 5, then we would have 4 combinations right. The combinations 1 with 2 with 3, 1 with 2 with 5, 1 with 3 with 5 and 2 with 3 with 5. We can then read the corresponding payouts from the corresponding line.
|Spiel 1||Spiel 2||Spiel 2||Quote 1||Quote 2||Quote 2||Gewinn in Einheiten||Auszahlung in Euro €|
Of course, you can now check this in detail or just look at selected lines. One will bring a little more if it comes, the other less. The best thing is just to have them all come. Then we get back 2426.12 units, that is 2426.12 * 20 Euro = 48522.40 Euro.
Note: For beginners in system betting it is very important either to understand and understand this counting principle immediately, i.e. to be able to calculate the winnings easily, or at least to be able to deduce it again and again, according to which pattern one finds out and calculates the winning combinations. My recommendation in principle: bet in system bets. Study and understand system bets well.
After all, on Monday I can read from the list, depending on which games are correct, how much I would then get paid out in the corresponding combination/row. The sum of all the correct rows, multiplied by the stake, then gives the fictitious payout. The fact that there are a total of exactly 512 possibilities is only a side issue here. All possible payouts are listed above. Which ones can then be put together is actually irrelevant.
As an alternative to the “reading from the list” method, I can of course also consult my computer program. It reliably calculates the payout, if one comes.
By the way, my self-developed programme answers several other questions. For example, the highly relevant question of how much I can expect to win on this bet. Since we have concluded all the individual games with an advantage (in the sense of the fair odds, which are also fictitious, but assumed by me to be exactly the same). In addition, I can determine the possible probabilities of occurrence for the certain individual combos or also for 5 or 6 correct ones in the sum, or what could interest one. In addition, I can determine the value of the bet after each individual match. This becomes interesting, for example, when a match (e.g. the Friday match) is played (calculating is also possible when it is not played, but then it is not interesting, of course).
Above all, it can be important to know something like that. Here again the two possibilities: the bet looks good. One hits a few games. Then you have changed bets on the Sunday games, for example. It is then no longer 560 euros, but, depending on the number and odds on the right tips, more or even much more. But this leads to the second aspect: you have scored badly, little or not at all. Then you have either less money or no money at all on the Sunday games. But you would like to have money on them. So you have to play them again.
In the more pleasant case of getting many correct ones, you can of course also react. And of course that applies to different game selections. In the Bundesliga, i.e. in our selection, we only have games on Friday, Saturday and Sunday. Most of them kick off at the same time. But of course it can happen that you have a match from another league at 3 p.m., the next one at 5 p.m. and then two at 8 p.m.. The stakes always change for the following games. It becomes more or less. Depending on that, you can react. If it is bigger, maybe even too big, you can insure. This means that you simply play the opposite side. If too small or 0 one can replay, as one would like to have stake on the games (be it for the joy of playing or as a professional who has to ensure turnover, preferably cheap, in the first place).
So let’s assume we score 6 goals on Friday and Saturday. Then we might have quite a high stake on Leverkusen for Sunday (also depending on which games were right and their odds). Then we simply play either X and 2 on the match beforehand, or also “Hamburg in the handicap”, which then means that Hamburg does not lose. This secures a part of the winnings, even in case Leverkusen does not win. If we have few matches and absolutely have money on the last match, we can try to play Leverkusen still individually or also a new system bet with other matches from other leagues. This procedure was by no means unusual in my practice.
Whereby the insuring has to be done very carefully. The reason is clear: one has deliberately made the system bet. The advantage is that the advantage in the sense of an expectation of winning is increased by combining, because the advantage is “pushed on” to the next game in the form of multiplication. If one then insures, one deprives oneself of this advantage again. Above all, one probably has to play the opposite side with a calculated disadvantage. And despite the aspect of “securing a profit”, one cannot feed on disadvantageous bets in the long run.
So insuring only comes into question if the stakes are simply too high, so the reasonableness aspect plays a role. So let’s say we have all 8 games coming up on Friday and Saturday. Then we would have a stake of 5843.85 euros on the last game, i.e. Leverkusen’s victory. And that is a stake that we would never bet on this game. We are even exposing ourselves to a swing of 13148.70 euros. That is the difference between winning and losing this game.
So you could insure a little something with a clear conscience, even if you know you are making a bad bet. You take out a part of the very high swing or you secure a profit. That is quite reasonable and also my practice. Too much insurance is certainly unhealthy at some point. One bets, sometimes consciously, at a disadvantage.
