1) Review of the matches
Results of the 20th matchday
Bayer Leverkusen – Hannover 96 2:0 (2:0)
Werder Bremen – FC Bayern Munich 1:3 (0:0)
VfL Wolfsburg – Borussia Dortmund 0:3 (0:2)
- FC Nuremberg – Hamburger SV 2:0 (0:0)
FC Schalke 04 – TSG Hoffenheim 0:1 (0:1)
FC St. Pauli – 1.FC Köln 3:0 (2:0) - FC Kaiserslautern – FSV Mainz 05 0:1 (0:1)
VfB Stuttgart – SC Freiburg 0:1 (0:1)
Eintracht Frankfurt – Borussia Mönchengladbach 0:1 (0:0)
General assessment:
It is certainly permissible to ask (from the reader’s side) which core statements one intends to concentrate on. It is equally clear that these will emerge if one actually reads all the texts offered. So if a reader only glances at some of the texts, he or she may very well miss what they are actually about. For the match reports, you have the Sportschau and the Kicker, otherwise you have probably long since realised that only Borussia Dortmund can do it this season and that it is a season full of surprises, but that these are perceived as doing a lot of good, unless you are a Stuttgart or Werder supporter …
Apart from that, the confirmation of theses made elsewhere (which are of course available in texts and would be made available to those interested) is sought in a very general way. Today, a brief summary of what should be emphasised here, i.e. what is the occasion for the author:
1) The German Football Bundesliga is very eventful, exciting and rich in goals. This can already be recognised and felt without a comparison, but can be emphasised even more in a comparison with other countries. This perceived excitement should be made measurable at some point.
2) A few measures of this were presented. One measures the disorder in the table by calculating the deviations of each team from its expectation.
3) These expectations are “only” calculated by a specially developed computer programme, but they have proven their reliability in the betting market over 20 years. There are also a few figures that are suitable to prove this reliability. This is introduced, explained and prepared very carefully and gradually in the texts.
4) Foreign countries envy the Germans this tension, as it is not found there in the same way. The table pictures are much more uniform, in line with expectations and therefore also more boring. This also includes the question of the essential decisions, which is perceived as much more open in this country (abroad).
5) The German “flood of goals” has causes and consequences. Of course, a certain tradition has long been identified as one cause, since it has always been like this and is therefore easier to maintain. In addition, however, there is the very positive performance of the Germans (specifically for this season) at the 2010 World Cup, which set certain standards. Domestically, of course, this positive, forward-looking game is used as a model.
6) Whether this “style” will prevail will be seen on the international stage, where at least no downward trend is discernible. So: Offensive football could be on the rise again and possibly stand for success after all, in contrast to the almost decade-long development that has produced more and more pure results football.
7) Nevertheless, the theses stand: As soon as decisions are made, tactical considerations become more and more important. This inevitably means that there are fewer goals, because people are not prepared to free themselves from tactical constraints. Even teams with nothing to lose in the table are starting to think more conservatively. The time of year with frosty temperatures at that stage as well as worse playing conditions also contribute.
8) Referees are very much adjusting to the importance of results. They do not want to be held responsible for any tragedies. Here is a very important thesis in this context: A decision that prevents a goal or does not allow a goal is not perceived as dramatic, if wrong, whereas there is a huge outcry if a wrong decision results in a goal. As a result, the referees very often decide for offside, for a striker’s foul, and against the penalty kick. This contributes to the lack of goals and, unfortunately, to the reduction of tension.
9) Because: Goals create tension, and in fact, here is another thesis, the more goals, the more tension, and here, even when resistance sets in (“No, why, I don’t think there should be too many goals, then it gets boring. Handball is no fun either, but if you want to see goals, go there. I’ll stick to football, because the one goal you’ve been waiting for for a long time makes you really enthusiastic: Such “saturation” (analogous to a chemical solution) is a long, long way off. So even five goals on average per game could easily be coped with or, even more, decisively (!) increase the excitement level.
10) As proof of this: Which games do people remember? They are always those in which four goals or more were scored, hand on heart.
The confirmation can be seen, for example, in the results of this weekend. There were a multitude of referee decisions against penalties, for offside or even (Frankfurt) against the ball crossing the goal line, thus preventing goals. Even if fans get upset about this here or there (as they have experienced themselves) at the bar, the true cause is not investigated. This is described above.
