The Three-Point Rule

This rule is ideally suited to point out a few basic things, especially since the rule itself seems to be generally recognised and not in question, and has thus remained largely unnoticed, so that at this point it is by no means possible to serve common clichés, but rather it is immediately apparent that the considerations made here take a side path, which should nevertheless ultimately be purposeful.

The sub-points listed here are to be discussed, already with their transcription and formulation suggesting as far as possible that there are definitely a few special features that make the study worthwhile.

1) What was the reason for introducing the rule?

2. how long has it existed?
3. the injustice involved
4. the hypothetically conceivable “possibility of manipulation
5. a statistic that is as representative as possible to verify its effectiveness
   6) How, when and by what means should the effectiveness be verified? Did the hoped-for effects occur? 7.
6. an intuitive check and assessment of the effect
7. a little mathematics
8. causal analysis of the statistically determined ineffectiveness of the rule change
9. overall assessment
10. alternative proposal
11. what was the reason for introducing the rule?

Please a) emphasise this point and b) do not deny it. The only possible reason for coming up with this idea could only have been an obvious lack of entertainment, which one wanted to eliminate as fundamentally as possible by increasing the reward for a victory.

The basic idea thus conforms to the general statement made throughout the text: more goals, more action, more excitement are desirable. Football is great, many people love it, play football themselves, as a hobby, in the park, on the football pitch, organised, recreationally, in the amateur sector and one or two make the breakthrough into the professional sector, hats off, earn their living with it, and many more look forward to the broadcasts, the sports show, the Bundesliga, the international matches, the European Cup evenings. But improving can’t hurt in any case.

The idea was born to offer three points for a win. Surely it would be tempting, if the game was tied, to increase the risk, to push the attack, to expose the defence in order to force the winning goal and thus create more spectacle in front of both goals and certainly one or two more dramas? It was simply observed that in professional football, from time to time both sides were satisfied with a draw and the result was boring ball-shuffling, almost like not being able to refuse a friendly “draw offer”, as happens in chess from time to time. Motto: “If you don’t do anything to me, I won’t do anything to you”. More sorrowful: the football and the spectator. “Nothing more happens, we can go home.”

So much for the basic idea and the theory behind it. “It would have to make for more spectacle, and this is what we want, this is what we all want to see, this is what we want to push.” There is hardly any question of denying this insight!

2. how long have they been around?

In England, it has been around for much longer, since 1981, and several other countries followed suit (Israel, Norway, New Zealand, Turkey, gradually).

FIFA introduced it for the first time for the 1994 World Cup in the USA. This was by no means a coincidence, because the USA, as host, had recognised the same grievance and had also tried to implement some other rule changes with the intention of increasing the attractiveness through more goals. No wonder, then, that FIFA “gave in” to minor modifications that had already proven themselves elsewhere to such an extent that at least no damage had been done.

So for the 1994 World Cup in the USA, this little test was quite logical. Apart from that, there is something to be said for the rule in relation to the groups of four. At the 1990 World Cup in Italy, there was a group with the Netherlands, England, Egypt and Ireland. The results in the group phase were: 1:1, 0:0, 0:0, 1:1, 1:0, 1:1. There was only one decisive game, no team scored more than one goal in a game, a total of 7 goals were scored in 6 games and Egypt, as the only loser of a game, was out, due to the rule of the best four third-placed teams, the Netherlands and Ireland progressed with equal points and goals.

Even if it was exciting until the end, because everyone could still get further: a little more action couldn’t hurt. And obviously: these four participants could have had much more trouble advancing to the round of 16 if the behaviour in 1994 had continued. In other groups, the third-placed teams might already have passed them thanks to a single victory?

In any case, the idea was implemented here without having to fear major downsides (that’s just the way it is and, if you want to get further, you probably need a win; no harm done). And, without wanting to get ahead of the statistical part: it has definitely proven itself for the World Cup in the USA. If not statistically proven here, at least from memory: there were a lot of exciting and high-scoring games. Whether this is due to the three-point rule or the other small changes or simply to the spirit of the times, especially in the USA, to be allowed to “play ahead” and thus only want to give the Americans the impression of a little more excitement and action, remains to be seen. This World Cup was fun – let’s say until the final…

From the 1995/1996 season onwards, the rule was officially introduced worldwide for all leagues. 3.