Another aspect that speaks against insurance is that in a case like this, having eight correct games already means a handsome profit. The payout with the eight correct numbers is already 35373.74 euros. And for that, if I may say so, an old woman has to knit for a relatively long time. So, reassured by the high winnings, one could also quite well do without the insurance.
It is always necessary to weigh things up. Even if you now have this win for sure and the tension eases a little, you have to ask yourself whether you would actually bet 5,000 euros or more on the next game, which you might want to bet on as a single game and could do so, even if you won that one? You probably wouldn’t. So one should then take something down again, secure a part of the winnings.
Back to the winning expectation: my computer calculates it for me as 414.09 euros. All the games individually offer an advantage, in the system bet it adds up to 414.09 euros. Doesn’t that sound good? 1680 Euro stake, 414.09 Euro expected profit. It’s a pity that the odds are fictitious and the win expectation is only Monopoly money…
d. The evaluation
Well, today is Tuesday, 24 February. The games are over. I almost forgot about the bet because of the day’s business. But now I have to go and evaluate. And what do I see?
First of all, we actually have four games right. Gladbach, Wolfsburg, Frankfurt and Cologne. The odds were 2.60, 2.25, 3.40 and 8.50. Cologne and never come. But I heard the other day that the Eiffel Tower also shook for a moment! Oh, it was just a gust of wind, all right. So good odds in part. Results in the (here manual) calculation:
The 1st winning row: 2.60 * 3.25 * 2.25 = 19.01 units. (3, 4, 5)
The 2nd profit series: 2.60 * 3.25 * 8.50 = 71.83 units. (3, 4, 8)
The 3rd winning series: 2.60 * 2.25 * 8.50 = 49.73 units. (3, 5, 8)
The 4th winning series: 3.25 * 2.25 * 8.50 = 62.16 units. (4, 5, 8)
(in the overview of all possible payouts we also find the values, it’s obvious. Since we have the games 3, 4, 5, 8 right, we find them in all the rows where three of these four numbers appear in front).
Adding up all the units gives 202.73 units. Each unit counts as 20 euros, making a total payout of 4054.60 euros. With a stake of 1680 euros. We have already more than doubled our money with four correct numbers! And who says: betting is stupid. Of course, it was all down to Cologne, but there’s always a chance.
But if you go through the games again: Schalke was already leading 1:0 early on. Another huge shot by Kuranyi, missed. 83rd minute the equaliser. Werder was clearly better in Cottbus, had a huge chance shortly before the end, Tremmel held, throw-off, Cottbus counter-attack, 2:1 Cottbus, final whistle. Yes, we could have…
Bielefeld wasn’t that good, was behind early on, but after the equaliser, well, you can’t win them all.
But now: Stuttgart – Hoffenheim. Penalty in injury time for Hoffenheim. Salihovic into the early evening sky. That would have been it, another 3.40!
And Leverkusen also put on a lot of pressure for a long time, could have… but what the hell. The result is good. Here’s just the value of the missed penalty: payout if he scores: 10205.82 euros, instead of the 4195.60. Difference, i.e. the much quoted “swing” on the (mis)shot: 6010.22 euros!
Of course there is a very effective method to check the quality of one’s bets on a daily basis. This is: count the money. If there is some, it was ok. If there is a lot, it was probably good. Who cares if it was lucky or deserved? If there is little, you have to think. And if there’s all of it, you have to say: too late.
Nevertheless, mathematics has its own laws. It’s like in the cup. Even the little one can annoy the big one, kick him out. It’s the same with betting: you can live on luck for a while. You play at a disadvantage and still win. Unfortunately, these careers usually turn into tragic ones. The person who has had luck on his side for a long time certainly cannot understand it when it is gone at some point. Used up. “Eaten up” by the mathematical laws. They apply, especially in relation to statistics, over “long periods of time”. But no one really knows what a long period is. Only one thing is certain: the longer you play at a disadvantage, the more likely it is that you will end up in the red at some point. But the reverse is just as true: those who play with an advantage will also be rewarded for it at some point. When “sometime” is, you don’t know. It can start today or after 1000 bets. The probability always increases with the number of bets, games and events on which you bet your money with an advantage. It is never certain. Just as little as losing.