The reason for the result is therefore not only the tactical attitude of the teams (example: Gladbach, who wanted to keep the back tight at all costs), but at the same time this referee cause, which, however, also rubs off backwards on the behaviour on the pitch: In the awareness of hardly being able to make up for a goal, due to the referees’ reluctance to give a penalty, to let it go in the critical offside question and not to raise the flag in panic just because, as is actually always the case, it is “once again extremely close”, people act even more cautiously (which, for example, is by no means as pronounced in the Hinserie, as one loosely has the feeling, if not in the game just played, then at least in the long term, of being able to make up for a mistake, a defeat).
The surprises, however, have remained, as evidenced later by the readable figures. Whether the table itself provides suspense is probably not the case, especially in the title question, but in other places it probably does.
The games in detail:
Bayer Leverkusen – Hannover 96 2:0 (2:0)
The match produced a result that seemed very logical. Hannover played above their value for a long time and Leverkusen didn’t necessarily exploit everything. However, it looks a little different in the match report. At the moment, Hannover don’t have the luck they had for a long time. The ball doesn’t want to go in. The kicker has provided a perfect reflection of the game shares with the chance ratio of 5:3. Surely Leverkusen was better, but there could have been a surprise and it just doesn’t look like pure dominance (and it wasn’t).
Werder Bremen – FC Bayern Munich 1:3 (0:0)
Bayern have played very well all season (as has been mentioned repeatedly here). Their crisis was on the one hand a pure results crisis of their own, the other part a “Dortmund just wins everything” crisis, so the gap was too big.
The 0:1 against them only came in the second half, so from Werder’s point of view you could hope for a surprise (which it definitely would be these days). This was averted quite sovereignly, the victory deserved.
VfL Wolfsburg – Borussia Dortmund 0:3 (0:2)
Dortmund kept up the tempo of the entire season, paired of course with an absolutely outstanding playing class. The goals were so naturally played out that even as an opponent you can only click your tongue. The (undeserved, because equally superior) 1:1 against Stuttgart did not set them back a millimetre.
- FC Nürnberg – Hamburger SV 2:0 (0:0)
The game probably rather balanced, geared to result (!). After the sending-off against Hamburg, a deserved victory. Whether it was justified, however, is a little questionable, although at this point such interpretations are generally advocated. Kacar is guaranteed to want to impede the opponent who is threatening to get away, yet it was very, very lenient compared to many other often unpunished situations (and of course there is a case for equal treatment here too, but a much more striker-friendly one in general).
FC Schalke 04 – TSG Hoffenheim 0:1 (0:1)
These teams have also adapted to results football. In any case, there is no talk of fresh, liberated attacking football. They tried, perhaps without taking too many risks, to score a goal and then to save it over time. An example of a game that could turn away the fans.
It is astonishing that the Kicker, despite the rather uniform description of the game (everywhere), wants to have counted a chance ratio of 9:4.
FC St. Pauli – 1.FC Köln 3:0 (2:0)
A very important duel in the relegation battle, of which one can already make the general observation that it is developing in favour of the home side.
The dream goal from 30 metres (some like to call such a thing a “Sunday shot”) set the victory on its way, the justification for which should not be doubted. The effect will become apparent in numbers later.
- FC Kaiserslautern – FSV Mainz 05 0:1 (0:1)
An incredibly committed Mainz eleven who, like Dortmund, backed up this willingness to run with playful class (a game watched live by the author’s side). That’s how they climbed to the top of the table in the early autumn and didn’t miss anything in other games either, except ultimately the result. Just great to see something like that!
Nevertheless, the realisation remains here as well: all shackles can never be thrown off. Here, too, a chance ratio at the lower limit: 3:5, which, however, correctly reflects the circumstances.
VfB Stuttgart – SC Freiburg 0:1 (0:1)
Certainly, the Freiburg victory can be called “lucky”, considering the slightly incomprehensible chance ratio of 5:2 (the impression: there were more of them on both sides). Such a game should “normally” have resulted in a home victory, not only because of the share of the game, but also after a certain previous experience (Stuttgart must, Freiburg can hardly miss season goals). In a Baden-Württemberg duel, however, one can probably rather not count on shooting assistance?
