Since the beginning of these records here, there has been a steady rise in Dortmund’s title chances – quite inevitably, as there have only been wins to report. Now it has hit them for the first time, at the end of the Hinserie of all times – this only mentioned, as in their place one would now have the chance to spend a longer time with it, instead of with a win, and possibly even their self-confidence may suffer a little. Even if one had no reason to begrudge them anything, it at least serves the purpose of the (neutral, general) fan to let a little (more) tension arise.
This is certainly felt now, despite the continued exorbitant lead in the table and Leverkusen’s loss of points due to the draw, since the main chances are given to Bayern. Apart from the fact that one simply has to honestly say that they played good football throughout, they also started to score despite the minor setbacks, and did so quite confidently. For the interested reader here, however, part of the suspense may also derive from wanting to see this development depicted in bare figures. How many percentages have the Dortmund team lost, how many have the Bavarians gained?
Nevertheless, the…
1) Review of the games
must of course be included.
Here are the results at a glance:
Results of Matchday 17
Borussia Mönchengladbach – Hamburger SV 1:2 (0:0)
Werder Bremen – 1. FC Kaiserslautern 1:2 (1:1)
VfL Wolfsburg – TSG Hoffenheim 2:2 (0:2)
Eintracht Frankfurt – Borussia Dortmund 1:0 (0:0)
1.FC Nürnberg – Hannover 96 3:1 (2:0)
FC Schalke 04 – 1. FC Cologne 3:0 (1:0)
FC St. Pauli – FSV Mainz 05 2:4 (1:3)
Bayer Leverkusen – SC Freiburg 2:2 (1:1)
VfB Stuttgart – FC Bayern Munich 3:5 (0:3)
The games will only be mentioned briefly in detail today, as our own in-depth observation has had to be dispensed with so far.
Gladbach lost the game after all, after they had put the 0:1 away well with the quick equaliser. Well, the performance was quite ok, especially since two crisis clubs met (this Friday match could still be observed). The bad luck, which is always used as a citation, actually hit those at the back. But it is questionable whether the saying will be remembered when one of the two teams escapes the relegation battle once again?
Werder slides deeper into the crisis because of the result. Sure, the performances here and there were not absolutely top in the first half of the season, but you should still give the team and the coach time. The mix is right and the potential is high; it’s always a pleasure to watch the team play. It’s clear that those in charge should be careful about sugarcoating things, but here at least we should be encouraged.
Wolfsburg against Hoffenheim is only curious in terms of the result. But not because it doesn’t happen from time to time (in Germany, as shown, more often than elsewhere), but because both have a longer history.
Hoffenheim lost at home to Bayern and Freiburg in the last minute, as well as conceding the equaliser from Nürnberg (in the 86th). However, they also saved a point against Leverkusen with a last-minute goal. Away it happened to them in Dortmund – who doesn’t remember the (unjustified) free kick in the last action of the game that brought Dortmund the equaliser.
Wolfsburg, on the other hand, had the previous history with the games against Mainz and Leverkusen, in which they still turned a 2- and 3-goal lead, respectively, into a defeat.
So somehow there were special conditions for this game. And so it came to pass that Wolfsburg were able to polish up their shooting statistics a little, while Hoffenheim have now arrived at a 1:5 record. Of course, you can’t really measure how unlucky it was (since there are also deserved goals, where only the timing makes up the luck; see the game in Dortmund; while there is of course also the principle of “stupidly lining up”, which also wouldn’t directly count as bad luck; you had an influence on it), there would also be no right measure, but emotionally the Hoffenheimers are still the unlucky birds of the league.
Frankfurt actually managed to beat Dortmund, certainly not until shortly before the end, but still. Of course, Frankfurt also put in great performances, some of which were not rewarded (Freiburg, Schalke), and one could simply say “it had to happen sometime…”. Whether it was deserved or not is almost irrelevant.
A victory like Nuremberg’s against Hannover is a very typical one. Hanover is already quite satisfied and quite relaxed going into the game. Nuremberg, on the other hand, has a clear deficit in results despite some appealing performances recently. They are going into the game with full concentration, are favourites, have the crowd behind them and – win.
Schalke are on an upward trend, even if Cologne also had quite good results.