3. the injustice involved

At least it has to be mentioned that the rule brings a little injustice. Two teams fight each other, according to a well-known and desirable pattern, both want to win at all costs, so they have done their bit to underline the meaningfulness of the rule, two late goals are scored, 2-1 and 2-2, and yet both get half a point deducted. Because: actually, mathematically, they would be entitled to one and a half points. The old “division of points” extrapolated to three points.

This punishment is often made clear by the reporters – one must assume that they do this without thinking – that “this point does not really help either of the two”. They hit the nail on the head, but the remark is a) critical and therefore b) inappropriate, but at the same time c) it does not address the causes. “It doesn’t really help anyone” is what they say, which thus underlines this small injustice. Both have suffered a small loss, in the example even “undeservedly” because of their exemplary behaviour. “We have done everything you have asked of us. Why are we now being rewarded so inferiorly?” the protagonists on both sides might exclaim, slightly indignant. “This is mean and not fair.”

The crooked table pictures are also an unattractive sight in the view represented here. Also the impossibility of “extrapolating” anything. 33:17 points or 24:28, you knew immediately. But a record of 9-11-6, what does that tell you? European Cup or relegation? You don’t know. Depends on the other teams, games, results. 38 points in 26 games. Meaningless or only meaningful in comparison. Alternatively, it would have been (once upon a time…) 29:23 points. A much better statement, also, because fairer.

Even for the by no means rare case of match failures, the pictures are by no means easier to read. Some have 25 games and 43 points, others 23 games and 40 points. Who is better off now? We don’t really know. The order is always by plus points, there are no more minus points. Thus, part of the readability has been lost. 4.

4 The hypothetically conceivable “manipulation possibility

If “Aktenzeichen XY … unsolved”, the attention of one or the other crook was occasionally drawn to an ingenious “trick”, and, in contrast to the presumably preconceived intention of the programme to put a stop to criminals, used this trick to hunt for monetary gain, for which the broadcaster would also be responsible, then this small problem of responsibility would simply be denied here. For if the imitation effect should only occur through this text here and no one had previously been made aware of the fraudulent obtaining of an advantage in this way, then it would be most welcome. The responsibility is simply shifted to the rule officials. That could have been thought of and, by the way, the rule is considered to have turned into a dead end at this point anyway.

The little trick would be this – and without making any direct accusation or having a concrete case of suspicion in mind, it seemed to have happened in practice from time to time, as was leaked here and there and under the table or held up to the same — that two teams, which cultivate a kind of friendship among themselves, but at the same time know that in the upcoming season it is only a matter of keeping up with the class, divide the points in a different, superior way to the competing rivals. Namely in this way: “You win your home game against us, in front of your fans, we win ours in front of our fans. Everyone is happy.”

And the effect: double points shared, i.e. 6 divided by 2 equals 3 (in words THREE) for each team. The competition invests much more, both go all the way to win, in first and second legs, neither scoring here nor there, both games 1-1. This counter calculation gives: 4 divided by 2 = 2. So both competitors got only 2 (in words TWO) points for their efforts for the higher effort. A clear competitive advantage for the little rascals with the agreement.

A scoundrel who thinks evil of it.

5. a statistic as representative as possible to verify the effectiveness.

All the statistics available on the subject point uniformly in the identical direction: no effect has been achieved, or, if any, however small, it would be insignificant. Proponents of the rule could merely interject: “Wait a minute, before the introduction of the rule there was a drop in the goal average, since then it has only stagnated. So you see: it has brought a lot of benefits. Otherwise we’d have been averaging less than two goals per game for a long time now.” Yes, if he were right about that, there you go.