Eintracht Frankfurt – Borussia Mönchengladbach 0:1 (0:0)
The match report (of the match that was not watched) does not provide any clear information here. Because: The chance ratio shows a surprising 7:9, i.e. Gladbach’s advantage, while there is talk of one-way football in the first half, as well as the long overdue Frankfurt opening goal. Well, in any case, as long as it is still 0:0, Gladbach has no exaggerated reason to run forward excitedly. They try to keep tight, and if they don’t succeed, they can still attack unconditionally. Towards the end, I think they did take the initiative.
2) The table situation
Sp S U N Pkt T GT Diff1 Borussia Dortmund 20 16 2 50 46 – 12 +34
2 Bayer Leverkusen 20 11 6 3 39 41 – 29 +12
3 FC Bayern Munich 20 10 6 4 36 40 – 23 +17
4 FSV Mainz 05 20 12 0 8 36 31 – 21 +10
5 Hannover 96 20 11 1 8 34 28 – 30 -2
6 SC Freiburg 20 10 3 7 33 29 – 28 +1
7 Hamburger SV 20 9 3 8 30 29 – 30 -1
8 TSG Hoffenheim 20 7 8 5 29 36 – 26 +10
9 Eintracht Frankfurt 20 8 2 10 26 24 – 26 -2
10 1.FC Nürnberg 20 7 5 8 26 25 – 30 -5
11 FC Schalke 04 20 7 4 9 25 26 – 26 +0
12 VfL Wolfsburg 20 5 8 7 23 26 – 29 -3
13 1.FC Kaiserslautern 20 6 4 10 22 29 – 34 -5
14 FC St. Pauli 20 6 4 10 22 23 – 34 -11
15 Werder Bremen 20 6 4 10 22 26 – 42 -16
16 1.FC Köln 20 5 4 11 19 22 – 37 -15
17 VfB Stuttgart 20 4 4 12 16 34 – 37 -3
18 Borussia Mönchengladbach 20 4 4 12 16 29 – 50 -21
544 544 0
Goals ø 3.02 Of course, such a table can be read everywhere. What is to be discerned here? Is there an emerging order that corresponds to certain pre-season ideas? And this is not really the case, despite the advance of Bayern (and thus the ousting of the outsiders Mainz, Hannover, Freiburg) and the stabilisation of Leverkusen.
For the problem children remain almost the same in number, but in some cases their situation is getting worse: Schalke, Wolfsburg, Werder, Stuttgart. The measure of the disorder will be given later – and commented on.
3) The title question
Exactly: it’s not really a question, even if 96% is far from a “guarantee” (for example, in roulette you’d hit a single number with a chance of 1/37 = 2.7%, and who would want to guarantee that you wouldn’t hit it? Well then, the ball is still rolling, (well, actually both balls), and in this roulette wheel Football Bundesliga there are even “only” 25 numbers, of which there is still one left for Bayern and Leverkusen…
Explanation: these numbers are the result of a computer simulation, which is based on the current playing strengths of the teams given below. The games are simulated individually on the basis of goal expectations (also given in the text below) and the final table is used to determine the winner.
Team Number of German champions in 5000 simulations Championships in percent Fair odds as reciprocal of probabilities1 Borussia Dortmund 4801 96.02% 1.04
2 FC Bayern Munich 131 2.62% 38.17
3 Bayer Leverkusen 67 1.34% 75
4 FSV Mainz 05 1 0.02% 5000
5000 100.00%
Chance changes compared to the previous week due to the results of matchday 20
Team Changes absolute compared to previous week Championships in percent
Borussia Dortmund 88 1.76%
FC Schalke 04 -1 -0.02%
Hannover 96 -2 -0.04%
SC Freiburg -2 -0.04%
FSV Mainz 05 -4 -0.08%
Hamburger SV -4 -0.08%
Bayer Leverkusen -31 -0.62%
FC Bayern Munich -44 -0.88%
0 0.00%
There is not much more to be gained, but a clear away win at a team that is strong in itself (which Bayern also managed to do, but they only feed their tiny chances on their own wins and Dortmund’s simultaneous loss of points), just brings an increase.
