Wanja talks to his children, today about…
The rule of three points
“Maybe there were people on Earth who seemed to have noticed something from time to time after all,” Wanja opened today’s round. “You mean there was something wrong with the rules?” asked one of the boys. “No, well, this time I meant more that it was too bland for many, that there could be a bit more goals, more action, more excitement. Although that seemed to be of little interest in principle. Arguments like ‘it’s always been like this’ and ‘football is so big, you shouldn’t, actually you shouldn’t change anything, otherwise it might shrink’ had, even if not necessarily expressed like that, the idea was only in the heads, but nevertheless they had the right of way. Perhaps the original thought summed up: ‘football is only so big because we’ve always left it like this.’ There was no reason to change anything fundamental.”
“But that’s understandable, isn’t it?” objected one of the children.
“Hmm, yes, in a way it is. But still, it could have been noticed at some point that at least the discussions on important decisions could not be contained, not even with the supposedly so reliable video assistant, who finally provided for justice. So there were signs that it might be worthwhile to take a closer look at where the problems came from. But before we do that, could we summarise the core issue again?”
“Well,” the eldest took the floor again today, “offside and penalties were the critical decisions. These were the most likely to result in goals. In numerous attacks in the dangerous zone near the goal – that is, the penalty area – there were constantly situations in which one of the two decisions was at least up for discussion: wasn’t a striker a foot’s breadth closer to the goal than two defenders, was the brief tugging, pulling, holding, blocking, tugging, pushing that constantly occurred sufficient for a penalty kick?”
“To the point. And, what was the general interpretation?” “If it was close, it was offside – and it was always close – and to the other question the answer was ‘no, it wasn’t enough in that case’. But when it did happen, there was heated discussion and the decision was often deemed ‘too harsh’, which subsequently meant that the defenders were allowed a bit more and the referees were even less likely to point to the spot. We understood that, didn’t we Dad?”
“Can’t put it any other way. But there was a deeper problem here….” “….that there were so few goals that any one of them could decide the game and was therefore scrutinised even more critically to see if everything was going right”, the youngest continued this time. Vanya was amazed.
“But two other things could be observed. Who can help me with that?” This time there were questioning looks. What did he mean this time?
“Well, one was always allowed to wonder who actually had the main interest in obstruction in the tougher and tougher duels?”
“Oh, that’s what you mean. Even when the duels could be described as ‘hard’ to later ‘over-hard’, there was the aggressor, the one who opened the rule violations. I remember,” the middle man said this time. “It was the defender. The striker reacted to it – and yet his corresponding counter-behaviour was punished, but that of the defender was generously overlooked, passed over.”
“Exactly. But at the World Cup in the USA, there was a good idea to do something about it. Because the problem was recognised much earlier there: we need more goals.”
“Right, right, now I know,” the youngest took the floor again. “When in doubt, give the attacker the benefit of the doubt. That was the idea.”
“Another hundred points for you. It was initially only related to offside – since the nervous arms of the assistants at the line were probably the first thing the Yanks noticed unpleasantly — but it would also have made perfect sense in the case of foul play or handball. Because here, too, it was mostly the defenders who did not follow the rules at first. Also in hand games, it happened to the striker, if at all, sometimes unhappily, while the defender deliberately widened his body and hoped – often with success – that the referee, if the ball touched his arm, would judge this as unhappy, which, conversely, he never did with the striker.”
“Ok, it was just a repetition, but it can’t hurt to remember it now and then. So someone did seem to notice something and an idea was conceived: we award three points for a win, and one per team for a draw. Is that a good idea, do you think?”
“We don’t have that here, what’s the point? But at first glance it could lead to more spectacle, more goals to see? At least it seemed to be an attempt.”
“Yes, that’s probably how it should be. Whereas to that end, after the rule was introduced, you hardly ever heard that anyone cared or even cared anymore. What did it bring about, were the games more exciting, were there more goals, was there less ball-shuffling and fewer draws? I would have loved to ask a FIFA official about this. But it was really strange that they just changed a fundamental rule on a whim – but never looked at the consequences?”
“Yes, that sounds incredible. But tell us: what good did it do?”
“Nothing at all. That is the result of my analyses. As an example, I made the statistics for the Bundesliga from 1993 to 2019. Here is the diagram:”
And Vanya had made statistics for many things. He was, in former times, on earth, one of the first who had made statistical models with which forecasts could be made, with which probabilities games turned out one way or the other and even fed himself for many years by successfully betting on the games. His calculations were simply far superior to the more intuitive bookmakers and betting providers working at the time. So the children had known about such things for a long time. But that didn’t mean it was any less interesting.