Since there are no doubtless statistics (but you should supposedly only trust those that you have falsified yourself…), here is a short review of a few facts. Since these are verifiable, falsifications were not necessary. Here are the values – the draw percentage and the goal average considered relevant — from the First Bundesliga before and after the introduction, extended to three years (this would then be the possible falsifying percentage, in which one selects an ideal period to suit one’s own purposes; here, however, this did not happen either):

Two-point rule

1993: Draw: 29.29% Goals ø: 2.936
1994: Draw: 27.21% Goals ø: 2.918
1995: Draw: 28.10% Goals: ø 3.016
Three-point rule
1996: Draw: 35.29% Goals ø: 2.715
1997: Draw: 22.87% Goals ø: 2.977
1998: Draw: 27.78% Goals ø: 2.879

Average with two-point rule: Draw: 28.20%
Goals ø: 2.957
Average with three-point rule: Draw: 28.64%
Goals ø: 2.857

It is quite clear: the rule has not had the effect it was hoped for. The number of draws has risen, the average number of goals has fallen, and one can gladly describe it as stagnation, which continues to persist. Here are three more recent examples (as of June 2017):

2015: Draw: 26.79% Goals ø: 2.754
2016: Draw: 23.20% Goals ø: 2,830
2017: Draw: 24.18% Goals ø: 2,866

In fact, the draw frequency would have gone down slightly, but on the other hand, the goal average would not have gone up. Sure, the Bundesliga is booming and it’s just not an issue, boredom. “Draw shenanigans” do not exist – however they ever did. Nevertheless, the overall verdict remains: the introduction of the three-point rule has had no discernible effect on match behaviour (to be read from statistics).

It seems helpful to compare at least one other league. The second German football league is a good example. Here are the figures before and after the introduction of the three-point rule in the 1995/1996 season, for three seasons each, analogous to the First Division:

Two-point rule

1993: Draw: 30.04% Goals ø: 2.618
1994: Draw: 30.26% Goals ø: 2.500
1995: Draw: 33.33% Goals: ø 2.816
Three-point rule
1996: Draw: 26.14% Goals ø: 2.584
1997: Draw: 30.39% Goals ø: 2.686
1998: Draw: 32.45% Goals ø: 2.534

Average with two-point rule: Draw: 31.00%
Goals ø: 2.632
Average with three-point rule: Draw: 29.66%
Goals ø: 2.601

In the second league, therefore, the number of draws would actually have decreased slightly (in total, 12 games out of 918 were saved in draws; this would be negligible or simply subject to other statistical fluctuations; in other words, the statistician would have to classify this deviation as coincidental and not be able to attribute it to a rule change).
The goal average has not risen over time anyway, so that at least this (assumed hoped-for) partial effect has not occurred.

Alternatively, here too are some more recent examples:

2015: Draw: 31.69% Goals ø: 2,493
2016: Draw: 28.10% Goals ø: 2,640
2017: Draw: 28.75% Goals ø: 2,486

These examples also prove: nothing has moved. The average of goals slightly lower lately. The number of draws has risen slightly, i.e. the opposite of the hoped-for effect.

Now we are urgently called upon to investigate the causes: why does the lure of the possible three points, which would so significantly increase the value of the one point currently in hand in the event of a drawn match, not have any discernible effect on the pitch?

6. how, when, by what means should the effectiveness be verified? Did the hoped-for effects occur?

Most of the section here is based on interpretation. The rule is simply no longer discussed. Think about it, check what you want, we are no longer interested, end, over, basta, your FIFA.

“Has it proved its worth” no longer seems to appear in the list of questions. But shouldn’t it, on reflection? What did we have in mind and to what extent does reality correspond to it? Have the goals been achieved or do other measures have to be taken?

After all, the following review of effectiveness has been encountered here and there. Namely, that the three-point rule allegedly “had no effect”, “calculated” by some statisticians. However, this was accompanied by a very strange explanation as to why they wanted to establish this. The reasoning was as follows: the table pictures would turn out almost identically, regardless of whether they were drawn up according to the old two-point rule or the three-point rule.
This analysis stands out for its complete lack of substance. Some self-styled statistician once checked the tables – i.e. created them as if they were calculated with two points or with three points – and found that there were only very slight changes.

Yes, even if there were, – unchecked here – was that to be read off somewhere as a default? Did they just want to mix up the tables with a random effect to make it a bit more fun?