4) The title chances in development
Here is the promised graph of the development of the chances since the beginning of the records:
Well, it is neither overly vivid nor overly exciting, even after interpretation: Dortmund has been sailing around close to 100% since matchday 15, while “the rest” (including Bayern) are allowed to split the remaining percentages. Still, it is striking that Bayern’s red line tends slightly upwards. They are outstripping the rest, which raises the question of whether such a development is inevitable? At any rate, the betting providers (who presumably do not have such software) always revolved around the question: Dortmund or Bayern? The computer had a harder time with it. Whether it was right to do so is the philosophical question behind it.
5) Direct Champions League qualification via 2nd place
Here we can clearly state that it will come down to a duel between Bayern and Leverkusen, which does not completely rob this duel of its suspense, as it has remained a “duel”, but nevertheless larger parts of it, which the refreshing Mainz performances, but also Hanover’s series of successes over a longer period of time, promised us.
The probability distribution for 2nd place after the 20th matchday
Team Number 2nd place 2nd place in percent Fair odds as inverse of probabilities
FC Bayern Munich 2515 50.30% 1.99
Bayer Leverkusen 1899 37.98% 2.63
FSV Mainz 05 234 4.68% 21.37
Borussia Dortmund 179 3.58% 27.93
Hamburger SV 48 0.96% 104.17
Hannover 96 44 0.88% 113.64
TSG Hoffenheim 37 0.74% 135.14
SC Freiburg 33 0.66% 151.52
FC Schalke 04 7 0.14% 714.29
VfL Wolfsburg 3 0.06% 1666.67
Eintracht Frankfurt 1 0.02% 5000.00
5000 100.00%
Bayern and Leverkusen already account for an impressive 89%, despite the far from clear distribution of points. The reason for this : the superior playing strength of the two.
The changes compared to the previous week:
Team Win/Loss absolute Win/Loss in per cent
FC Bayern Munich 187 3.74%
Bayer Leverkusen 155 3.10%
TSG Hoffenheim 8 0.16%
FSV Mainz 05 7 0.14%
SC Freiburg 6 0.12%
Eintracht Frankfurt -3 -0.06%
Werder Bremen -4 -0.08%
VfL Wolfsburg -10 -0.20%
FC Schalke 04 -44 -0.88%
Borussia Dortmund -64 -1.28%
Hannover 96 -83 -1.66%
Hamburger SV -155 -3.10%
0 0.00%
An increase of 6.84% for the two winners. The losses mainly, of course, for the losers Hamburg and Hannover, a slightly smaller one for Dortmund, who, however, are happy to take these chances to win the title.
6) The relegation question
Whether it has become more exciting or not is for you to decide.
The distribution of relegation percentages
Team Direct relegation (17th or 18th place) Relegation via relegation Total1 Borussia Mönchengladbach 76.38% 3.69% 80.07%
2 1.FC Cologne 46.10% 6.54% 52.64%
3 FC St. Pauli 27.98% 6.18% 34.16%
4 VfB Stuttgart 20.24% 4.37% 24.61%
5 1.FC Kaiserslautern 14.66% 4.73% 19.39%
6 1.FC Nürnberg 5.04% 2.49% 7.53%
7 Werder Bremen 4.28% 1.82% 6.10%
8 Eintracht Frankfurt 3.36% 2.29% 5.65%
9 VfL Wolfsburg 1.28% 0.81% 2.09%
10 FC Schalke 04 0.46% 0.23% 0.69%
11 Hamburger SV 0.14% 0.08% 0.22%
12 TSG Hoffenheim 0.06% 0.05% 0.11%
13 Hannover 96 0.02% 0.03% 0.05%
14 SC Freiburg 0.00% 0.04% 0.04%
15 FC Bayern Munich 0.00% 0.00% 0.00%
16 Bayer Leverkusen 0.00% 0.00% 0.00%
17 Borussia Dortmund 0.00% 0.00% 0.00%
18 FSV Mainz 05 0.00% 0.00% 0.00%
200.00% 33.33% 233.33%
The change in chances from matchday 19 to matchday 20 with regard to relegation
Team Change in chances
1 FC St. Pauli -20.84%
2 1.FC Nuremberg -9.81%
3 Borussia Mönchengladbach -8.28%
4 TSG Hoffenheim -0.39%
5 SC Freiburg -0.21%
6 FSV Mainz 05 -0.03%
7 Bayer Leverkusen 0.00%
8 Borussia Dortmund 0.00%
9 FC Bayern Munich 0.00%
10 Hannover 96 0.00%
11 Hamburger SV 0.19%
12 FC Schalke 04 0.44%
13 VfL Wolfsburg 0.95%
14 Werder Bremen 2.36%
15 Eintracht Frankfurt 2.89%
16 1.FC Kaiserslautern 5.65%
17 VfB Stuttgart 9.39%
18 1.FC Cologne 17.69%
0.00%
7) The relegation question in development
Here, too, is a graph of the development. For the sake of clarity, we have concentrated on the (currently) most important candidates. This means that the sum of all values is not always 100%.