That’s why I’ve helped myself with other kinds of statistics. These can be just as deceptive as any other statistics. But since I try to keep them neutral and I don’t expect too much from self-deception (the children are hungry again), I can provide you with a few more figures to check my forecasts.
An even larger, very essential part about this can also be found in the chapter “Getting to grips with the problem of checking forecasts”. Here are the supplementary parts:
i. Hits expected/accomplished
In the long run, one can check and compare the expected hits with the actual hits. Of course, the hit expectation presupposes a correct, preferably good, probability assessment of the events on which the bet is placed. But any estimate would be enough to have a point of reference.
Let us take our example above. We have bet on 9 football matches. Each at a certain odds. I will explain the relevance of the odds in the next part. Here, for our hit expectation, the probability estimate is decisive for the events we have bet on.
This is quite simple. I’ll give you the 9 games with the probabilities again here instead of the fair odds. As you know, the probabilities are merely the reciprocals of these:
|FC Bayern||FC Köln||1.46||5.62||7.24||68.40%||17.79%||13.81%|
The events we ended up betting on are highlighted in bold. The fair odds are also shown. The probabilities at the back are the reciprocals of the fair odds.
Now we can simply add up the probabilities on the events played and logically get our total hit expectation (for these 9 games). We have assigned a probability to each event. As high as this is, so many hits we expect. In other words, a 50% chance comes to 50%. I expect half a hit. Two times a coin is tossed, I expect half a hit each time, making a total of one. And who wouldn’t expect heads to come once for two tosses (it’s quite different for me!)?
So the sum that results is 52.06% + 49.5% + 39.83% + 32.90% + 47.08% + 45.90% + 31.55% + 13.81% + 47.23% = 359.86% or 3.5986 hits, i.e. 3.6 hits. We actually achieved 4 hits in the example. Certainly, our gain comes partly from exceeding the expectation. But an even more important part is due to the fact that we hit the smaller chances but the higher odds (especially Cologne). Still: the result is encouraging. The numbers match up well. But you can’t really make statistics out of 9 games yet. It’s just a welcome coincidence here.
I have made this kind of statistics over all years. For that, of course, I looked at the annual balance but also at the overall balance. And the results were sufficiently good in many respects. But before I discuss in more detail the little curiosity that arose, I would like to draw attention to an essential basic requirement for professional gambling, betting, that is the…
ii. Minimum required hit yield
When looking at the pure hit expectation compared to the hits achieved, one does not yet have a statement strong enough to judge whether professional gambling is worthwhile in the long run. Especially not if one does not (completely) reach the hit expectation. If someone manages to exactly reach the hit expectation on which he bases his bets, and if he also places all his bets with an advantage, i.e. with the prerequisite of payment odds > fair odds, then this person will also quite certainly win in the period in question (here, too, there is the tiny restriction that it would be possible to hit all the small odds and miss all the high odds, so that this would still not result in a plus).
To understand how difficult it is to meet one’s hit expectation exactly, especially over a longer period of time, we need to keep another principle in mind. I would like to explain this in the following. One prerequisite, however, is to find a plausible answer to the question: What role does the odds at which we bet play?
Of course the odds play a role. This role is first of all that it reflects the assessment of our opponent, the one who holds the bet. And beyond that, it gives an indication of how many hits we need to score to be at par. That would be the minimum number of hits above which it would be worthwhile to continue. The rationale is this:
If you bet 1000 times on a coin toss and always get paid odds of 2.0, then in that sense it would be a fair bet. If we don’t know the exact odds, then we would only have the statistics. But this would hopefully spit out a number in the order of 500 hits after 1000 throws. So we would have a payout ratio of 2.0. And a minimum required number of hits of 500. If we should reach the 500 hits exactly, we would be exactly at par, true to the experimental design. We would have lost 100 euros 500 times and won 100 euros 500 times.
We calculate this minimum number of hits just as easily as before: We take the reciprocal of the payout ratio. That is absolutely logical. Our dream probability of a home win in the Schalke – Dortmund match is 52.06%. The inverse of this, the fair odds, is 1.92. The provider who pays us the odds of 2.1 assumes a completely different assessment, otherwise he would not pay such high odds. He calculates with a maximum probability of occurrence of 1/2.1, i.e. 47.62%. As I said, maximum, because he also calculates with profit, so he would have to assume 45% or even less. And always keep in mind: we are talking all the time about probabilities whose values are completely unknown. All participants in the game are guessing.