No, there is nothing to be seen of that. It was about increasing the attractiveness – any instruction in a different direction is also gladly accepted by the official side –, more suspense in the closing minutes and generally more goals. All the entertainment values called for in the overall text, while respecting sportsmanship, the competitive character, fairness and justice (even if the latter is slightly violated at this point, but generally accepted and, since it is equally valid for all, accepted).

All in all, it must be stated that the meaningfulness of the rule is not seriously examined, and ever has been, by the official side, that the conscientious examinee – supposedly available here – however, encounters absolute irrelevance – which, by the way, was the result even in the completely inane analysis mentioned, there probably more by chance.

Football was as it was and is as it is, old or new scoring, and the differences if at all reduced to nuances and if, not induced by the rule, thus subject to general other developments.

This inevitably raises the question of the cause of the ineffectiveness.
Nevertheless, the intuitive analysis of the situation as well as the brief detour into mathematics are sent in advance. 7.

7 An intuitive examination and assessment of the impact

Of course, one may simply ask oneself: has something been done? Does one see an induced offensive spirit since then, has the number of dramas or spectacles experienced increased? Do you hear coaches talking about “deliberately increasing the risk” because they were desperate for a three-pointer?

It does happen from time to time that sometimes one team, sometimes the other, sometimes even both teams play more forward and that even a commentator recognises: “Both want the three-pointer”. But such games would have been seen earlier (whether one becomes two or one becomes three: more is more and even the smaller gain is a gain). Moreover, they are often games of the type “high favourite against clear underdog”, and the higher favourite then naturally wants the victory anyway (but also wanted it in the past), with which the spectacle would go in the desired direction (forward! ) and occasionally it happens that players on the pitch sense – the coach may also have recognised this and instructed his players accordingly – that the opponent is now soft or weakened and that it is now worthwhile to step up the forward gear (even substituting an offensive player, although still the bird in the hand, which is proverbially said to be better here and there than…).

There were exciting games in the past, and there are still exciting games today. But there was and is also the opposite: the score is even, there is nothing going on and no one is thinking of doing anything about it. No recognisable, noticeable, sustainable change can be observed. At least none that went in the direction of the intended increase in tension.
If one is also looking for a positive way of expressing this: “Everything could have been much worse. We succeeded in stopping a downward trend. The preservation of the condition was aimed for and has occurred.”

8 A little mathematics on the subject

For reasons of deterrence, I would like to emphasise: just a little bit of mathematics: it would be worth the risk to go for the winning goal in an even match – irrespective of other considerations subordinate to table or seasonal goals — if the distribution of chances to score a goal versus to concede one were in the ratio of 1/3 to 2/3.

The simple reasoning for this: 1/3 wins you two points, 2/3 loses you one. The multiplication of the values, thus calculating an expected value, would result in: 1/3 * 2 – 2/3 * 1 = 0. This would be the famous zero-sum game. Accordingly, it would not matter which one was chosen. In one third of the cases in which one scored the winning goal, thus deciding the game in one’s own favour, one would have made three points out of one point, in the other two thirds one would have conceded a goal and thereby only forfeited the one point.

It would be an equal ratio provided that the chances are split 1/3 to 2/3. As soon as the chance for one’s own goal would be more favourable than this one third, the deal would be worthwhile. And basically one should assume that it was about 50% for both sides, so guaranteed the risk would be worthwhile?

Now you probably have to know football as a whole a little better to find answers to this question, in search of why the risk is not increased? This search reveals two conceivable answers.

The first possibility, purely related to the distribution of chances: every coach knows – and transfers this to the players – that the term “increased risk” is not pure fantasy. The risk of playing on the attack, of trying to score a goal, is not possible without the risk of conceding a goal. This risk, however, increases proportionally more — depending on the size of the offensive alignment entered into — than the chance of scoring the goal (hence: “increased risk”, otherwise it should just read “risk”; chance increased here AND increased there; a little gambled, but no disproportion).

There are even a few more exact calculation possibilities, but these would be too complex and would clearly go beyond the scope of this article (and probably put the reader to sleep). In this respect, an estimate is given here, which may correspond to the actual distribution of chances, always assuming that we are dealing with two teams on roughly equal terms: the distribution of chances would not be 50 : 50, nor 33.33 : 66.67. It would be somewhere in between, with 40 : 60 probably being the best approximation.