It becomes philosophical when the chances are approaching 100%. Does it then inevitably always go to 100% or is there a counter-chance after all? Well, both Bayern and Gladbach are working on such proof, but in doing so they tend to cast doubt on the level of the stated probabilities. Both Dortmund (in the title question) and Gladbach (in the relegation question) have long wanted to impute an almost certainty. The one has not yet been able to take the positive step, the other refuses to accept the negative. But the fact is that they are not moving steadily towards it. Gladbach, in any case, has made a kind of lifeline out of the straw with the two 1:0 away victories….
Stuttgart and Werder also simply don’t want to reduce their chances, even if you might still say today – with the probability of correspondingly lower — persuasiveness: “They’re both still coming out at the bottom”.
8) The point expectations and the deviations
Explanation: For each match, the computer has calculated the chances for 1, X and 2. On the basis of these, a point expectation is mathematically calculated for each team per game according to the formula probability of winning * 3 points + probability of drawing * 1 point. The deviations given below compare the points actually achieved with those expected by the computer. In total, the deviation does not have to be 0 for all teams, as the number of expected draws does not have to be congruent with the expected ones, but the three-point rule forces an imbalance. Too many points scored means that there were too few draws.
Team Name Points expected Points scored Deviation Deviation absolute1 Borussia Dortmund 35.23 50 14.77 14.77
2 Hannover 96 22.83 34 11.17 11.17
3 FSV Mainz 05 27.26 36 8.74 8.74
4 SC Freiburg 24.50 33 8.50 8.50
5 Bayer Leverkusen 33.55 39 5.45 5.45
6 1.FC Nürnberg 21.91 26 4.09 4.09
7 FC St. Pauli 20.85 22 1.15 1.15
8 Eintracht Frankfurt 25.23 26 0.77 0.77
9 TSG Hoffenheim 29.51 29 -0.51 0.51
10 Hamburger SV 30.59 30 -0.59 0.59
11 1.FC Kaiserslautern 22.82 22 -0.82 0.82
12 1.FC Köln 21.58 19 -2.58 2.58
13 FC Bayern Munich 38.86 36 -2.86 2.86
14 Borussia Mönchengladbach 21.34 16 -5.34 5.34
15 FC Schalke 04 31.50 25 -6.50 6.50
16 VfL Wolfsburg 29.56 23 -6.56 6.56
17 Werder Bremen 30.88 22 -8.88 8.88
18 VfB Stuttgart 29.38 16 -13.38 13.38
6.60 102.67
ø Deviation 5.70Hannover hold a commanding 2nd place. However, their decrease in (positive) missing their expectation is quite small (from 12.01 to 11.17). The reason for this is clear: in Leverkusen “there was not much to get”, the expectation was correspondingly low, hence the loss.
At the bottom end, Stuttgart have dug themselves in even tighter due to the home defeat. But Werder are also competing with them, as well as the old problem children Wolfsburg and Schalke, as already indicated in the table.
After all, Bayern are only 2.86 points away, so a ridiculous win (instead of a defeat), and they would already be on target (without knowing it, since their target always consists of first place).
The average deviation, as a measure of the disorder in the table, has grown again, which is quite obvious when you look at the results. Many who were below par have lost, many who were above par have won. There is no balance, hence the rise from 5.3 points last week to 5.7 today. Exciting yes, as expected: no.
Here again is the comparison with other countries in terms of the level of tension indicated by this measure:
Germany 5.70
Italy 4.11
France 4.11
Spain 4.07
England 3.07
Germany continues to lead this table quite comfortably, but not as clearly as in the autumn. The number in this country has dropped somewhat, while abroad there has been a little more movement.