But we take its maximum value as a lower limit for us, which we need in order to be able to expect a balanced result, at least in the long run. As in the coin toss example. If you bet on a coin toss all your life and always get paid the odds of 2.0, then you can confidently continue. Your odds are about even. Gambling or being left out makes no difference. If you enjoy it, you keep going.
So we have our own hit expectation. This was an (optimistic) 3.6 hits. The minimum number of goals we needed for our bet can be seen in the following graph:
|FC Bayern||FC Köln||8.50||11.76%|
Only the odds we actually bet on are shown here. However, the values entered correspond to the payout odds at the front and the reciprocal of these odds at the back. The other odds that we did not bet on are not shown. They are irrelevant for us, we do not even know them. Nevertheless, we can add up the hits here in the form of the indicated reciprocals that we would need at least to earn a par chance. The total comes out as 47.62% + 46.51% + 38.46% + 30.77% + 44.44% + 43.48% + 29.41% + 11.76% + 44.44% = 336.91% or 3.37 hits.
With our fair odds and estimations we “trusted” ourselves with 3.6 hits. According to the minimum assessment as the sum of the reciprocals of the paid odds, we only need 3.37 hits. In the long run, of course, the truth must lie between 3.37 and 3.6 in order to work with advantage. On 9 games the difference is “only” 0.23 hits, but on 100 games it would already be 11*0.23 = 2.53 hits, on 1000 games already 25 hits difference. These are the margins that are needed.
But it gets interesting when you look at my long-term results. But this also only after a preliminary consideration. Namely: every game in which a bet is made is a game with extremely divergent assessments. Two reasons for this.
a) Two good players, two (self-proclaimed) experts, meet, one in the bookmaker or provider role, the other in the player role. Both pretend to understand something about it. Both sides calculate that they have an advantage. This means that one could expect that the truth, as with Solomon, lies somewhere in the middle.
b) there are certainly many games where there are also discrepancies, practically speaking there are hardly any exactly congruent assessments. But this does not automatically lead to a bet. If my fair odds are 1.92 and I get a 1.90, then I also have a different assessment. The provider of the odds must, in order to expect a profit, assume a much lower estimate, i.e. a fair odds of 1.82 or so. The only difference is that the difference in our estimates is not sufficient to “persuade” us to place a bet.
So, in the cases where a bet is made, the estimates are quite far apart. Therefore, we go in search of who makes the mistake, the formulation would fit better here: who makes the bigger mistake. But that is rather the result of the consideration that follows here::
If it were the case that the truth lay in the middle, then this truth would therefore be close to the paid quota. Both representatives make a (small to medium) mistake. One, the gambler, overestimates the chance of the party he is betting on. The other, the provider, underestimates this chance. Truth in the middle would result, estimated: neither of the two has a long-term advantage. That would be nice and for many players a desirable goal, namely to be able to play without having a disadvantage. But it is not enough for a professional player. You have to have an advantage to be able to feed yourself. And even if the same applies to both sides: what do I care about the misery of the other in this case? In this sense, we are in the shark tank. Moreover, I always took the view that each of the participants would have the chance to ask me for advice if they capitulated or noticed that I was gaining money from them over a longer period of time.
My long-term result was that the truth did not lie with me. Nor did it lie with the others, the providers. But it was not in the middle either, which, as stated above, would not have been enough for me. Instead, and this is really a very long-term value, it was always in the middle between my hit expectation and my required minimum expectation. And this result has been confirmed again and again.
Note: It’s already getting very philosophical here, just as the whole part of mathematics called “probability theory” is the closest thing to philosophy for me. One can always think about fate or predestination, providence. One considers events to be “random” because one does not foresee their outcome. At the same time, however, one is constantly searching for answers to the question of whether it was really just “coincidence” or providence, fate. Moreover, all events that occur are “irreversible” according to human judgement.
Related to this: I have developed a computer programme that calculates probabilities for football matches. The very question “Are the values correct?” is unsuitable. Perhaps some or all of the outcomes have already been determined, providence, fate. I have no knowledge of this and stick to my values. None of these values can reflect the truth, can be exact. It deviates from reality, whereby a reality in probabilities is none at all. “It only seems true”. Some values are overestimated, others too low. But when it comes to a bet and extremely opposing opinions clash, it seems impossible to me that the truth of the estimate is (paradoxically!) still outside my value. If the value is erroneous, which is actually guaranteed, then of course in the direction of the other. So it follows that for me it was ruled out from the beginning that I could achieve my hit expectation, at least not on the games I chose to play for a living.