However, this estimated 40% per own goal would still be in a dimension that would make following up mathematically sensible or actually necessary. Anyone who didn’t would be stupid. Just to put this into the simple formula and calculate the gain in expectation: 40% * 2 points – 60% * 1 point = 0.8 – 0.6 = 0.2. So you would mathematically gain 0.2 points if you took the risk: 40% with success, a win, 60% a failure, a defeat. Well done, more out of it.

Even if all these calculations and considerations were guaranteed not to have been made on the part of the officials when the rule change was agreed: they would still have made a “sensible” decision: “We want more goals – we get more goals.” No matter how the mathematician would have calculated this afterwards.

So it’s time to get to grips with the

9. research the causes for the statistically determined ineffectiveness of the rule change.

of the rule change.

Now, one may first assume that even mathematically educated coaches do not really go so far as to carry out this risk/benefit analysis. Decisions are made intuitively and one knows that one can’t be that wrong. And in fact, a closer look shows that intuition delivers the better results.

Of course, this must sound strange at first – for anyone who has thought this far along. Mathematically right to take a risk, intuitively right not to? And it is precisely mathematics that has an “infallible” quality?

This is not the case in the present situation. However, first of all, there is a very important preliminary consideration that plays a huge role and would alone suffice as a justification. It goes in the following direction:
The media are known to be “to blame for everything”, which is true, but should better be expressed this way to leave sarcasm and polemics out of it: they take a high responsibility for what is discussed. They make a kind of topic pre-selection and direct their focus where they would like it to go, but in doing so they achieve – intentionally or unintentionally — that exactly this topic pre-selection, this scene, this situation, this game, this decision, this coach discussion to dismissal at the regulars’ table, translated thus: by everyone, becomes the “big talking point”.

The bottom line: the losers are not and do not remain losers and are treated as such, portrayed, questioned, made fun of. There is no such thing as “well played”. There is only “good result achieved”, whereby the means used – which, at least these days, are increasingly being labelled “dirty” -, the achievement of the result, the course of the game, are no longer questioned. There are only beaming winners who did everything right, and by no means ever tragic losers because, in a kind of tautology – see result – they demonstrably did everything wrong.

The coach does not want to end up in this state of “having demonstrably done everything wrong”. To put it quite simply. The players take this on, but their position – apart from the chair placed in front of the door – is not particularly superior to that of the coach. They have also drawn the card with the fat “A…”, provided there is a defeat on the books.

These two main representatives (players, coach) for the direction taken on the field thus decide to subordinate themselves to the maxim that the media set with their way of reporting: “Any result is fine. Except a defeat.” Losing is forbidden. You’re gone, your place in jeopardy, your chair sawed on to off. Three points for victory? Yeah, on TV, maybe. No point at all, and certainly not a “risk” taken for it. Coach’s instructions: “Stay at the back and keep it tight, a point is a point. Player: “We would have done the same. But thanks for the tip.”

As much as this phenomenon would already suffice, two more occur in total. Amazing? Surely so.

The first only very briefly touched upon. It is possible that it would be too obvious, but it is also conceivable that its very simplicity means that it is readily overlooked – and of course completely disregarded when the rule was introduced. Here is the psychological impact, responsible for the statistically invisible impact of a change:

The three points awarded for a win do not only apply to even scores, where an increase would be mathematically worthwhile, but, at the same time, is successfully suppressed by the media. It also applies to narrow leads (it ALWAYS applies; the final result is calculated afterwards, the course of the game is irrelevant anyway). As soon as a team has scored a single goal (the answer to the question: “What’s the score in a football match?” is “0:0” and, in the other cases, “1:0”. In any case, regardless of the actual level of knowledge, this would give them the highest score), they immediately switch over: “Everybody back, on the goal line, we’ve got the three-goal lead and we mustn’t give it away again under any circumstances”. Compared to their earlier 1-0 lead, they now had a lot to lose. Mathematically twice as much.