“Could you guess from this graphic when the three-point rule was introduced?” “Hmm, I don’t think so,” the children said almost simultaneously, but at least in the same sense.
“No, the goals sometimes went up a little, sometimes down a little, usually something like just around three goals per game…” “What, so few? And people enjoyed that? I can hardly imagine that,” once again the youngest interrupted.
“No,” Wanja could only agree, “it wasn’t that much fun. You could compare it to a caveman who has never seen anything but his cave and therefore doesn’t know how beautiful it is in the sun. If he were to step out just once, he would question his entire previous life. So he would even stay inside if he had the chance and someone raved to him about how beautiful it was outside.”
These kinds of comparisons forced you to stop and think about it for a moment, but nevertheless they made the situation vivid once you grasped it. Earthlings knew nothing about how beautiful, exciting, entertaining football could be. And change anything? They were kind of panic-stricken about that. Just don’t leave the cave!
“Sometimes there were a few more goals, sometimes a few less, very rarely more than three per game, but the German Bundesliga was even ahead of other leagues in that respect, because there were even fewer goals. But that doesn’t belong here. It is also difficult to see any development in the number of draws. Incidentally, the rule was introduced in the 1995/1996 season, which is exactly when the number of draws started to rise. To a peak never reached before or since. Curious, isn’t it?”
“That would mean that the players and coaches didn’t understand the rule at all?” “Something like that. Later it returned to normal. It fluctuated around 25%. You could say it was inconspicuous overall. As far as the draws are concerned: hardly any effects, but if there were, they would probably not be the desired ones? After all, one did not hear any comments. The rule was introduced and then left unnoticed, uncommented. But it can be assumed that they were actually hoping for more goals, right?”
“That would be the assumption,” the elder said. “If it had been about more spectacle or more action or more attacking momentum or more enterprise, then surely that too would only have had to be reflected in goals at some point, and to that extent could have been verified? Wouldn’t it be nonsensical to introduce the rule, hope for more, let’s use one of the terms, action, get it, but the goal average would remain the same? They would both have tried harder – but not succeeded in doing so?”
“Very perceptive. Yes. It should have actually and theoretically translated into more goals. That’s why here are these statistics:”
“Now that you know when it was introduced, the question of recognisability is not applicable. Only two seasons with the old rule are recorded here, but there you can see that there tended to be slightly more goals than in the sequel, with things going up a bit in between and at the very end. In general, one would also conclude from this graph: the three-point rule didn’t bring anything.”
“That is evident. So if you had wanted more, you would have had to review, at the latest after a few years, and look for new means to achieve the goals. Surely that’s what you’re trying to tell us?”
“Caught. And the means were actually obvious. But now let’s not start that again. The questions that still preoccupied me were: why didn’t it have an effect? There must be a logic behind it?”
“Maybe the practitioners just didn’t understand how to handle it properly? But you said ‘questions’. That has been only one so far. Please name the other one. What other questions could you ask?”
“Very clever fellow. The other question was about justice. Does that make any sense?”
“Um, yeah, sure, you can always ask that one. Only in that case : what could be unfair about a rule that is the same for everyone? It’s just the way it is now and it applies to everyone. Full stop.”
“Here, too, you have to think one step further. But first I would like to comment on why the rule failed to have its effect – where you had to think up the effect yourself. I have often asked people about it and somehow they were already puzzled by the question. This is probably mainly because you never heard anything about it in the media. And most people – whether they wanted to or not – were so influenced by the power of the media that they submitted to its dictates. The three-point rule is like that because it is like that. Nobody talks about that.”
“That also makes sense, but it still doesn’t answer the question of impact or lack of impact?”
“Well, when you think, you just pass by this or that consideration and deal with it. But still right: I digress a bit. The rule did nothing for several reasons.
A first one was that coaches often had to fear for their jobs after losing games. Especially if it was two or even three in a row. Draws – somehow everyone knew that – didn’t get you any further, as it was always so nicely and self-convincingly put, but you could count on continuing your job. If you won the fourth game after three draws, it would even mean: ‘unbeaten for four games’. A success story. The coaches’ goal was not to lose. The promised three points, if you risked something, could cost you your job. Nice and cautious. That was the tactic. Passed on to the players, implemented by them like that.”