The deviation indicates the extent to which actual results coincide with expectations, which therefore, if frequently and clearly missed, results in a certain form of suspense that can be expressed like this: “Today Team A is playing against Team B. How do you think it will turn out?” “I have no idea, anything can happen there” (and you can put almost any name for Team A and B). In Germany, so to speak, the uncertainty about the outcome (which was explained as a “tension maker” in an earlier text) is the greatest.
9) Goal expectations and their deviations
Included for the sake of completeness, but a few explanations can still be found at the end of the statistics.
Explanation: Almost the same applies to the goals as to the points. The expected goals scored and the expected goals conceded are compared with reality. Too few goals scored count negatively just as too many goals conceded count negatively, the reverse counts positively in each case. Here, the sum of the deviations must be 0, because all expected and not scored goals were not conceded somewhere. The goal average, however, can show a deviation.
Team Name Goal expectation Goals scored Goals conceded expected Goals conceded Total deviation1 Borussia Dortmund 35.13 46 22.96 12 21.83
2 FSV Mainz 05 28.34 31 29.04 21 10.70
3 TSG Hoffenheim 30.83 36 27.57 26 6.74
4 SC Freiburg 26.89 29 31.91 28 6.03
5 Hannover 96 25.13 28 32.75 30 5.62
6 1.FC Nürnberg 24.22 25 33.28 30 4.05
7 1.FC Kaiserslautern 25.39 29 33.22 34 2.83
8 Bayer Leverkusen 35.20 41 25.67 29 2.48
9 Eintracht Frankfurt 26.72 24 30.33 26 1.61
10 FC St. Pauli 22.78 23 33.26 34 -0.51
11 FC Bayern Munich 37.11 40 19.28 23 -0.83
12 1.FC Köln 24.39 22 34.22 37 -5.17
13 VfB Stuttgart 32.06 34 29.36 37 -5.70
14 Hamburger SV 31.36 29 26.62 30 -5.74
15 VfL Wolfsburg 30.61 26 27.39 29 -6.23
16 FC Schalke 04 31.97 26 25.62 26 -6.35
17 Borussia Mönchengladbach 26.70 29 37.57 50 -10.13
18 Werder Bremen 33.21 26 27.98 42 -21.23
528.04 544 528.04 544 0.00
Goals ø expected: Goals ø scored: ø Deviation 6.88
2.93 3.02 Interesting, perhaps, that Bayern have almost completely made up their deficit here – as announced a few weeks ago, as a possibility. Werder here remain firmly anchored in the bottom of the table due to their disastrous goal ratio. In the case of Stuttgart, one could say here that they have divided up their goals badly. Here, for example, Mainz is clearly ahead of Hannover because they have a goal ratio that corresponds to their position in the table. About Hannover one might also say – as is consistent with observation – that they have been somewhat lucky with many narrow victories.
The overall goal average is gradually adjusting. The deviation has come within a reasonable range, which was incidentally suggested in an early such record (namely that it was not a real turnaround, that {much} too many goals had been scored up to that point).
10) The playing strength ranking
Team For Against Quotient For/Again Shift1 Borussia Dortmund 1.92 0.92 2.09 +0
2 FC Bayern Munich 2.05 1.04 1.97 +0
3 Bayer Leverkusen 1.86 1.32 1.41 +0
4 FC Schalke 04 1.49 1.17 1.27 +0
5 Hamburger SV 1.53 1.37 1.12 +1
6 TSG Hoffenheim 1.57 1.41 1.11 +1
7 VfL Wolfsburg 1.46 1.32 1.11 -2
8 VfB Stuttgart 1.59 1.55 1.03 +1
9 FSV Mainz 05 1.36 1.33 1.02 +1
10 Werder Bremen 1.55 1.52 1.02 -2
11 SC Freiburg 1.36 1.45 0.94 +0
12 Hannover 96 1.31 1.57 0.83 +0
13 Eintracht Frankfurt 1.16 1.47 0.79 +0
14 1.FC Kaiserslautern 1.25 1.71 0.73 +0
15 1.FC Nürnberg 1.17 1.62 0.72 +1
16 1.FC Köln 1.18 1.69 0.70 -1
17 FC St. Pauli 1.14 1.76 0.65 +1
18 Borussia Mönchengladbach 1.29 2.04 0.63 -1
26.24 26.26
Goals ø expected
2.917 Not much movement was expected. The arrangement of the teams may cause surprise, but there is no one you could clearly put at position 4, because even the outsiders who have climbed the table positions do not play consistently enough. Mainz, for example, had two defeats before the victory, and Hannover never kept pace anyway. Incidentally, the odds determined on the basis of these match strengths (probabilities for the match outcomes) are still competitive on the betting market, and can best be called “comparable with common assessments”, although of course in this season of surprises the betting market also has some difficulty interpreting the results correctly.