Not only the players and the coach can make this simple calculation – even if not in the form of a calculation but intuitively – no, even the fans carry this behaviour, also calculating this greater effect of the three points into their support. In the past, a leading favourite would not have been allowed to switch gears at all in a home game because the fans didn’t want to see it. Reverse gear, at home? We don’t. Today it’s standard industry practice. Whoever leads defends. Automatically and almost without alternative, assuming teams are still at eye level – which, however, is where an increasing number are. Wolfsburg, HSV, Cologne, Werder, Hertha, Gladbach, Schalke? These are just a few: who is better? If at all, very temporarily this one or, no, this one…

It means for the overall calculation: one has not only implanted an offensive spirit or at least made the attempt, but at the same time the defensive spirit. It is therefore conceivable that the offensive spirit would have grown, that there would be more games that offer an increased spectacle when the score is even. However, these are directly neutralised by the counter expression “We lead 1:0, Scots close!”.
This effect, too, is such that the rule change (so obvious) could/should/must have been dispensed with, but other ideas are needed to remedy the recognised grievance.

Now, however, one last point, which perhaps provides the ultimate answer:
There is a well-known phenomenon which might be known as the “prisoner’s dilemma”. Here, two prisoners are offered a complex deal, which will not be explained in detail here. Confessing or denying are the possible choices and in each case there is a punishment, but depending on what the other has decided. An “optimal strategy” may exist, but practical experiments have produced curious results. Should we try to work together or compete against each other? Decisions are made independently of each other and without collusion.

The explanation already given here perhaps already leads a little too far. In any case, there are precedents for the behaviour cited below that illustrate this problem.

For a football match between two teams on an equal footing with the score tied, this description, which is similar to the dilemma, applies: in purely mathematical terms, both would know that it was worth playing to win. However, it was even more worthwhile to let the other use his mathematically correct calculations and apply the counter-strategy himself. The motto was: “Let them come quietly, then WE will score the goal.” Since the distribution of chances, as explained above, favours the defensive team, it is wiser to let the opponent make the first move.

As a small justification for the advantage that the defending team would have: as a rule, it gets fewer chances – the opponent is attacking, after all – but the chances that arise from the counterattack situations are incomparably greater and exceed them – depending on the offensive readiness of the opponent – in the total sum of size. Mathematically, this means: 30.2 is greater than 80.05. The one has eight goal-scoring chances with little exploitation potential, the other only three, but these are large. Mathematically, in the example, 0.6 is greater than 0.4. It is a coincidence that it adds up to 1, but one team scores 60% of the time (the defensive side), the other 40% (the one that takes the initiative).

The behaviour of the two teams can therefore be interpreted as a kind of “stalking”. “You know you have to come, don’t you?” “Yes, we know, but so do you.” And nobody does anything. Wouldn’t that be the wiser decision, after all? Dilemma is dilemma, doesn’t help here, there is no way out, it remains as it is and always has been. Grapes are hanging somewhere, but pretty high up. Dove would also be there, but just on the roof, while the sparrow is reliably in hand and you can’t get the dove without first releasing the sparrow.

10. overall assessment

The rule has brought nothing, the injustices and possible manipulations remain as disadvantages. The justifications have been found and are conclusive in sum anyway – even if this or that is more effective than the other — to explain the ineffectiveness of the rule. An overall picture emerges: away with the rule. It simply does not work. If one had a good intention, then one has chosen a well-intentioned but ineffective means of fulfilling that intention.

11. alternative suggestion

There are the simple means mentioned to achieve the goals set. There should be more goals? Then take a look at the rulebook and start applying it fairly by giving equal treatment to strikers and defenders and come back to the US proposal: when in doubt, give the attacker the benefit of the doubt. Initially, this would only apply to the ubiquitous close offside decisions and foul situations in the penalty area. Extended to all game situations, it would be tantamount to a revolution. Great games, beautiful actions, shots, dribblings, goals guaranteed. Equal treatment (which in itself is self-evident) would be completely sufficient. The USA had only suggested the passage “in case of doubt for…” because they had noticed the disproportion in the decisions against the attackers and wanted to ensure at least a 50/50 error rate for/against the attackers. Otherwise, it would have been sufficient to simply point out that offside is a recognised rule, but that it should be applied correctly. Instead of “in doubt for the attacker” it could also have read “please always apply correctly.