After this little digression, now back to “reality”.
Typical numbers look like this, my computer keeps all these statistics. I made a purely random selection, on purpose (unfortunately unverifiable) and wanted to surprise myself with the result. My selection fell on the period from 1.7.1998 to 1.6.1999, so about a whole season. And the result once again confirms me in a positive way. The figures are as follows
Hits expected: 2826.99
Hits achieved: 2758
Hits for par (sum 1/quota): 2659.1
From these figures you can see that these statistics cover quite a lot of games. So I have bet a lot during this time (as in others). The total number of games I bet on during this period is 5576, and the number of bets is 2076. This shows that I made many system bets (more games than bets), but also many individual bets. In 1998, the upheaval in the betting market already began. I made the selection by chance, but nevertheless at the end of my betting time with the traditional bookmakers.
Initially, the figures also confirm that I was in profit. For par I would have needed only 2659 hits, but I achieved 100 hits more. The fact that I was even above the midpoint between my (exaggerated) expectation and the minimum number over this period is also a very good result and essentially confirms my statement above.
But if one still wants to interpret what it means that the statistically determined “truth” lay between the minimum number of hits I need and my expectation, then one encounters the following: The respective provider with whom I ultimately bet the games did, after all, have his own estimate. I do not have the number of this assessment and can only more or less “guess” at it. But it is logical that every betting offer is calculated by the provider with a profit. So the person who pays a 2.0 (just a reminder) assumes a probability of occurrence for the event of (significantly) less than 50%. After all, he wants to earn money. How he calculates his profit is also different for each provider, so that I cannot know this number. So I have to assume some figure, for example 47% or similar for odds 2.0. This reflects the provider’s assessment. This figure added to the above statistic as a total would look like this:
Hits awarded to me by the provider based on their assessment:
(For this figure, I put each individual odds offered into the reciprocal and then subtracted a realistic value from it. However, due to its complexity, I cannot explain the procedure used here).
I was supposed to lose dutifully, as presumably other players would have done, and would have been allowed to reach only the (estimated) hits of 2565 in return. So we have a total of four numbers that we would have to hold against each other:
The provider’s expectation (i.e. the hits granted to me).
The minimum number (from the provider’s point of view, the maximum number) that is likely to occur (from the point of view of the two protagonists), which offers both of them a roughly fair game.
Then my own expectation, which is an extremely contrary number to the provider.
And in the end the “truth”, which was determined statistically, but at least in the long term.
And in the very long term, it turned out that I am 75% right, so to speak, and the providers 25%.
Here’s the (helpless) attempt to make this illustrative:
I divided all the numbers by the number of games bet, i.e. by 5576. This results in a shift of all numbers into the percentage range. I was granted 46% hits, at just under 48% we would have been about par, at 49.3% was the final statistically determined “truth”, and 50.8% I had “dreamed”.
At least you can see that all the figures are in the order of 50%. This suggests that I might have bet favourites and outsiders in the same proportion. Moreover, one has to keep in mind that in the end it is such small percentage shifts that distinguish the winner from the loser. All the numbers are between 46% and 50.91%, a range of 5%. It is in these nuances that the whole business takes place. And: just think, you watch a football match and enter into a contest: one claims it’s 50% Hertha win, the other says: “Nonsense, look closely, it’s only 47%.” How, please, is one supposed to read that? In the long run, there are simply numbers for that. Mine were good (enough).
The number of games may seem very high. Do so many games take place in Europe at all in this period? A Bundesliga season has only 306 games. If you had 20 major leagues, plus cup and European Cup matches, you would certainly get 8000 – 10000 matches, but surely you can’t bet on all of them (with an advantage)? Surely every second match cannot be shown? That is correct. The large number is due to the fact that many games are in several system bets, according to the strategy explained above. The selected and particularly interesting games are played several times. This certainly results in a factor of 2. So, according to a rough estimate, I have bet on 2800 football matches.
Of course, this generally increases the significance. With 100 games, very random results can still occur, even with a few hundred games perhaps. But when the number gets that high, it becomes quite reliable. But I remind you of the statistics (and their operators), who have to prove every statement they make with a probability of error. So anyone who takes my figures as a reliable basis (I could write whatever I wanted) could still only say, as I myself did, “Presumably the man played with an advantage. The large basis of the numbers, however, gives the statement a reliability of about 99.8%, so that it is already more than a conjecture. But I was wrong about 0.2% of the time and the man was lucky after all.”