St. Pauli only overtake Gladbach because they scored an even higher victory.
11) The mathematical review of the matchday 20 results
Goal expectation
Home Away Result DeviationLeverkusen Hannover 2.06 1.18 2 0 -0.06 -1.18
Bremen FC Bayern 1.28 1.70 1 3 -0.28 1.30
Wolfsburg Dortmund 1.10 1.55 0 3 -1.10 1.45
Nuremberg HSV 1.25 1.51 2 0 0.75 -1.51
Schalke 04 Hoffenheim 1.79 1.07 0 1 -1.79 -0.07
St. Pauli FC Köln 1.38 1.36 3 0 1.62 -1.36
Kaiserslautern Mainz 1.42 1.40 0 1 -1.42 -0.40
Stuttgart Freiburg 1.86 1.36 0 1 -1.86 -0.36
Frankfurt Gladbach 1.90 1.21 0 1 -1.90 -0.21
14.31 12.28 8 10 -6.04 -2.33
Expected goal total Expected goal total: Goal total: Goal total
26.59 2.95 18 2
ø Goal difference: 2.07 As you can see, the goal average is far from fulfilled. In addition, despite the low yield, the average goal deviation is quite high at over 2 goals per game, which again stands for the large number of surprises. Over the long term, by the way, this figure is 1.83.
Frankfurt, Stuttgart and Schalke missed by the furthest, as they were expected to score goals.
Note: The determination is calculated as the sum of the squares of the individual probabilities. This measures how much one can commit to a favourite in a certain pairing. The higher a favourite position, the higher the sum of the squares, but also the more “certain” the occurrence of the event. The mathematical question in itself is even more how far one can commit, since one cannot really determine this value. Events are predicted whose probabilities are unknown. Nevertheless, one can check the quality in the long term by comparing expected/occurred.
The determination (expected)
Pairing 1 X 2
Leverkusen Hannover 57.55% 21.31% 21.14% 42.13%
Bremen FC Bayern 28.72% 24.23% 47.05% 36.26%
Wolfsburg Dortmund 26.91% 25.74% 47.35% 36.29%
Nuremberg HSV 31.10% 25.73% 43.18% 34.93%
Schalke 04 Hoffenheim 54.13% 23.51% 22.36% 39.83%
St. Pauli FC Köln 37.17% 26.18% 36.65% 34.10%
Kaiserslautern Mainz 37.60% 25.74% 36.66% 34.20%
Stuttgart Freiburg 49.14% 22.96% 27.90% 37.20%
Frankfurt Gladbach 53.48% 22.64% 23.89% 39.43%
3.76 2.18 3.06 3.34
Average expected commitment: 37.15% Here is the expected commitment in the graph shown last week. It was also explained, now the question is to what extent congruence has occurred through the real results.
The expected fixing of 37.15% is below the long-term average for this league, which is over 39%. The reason on this matchday: balanced pairings, especially the top favourites had to play away (Bayern, Dortmund).
The determination (arrived) Pairing 1 X 2 Tendency W-ness Arrived Event
Leverkusen Hannover 57.55% 21.31% 21.14% 2 57.55%
Bremen FC Bayern 28.72% 24.23% 47.05% 2 47.05%
Wolfsburg Dortmund 26.91% 25.74% 47.35% 2 47.35%
Nuremberg HSV 31.10% 25.73% 43.18% 1 31.10%
Schalke 04 Hoffenheim 54.13% 23.51% 22.36% 2 22.36%
St. Pauli FC Köln 37.17% 26.18% 36.65% 1 37.17%
Kaiserslautern Mainz 37.60% 25.74% 36.66% 2 36.66%
Stuttgart Freiburg 49.14% 22.96% 27.90% 2 27.90%
Frankfurt Gladbach 53.48% 22.64% 23.89% 2 23.89%
3.76 2.18 3.06 3.31
Average number of commitments received: 36.78% Of course, the question of whether the favourite events predominated or not is exciting. As you can see (from the “W-ness event arrived”), the smaller values came quite often, so that the outsider results prevailed again.