“Yes, that makes sense. Although we don’t hunt down coaches here. But we’ve already heard about that. Are there any other reasons?”
“Yes, absolutely. Another is that man has a certain disposition. According to this disposition, one has a certain dormant potential that one cannot reach in this way. But this potential suddenly shows itself when you panic. Many people have already mastered things in panic that they could never repeat or demonstrate in this way and they themselves or observers also cannot grasp how such a thing is supposed to be possible. You develop powers or an energy that you didn’t know about before.”
“Yes, we have heard of this before and have even experienced it ourselves.”
“So you don’t have access to this dormant potential, but it’s obviously there. Some of that potential can be accessed when you’re behind, even just in an everyday football match.”
“Yes, that’s true. I’ve noticed that already. As soon as my team is behind, there is often a jolt through everyone. ‘Now put some effort into it or we’ll lose the game’.”
“That’s exactly how it is. Even if it’s only parts of this potential: there are situations in life in which you can access parts of it. The more urgent the matter becomes, the more of the potential can be called up. And: this happens rather intuitively, not really consciously controlled.”
“That’s clear so far. But what does this have to do with the three-point rule?”
“Quite a lot. Because: when a game is tied, in normal league play, then both are always satisfied to that extent. The players, too, regardless of the coach. They don’t get any access to the panic potential I mentioned earlier in such a score.”
“We can also follow you that far now. Yes, that sounds logical. In fact, I can also confirm this from my own practice. As soon as you fall behind, you pull yourself together – which then finally activates these parts of the potential. If you achieve the balance, you are happy, but fall straight back into the old ‘satisfaction pattern’. All is well again.”
“Exactly. You just come to it when you think about it. So that means: three points for the win or two points for the win: people just don’t let themselves be duped by a random idea. You want to offer the spectator something, but you’ve done the math without the host. The host — in this case man — won’t let it be forced on him. It was a failure, even from that point of view. ‘It’s 1-1, now work twice as hard, you can get an extra point.’ ‘Fiddlesticks’ is the answer you get. “
“Yeah, all right. It was a pipe dream. Any more reasons?”
“Yes, in fact there are TWO more reasons. You’re amazed, aren’t you?”
“Well, first you have to convince us, then we might be amazed.”
Vanya already had a couple of understanding children who kept exposing him to his own lack of logic.
“Ok, smarty pants, then just marvel only after I explain it. The second reason that only comes to mind when you take a closer look, especially when you observe the behaviour of the players on the court at certain scores, is this: the three-point rule not only applies when the score is even, it also applies when the team is leading. What do you conclude from this? And, wise guy, I already said that.”
“Hmm,” the middle one pondered aloud — unquestionably the eldest often let the younger ones go first, even if he would also have known an answer — “so it’s 1-0, as you say a typical score. If the score was equalised, then the leading team forfeited TWO points and no longer just one, as in the old rule. So they had much more reason to hold on to that score. Instead of seeing more attack, with a score like that, they actually saw more defence! Eureka!”
Yes, his sons could be relied upon. That was exactly what happened. You had to watch for a good while to figure it out. But eventually it became obvious and once you had the thought, it wouldn’t let you go. It was 1-0, let’s say, for the home team, and it became a veritable defensive battle, which even the spectators accepted as it was, because they too knew, without having to say it, let alone consider causes or even question them, that it was imperative to hold on to the three-pointer. Always assuming – taken for granted but not the case in Putoia, on the contrary — that ‘football is purely a results sport’, for which the media bear the main responsibility.
“Ok, we are already astonished a bit, but we are sure that you will give us another reason in a moment,” this time the eldest spoke after all. “What is the final reason?”
“I’m glad you asked. At this point, strangely enough, we can’t quite do without mathematics. Are you ready?”
Vanya had already passed on quite a bit – if not a little more – of his mathematical disposition to his children. They were ready and indicated it with expectant nods.
“Since, purely theoretically, you can win more than you lose if you play to win in a draw, as the three-point rule should tell you to do, then it’s clear that you should increase the risk of that – purely mathematically.”
“Yes, I know that. If you can lose one point but win two, the chance would have to be at least a third that you score a goal versus the chance of conceding one.”
“Right. But you still have to know now that the calculation wouldn’t work out that easily yet. Because?”