For those who are more subtle, I would like to make the following comment: Of course, the statistics are minimally diluted by the multiple occurrence of certain games. Because a game that I have won in 5 system bets also appears in the statistics as having been won 5 times. However, as it is the same for lost games, this balances out again. The only difference is that the basic number of games bet on is slightly exaggerated (by an estimated factor of 2). This slightly reduces the reliability of the statement: “I had an advantage.
Note: Here I have only considered the period of one season. Overall, I have been betting in exactly the same way today for almost 20 years. And the reliability of the statement increases steadily as a result.
iii. Expectation of profit
But since we’re on the subject now, I’ll give you a few more figures that came out on the same basis over the same period:
∑ Gewinnerwartung: 208,182.98 DM
∑ Einsatz: 1,649,819.15 DM
∑ Auszahlung: 1,725,049.06 DM
∑ Gewinn: 75,229.90 DM
These figures are already slightly less pleasing. The fact that I actually won over the period is, of course, initially pleasing. But since my hit yield was far above the minimum number of hits for par, one could certainly expect a profit. What is sobering is the fact that the actual amount won was far below the expected amount. That itself would still be “normal”, but it was even below half the expectation. And that shouldn’t be the case, of course, since the number of hits was above half of the expected amount. So I would have had to win at least 104,000 DM, plus the small bonus for being above the middle.
But that’s just the way it is for unlucky people. If you look for interpretations, you only come across very banal ones, apart from the simple “Pg”, as my father used to say, i.e. “bad luck.” And it looks like this: Everything is coincidence. No, no, more like this: with expensive bets, things probably went less well. The distribution of the stakes is after all, for the most part deliberately, flexible. The stakes depend on the odds and the quality of the games. But in the end, there is the decisive factor: it is really random. There is no real explanation except that it can happen. After all, nothing that bad happened. If I were to look at a different period, it might look different again.
iv. Expected goal deviation
There are a few more numbers that can basically prove that my predictions themselves are pretty decent. Here I mention one more figure that gives me a good measure of reliability. And this figure relates to all matches, i.e. not specifically, like the one above, to the matches bet on. For that, though, you should sit back and make a cup of tea….
Everything runs on expected values, as we have seen before. The expected values can always be checked against the actual results. This is also the case with goal expectations. However, the number that I have determined and then statistically checked is the average expected goal deviation, which is somewhat related to the number of the average expected probability (chapter: “Approach to the problem…”).
My program calculates a probability for every possible football result. The sum of all results that represent a victory for team 1 reflects their probability of victory. The basis for determining the individual results are the goal expectations of the teams. These are shown in decimals, as shown earlier. For example, I expect 1.50 : 0.85 goals for the match Schalke – Dortmund. This results in the probabilities for a 2:1 victory, for a 0:0, for a 7:2 or a 3:3. In the event that one of these outcomes occurs, the result is a goal deviation from the goal expectation for the match.
To use the example results from earlier: If the match ends 2-1 for Schalke, the deviation is 1.5-2, expected goals minus arrived goals. So for the home team the absolute deviation is 0.5 goals, + (1-0.85) = 0.15 goals deviation for the away team. The total deviation for this match would therefore be 0.5 + 0.15 = 0.65 goals. Since at the same time the result 2:1 has a certain probability calculated by the computer, multiplying this deviation by the probability of occurrence would result in an expected value. For the result 3:3, the deviations would be much greater, i.e. (3 – 1.5) + (3 – 0.85) = 1.5 + 2.15 = 3.65.
(The probabilities that my computer calculates for these results are like this: the 2:1 comes to 8.95%, the 3:3 to 0.56%).
If you now multiply all possible calculated probabilities for all football results with the resulting goal deviations from the goal expectation, you get an expected goal deviation for the entire game. And at the end you get an actual final result for the match, which in turn deviates by an amount from the goal expectation for the match.
If you use this procedure for all games, then you can check quite well and exactly whether the estimates for the probabilities of occurrence were good. For if I had an incorrect estimate, i.e. an expectation for a match of 2.2 : 1.35 goals, where the truth (unknown to me) would be 1.65 : 1.03, then for each result I would also have an incorrect expectation for the possible deviation that could occur. And this error would add up and gradually lead to recognisable deviations reality – expectation.