Nevertheless, it was “worthwhile” to decide at all, i.e. to identify favourites (unlike in one of the previous weeks), since the value that arrived is above the minimum determination of 33.33% (which would be given if one were to say, I don’t know anything, i.e. all three outcomes are equally likely). The deviation of expected 37.15% from the arrived 36.78% is so small that one will of course tolerate it (it means that favourite and outsider events have occurred in healthy proportion to each other). On the other hand, a correction – which is pending for the season as a whole, so to speak – would mean that at some point one would have to expect more favourite victories.
It is also noticeable that despite the lack of goals (which should favour this effect), there were no draws this time.
12) Preview of matchday 20
Note: The computer calculates the goal expectations (and the individually maintained home advantage not shown here) according to a specially developed – of course explainable and highly logical – algorithm. These in turn are offset against the probabilities of occurrence, in the past by simulation, today long since by a function derived from the simulation results). These goal expectancy values have also long since proved to be competitive in goal number betting on the betting market.
Goal expectation
Home Away
Dortmund Schalke 04 1.77 0.77
Nuremberg Leverkusen 1.15 1.89
FC Cologne FC Bayern 0.99 1.99
Hoffenheim Kaiserslautern 2.07 1.13
Mainz Bremen 1.60 1.14
Hanover Wolfsburg 1.37 1.30
Gladbach Stuttgart 1.66 1.74
HSV St. Pauli 1.97 1.00
Freiburg Frankfurt 1.55 1.02
14.31 12.28
Explanation: The determination is calculated as the sum of the squares of the individual probabilities, for each match. You can easily check that the minimum fixing is 33.33%. This is the case when all outcomes have exactly the same probability, namely 33.33%.
What is measured by the fixing is the amount of favouritism overall. In the long-term average, the expected and the realised determination is quite exactly at just under 40%. This is the case when a distribution of 50% – 30% – 20% is given (for this, the determination would be 0.50.5 + 0.30.3 + 0.2*0.2 = 0.25 + 0.09 + 0.04 = 0.39 = 39%). This is roughly equivalent to the home advantage in the league.
The determination (expected)
Pairing 1 X 2
Dortmund Schalke 04 61.24% 22.92% 15.85% 45.26%
Nürnberg Leverkusen 22.98% 22.46% 54.56% 40.09%
FC Cologne FC Bayern 18.14% 21.33% 60.53% 44.48%
Hoffenheim Kaiserslautern 58.81% 20.97% 20.22% 43.07%
Mainz Bremen 47.89% 24.96% 27.15% 36.53%
Hanover Wolfsburg 38.60% 26.16% 35.24% 34.16%
Gladbach Stuttgart 37.07% 22.76% 40.18% 35.06%
HSV St. Pauli 60.01% 21.48% 18.51% 44.05%
Freiburg Frankfurt 49.46% 25.60% 24.94% 37.24%
3.94 2.09 2.97 3.60
average expected determination: 39.99% Of course, both the probabilities of occurrence can be read from this table, as well as the fair odds, but these are shown separately for today.
The expected average commitment is above the long-term average at just under 40%. So there are somewhat clearer favourites than “normally”.
Here now are the promised fair odds, which are the inverses of the probabilities. Such odds are used in the betting market. Theoretically, whenever you get higher odds on the betting market than the fair odds shown, you would have an advantage, i.e. a favourable bet, a so-called “value-bet” in technical language. Anyone who enjoys this is welcome to try it out.
Pairing 1 X 2
Dortmund Schalke 04 1.63 4.36 6.31
Nuremberg Leverkusen 4.35 4.45 1.83
FC Cologne FC Bayern 5.51 4.69 1.65
Hoffenheim Kaiserslautern 1.70 4.77 4.95
Mainz Bremen 2.09 4.01 3.68
Hannover Wolfsburg 2.59 3.82 2.84
Gladbach Stuttgart 2.70 4.39 2.49
HSV St. Pauli 1.67 4.65 5.40
Freiburg Frankfurt 2.02 3.91 4.01