The youngest continued, “… because, as you always say, the defence had the advantage and so the chance of scoring a goal versus conceding one was much less if you opened up the defence and played on the attack.”
“Absolutely right and listened and paid attention well. It was actually the case that playing on attack was actually even a little bit stupid – as was becoming more and more apparent. The good coaches always played each other as favourites before important games because they hoped that they would not be forced to play on the offensive, as they at least signalled to their fans. If the others were favourites, THEY had to make the play – and we score our goals from the counter-attack situation. All this was related to the fact, as your brother just said, that the defence always had the advantage, also from the interpretation of the rules.”
This thought had to settle first. Then Vanya continued: “Nevertheless, it could be that, from a purely mathematical point of view, it was wise to go for the winning goal when the score was 1-1 and, let’s say, there were still fifteen minutes to play. The chance was not about 50% of scoring a goal versus conceding one, nor was it less than 33%, as you minimally needed to make it worthwhile. It was something in between. This a purely theoretical consideration, but if it was maybe 40%, then it would have been worth it, wouldn’t it?”
“Of course,” the elder calculated directly. “At 40% you gain two points, so 0.4 * 2 is equal to 0.8, at 60% you lose one, so let’s subtract 0.6*1 = 0.6 from the 0.8, you are left with 0.2 points, which you gain on top.”
As a maths teacher I would have to say “Perfect”, but it’s still not quite right. Who knows what little detail needs to be corrected in this calculation?” Vanya waited for a moment, but this time no one could help out. Surely it wouldn’t take much longer…
“We have calculated that the chance is 40% to score a goal versus that to concede one. But it does NOT include the chance of NEITHER scoring one nor conceding one. But these cases remain the most frequent. So: not playing attacking football did not mean giving away 0.2 points, but much less, as correct as the calculation remains. But that would only be a small mathematical addition either way. What remains important are the consequences or the behaviour triggered by them. Mathematically, it seems to add up, which even the coaches possibly knew. Yet they didn’t – and I’m not talking about the previous reasons, but a separate reason here.”
Still no answer.
“So: if you actually had to open up yourself, play forward, because it pays off, then you would still make a small compromise, because you would allow the opponent a higher chance to score a goal on his part. You could put it this way: the first to attack is the stupid one. Because: the opposing team then has the remaining percentage for itself. The surplus. You score a goal 40% of the time – in all the games you score one at all – and the opponent 60% of the time. But this applies to BOTH teams. Increasing the risk would remain mathematically correct, but at the same time you would give something to the opponent. This is similar to the Prisoner’s Dilemma. BOTH would have to behave stupidly, from their point of view, in order to get the best chance TOGETHER. Kind of like football. Both would have to say: “We should attack now, but the opponent should do the same, provided he knows the laws of mathematics? So we wait and see. Both seem to behave cleverly, but then together they don’t. It’s a dilemma. It’s a dilemma. There is no way out of it. The consequences can be seen in the statistics: the three-point rule is useless. For several absolutely conclusive reasons, listed here.”
Yes, the children had now understood that too, and although they didn’t say it, you could see that they were once again amazed.
“On the point of justice, enough has actually been said overall: the rule is not just, in any respect, but it was already enough to abolish it for the other reasons mentioned. There is, nevertheless, the additional aspect that, for example, in the case of a 1:1, both teams submitted to the intended effect of the rule change and actually both played offensively. That still happened, of course, but it was no more frequent than before, let alone the rule. Every now and then they just played football that way and, above all, to pursue the aim of the game, which was to score goals – apart from that of entertaining the spectators, which was best done that way –. So both wanted the winning goal. The perfect implementation of the rule. Both manage to score a goal because they went for it and trusted the rule. They meet at 2:2. They did everything right, followed the rule, but nevertheless they are now penalised with a half-point deduction. Because actually both should get one and a half points. Or just one, if the winner got two, like in the past.”
“Yes, that’s a bit unfair, that’s true.”
“And there’s this thought, which observation forced on you a bit: imagine two teams, both of which are playing against relegation. Now they are fighting each other on equal terms in first and second legs. They both go all out, but both games end in a draw. Each has TWO points on the account, from the two duels.
Two other teams in a similar situation decide in advance: ‘You win your home game, we win ours. Deal?’ ‘Deal!`. Both now have THREE points on their account – and a lot of energy saved. It’s certainly happened here and there and is only due to the nonsense of the rule. So, now get out there and play!”
The boys didn’t have to be told twice….