For this purpose, I will give you a small statistic that illustrates how small the deviations were. I have taken the last 10 years of the 1st and 2nd Bundesliga as a basis. Here are the results:
Average expected goal deviation: 1.85 goals
Average goal difference: 1.89 goals
This result, contrary to what you probably think, is unfortunately shockingly bad for me. I had expected a maximum deviation of 0.02 goals. Especially in Germany, I thought my numbers were very reliable. Of course, the result standing alone does not have a particularly high significance. It would either have to be compared with an alternative estimate, or compared with other leagues from my database, or even interpreted reasonably, so that one gets a feeling for what such a deviation means in principle. How wrong were the assessments really?
For comparison, however, here are a few more edifying figures for the same period:
These numbers here also give some insight. I expected 2785 home wins, but there were 2823. 1495 draws were expected by the computer, but 1525 happened. The biggest “mistake”, however, was in the away victories. Instead of the expected 1605, there were only 1538.
The picture is confirmed by the goals: Home goals I had expected only 9546, but 9798 arrived. But the away teams also scored too many goals. Instead of the expected 6765, there were 6894. Better results, on the other hand, since the figures are in percentages, for expectations in percentages. Home wins seem to have been well hit, draws too, well, the relative deviation in away wins is also tolerated. Here are the deviations in absolute and percentage terms:
The deviations in percent look quite pleasing so far. Nevertheless, the relative deviation on away wins bothers me personally. Over 4%, that seems too high to me. Has something changed in Germany that my computer didn’t react to in time or appropriately? That’s the professional player in his daily work. Always follow the numbers and think about them: Random deviations or trends whose causes need to be investigated? Is it necessary to react, adjust parameters, improve assessments? Or simply wait for the balance over a longer period of time?
However, I have now at least found the cause for what I consider to be a rather high deviation in the expected goal deviation: the German leagues over the last 10 years have “gone a bit crazy”. This caused problems for my computer, because the goal average was also higher than I expected (deviations 2.57% and 1.87%, also quite high). But since the financial results were not so worrying, maybe I didn’t check these numbers regularly. Maybe others had similar problems?
For comparison, here are the figures from the Premier League in England over the same 10 years:
While there is also a comparable variance in these figures here, these figures are still better. The one indicator for this is that the expected goal deviation here exactly matched the one that arrived. This value was 1.78 goals in each case. Why is the value at all smaller than that in the Bundesliga, where it was 1.85? Good question. But the answer quickly becomes clear: the goal average in England is smaller than that in Germany. While there were about 2.9 goals per game in Germany, there were just under 2.6 in England. A smaller total of goals also results in a smaller deviation. Intuitively clear, I think. It can’t deviate that much if fewer goals are scored. The deviations in percent are still here:
Here you can see why I was better in England. It is the goal average that causes confusion in Germany. It has also risen in the last few years. If there are reasons, I missed them. The computer only reacts according to general guidelines. Foreseeable tendencies (for example rule changes) have to be “guessed” by hand, if possible. My interpretation is clear: the league is going a bit crazy. It’ll come back. Do not react. Let it run. The computer makes the adjustments in the form that has proven to be appropriate in the long term. That’s the way it’s supposed to stay.
In England, on the other hand, the numbers have been sufficiently constant, at least for the goal average. There the computer rejoices as a prophet. There are only slight deviations. I even hit the away goals in England quite accurately. 0.00% deviation.
After studying this chapter again, I am beginning to get the feeling that I have found a good answer to the question that concerns us all: “Is football predictable? And it is: “Yes!”
However, should I ever hear the fondly asked question again afterwards: “Well, you said football is predictable. How will the Dortmund – Frankfurt match on Saturday turn out?” Then I now have the right answer ready:
“I have no idea how the game will turn out. The 58% that my computer has calculated for a Dortmund home win is the highest of the three values. That means Dortmund is the favourite. I can also point out with a certain pride that this value is very close to the correct assessment based on long-term, verifiable statistics. Perhaps even closer than any other you can get. But if you now want to know whether this home victory will also happen, I can at least answer: ‘Yes, and 58% of the time.’ And this statement is valid, with all its consequences. One consequence is this: I would bet on the assessment if the odds were right.”
Are you smarter now?