With Pauli against Mainz, the big question now was whether Mainz could really be in the favourite role – as claimed by the computer. As it looks, it probably was.
On the other hand, the fact that Freiburg was able to confirm its high flight with a point in Leverkusen is really surprising. It looked like an easy home win, but it was not.
It was certainly foreseeable that Bayern would at some point convert a series of chances. Stuttgart were able to fight back, but could not resist.
2) The standings
The table after the end of the first half
Sp S U N Pkt T GT Diff1 Borussia Dortmund 17 14 1 2 43 39 – 10 +29
2 FSV Mainz 05 17 11 0 6 33 30 – 19 +11
3 Bayer Leverkusen 17 9 6 2 33 35 – 25 +10
4 Hannover 96 17 10 1 6 31 25 – 27 -2
5 FC Bayern Munich 17 8 5 4 29 31 – 20 +11
6 SC Freiburg 17 9 1 7 28 25 – 25 +0
7 Eintracht Frankfurt 17 8 2 7 26 24 – 21 +3
8 TSG Hoffenheim 17 6 7 4 25 32 – 22 +10
9 Hamburger SV 17 7 3 7 24 27 – 28 -1
10 FC Schalke 04 17 6 4 7 22 25 – 24 +1
11 1.FC Nürnberg 17 6 4 7 22 – 28 -6
12 1.FC Kaiserslautern 17 6 3 8 21 27 – 27 +0
13 VfL Wolfsburg 17 4 7 6 19 24 – 25 -1
14 Werder Bremen 17 5 4 8 19 23 – 35 -12
15 FC St. Pauli 17 5 2 10 17 16 – 30 -14
16 1.FC Köln 17 4 3 10 15 18 – 33 -15
17 VfB Stuttgart 17 3 3 11 12 32 – 35 -3
18 Borussia Mönchengladbach 17 2 4 11 10 26 – 47 -21
481 481 0
Goals ø 3.14 Today, a slightly shortened version will be offered. Pretty much everything has been said about the table. There is no correction at the moment. The teams at the top, such as Mainz, Freiburg, Hannover (in my opinion) or even Frankfurt, confirm week after week that their results are not products of chance. The revolution seems to be on its way. Typically, a few weeks’ break could see a certain return to normality in the sense that all the teams will sort themselves out again, with some personnel changes here and there, and a few things will be put out of their minds within the next few weeks, such as unfortunate defeats, for example, and they will be able to approach the game unencumbered, i.e. with their full potential at their disposal.
It’s not like before the start of the season, but it’s also not like it’s business as usual with the week-to-week fixtures. This is taught by many years of experience, also by observing the betting market, but equally or even more so by observing the performances after the (short) break in the winter.
So one should also be a little more cautious with forecasts if one intends to commit oneself to probabilities (in relation to phrases like “the second half of the season is long” or “a lot can still happen” or even “Bayern will still come close”). The “caution” means that the probability predictions become temporarily less reliable.
3) The title question
Now finally to the question of the development of the odds as far as winning the title in 2011 is concerned. Of course, attention automatically focuses on the two perceived biggest candidates: FC Bayern München and Borussia Dortmund, especially since their two results in particular were contrary. It’s logical to focus on them, since you always have to trust the Bavarians. It is worth repeating here that the fans are much more sensitive than the media, who know almost nothing except pure “result logic”. The fan simply senses that Bayern’s performances were very good in themselves, so there is, if anything, a crisis in results (the extent of which is proven by later figures). The bigger problem, however, is that there is one outlier – Dortmund Borussia — which makes the (Bayern) position seem so disastrous.
It has been stressed often enough, mentioned, that title contenders are allowed to have their say from an average of 2.0 points per game. So if we had a “normal title contender” in front of us who, according to Adam Riese, had 2 * 17, i.e. 34 points on their account – be it Dortmund or Leverkusen or someone else – and thus a very impressive record, then Bayern would still sit back and enjoy themselves and with the completely justified “mir san mir”, with a 5-point deficit, have a cosy Christmas – and then start the second half of the season, after which it would again be said everywhere (but wrongly): “The others are just too stupid. When the Bavarians are weak, there is no one to take the butter off their bread.
The error in this is that you give away more or fewer points depending on your playing strength. In the Bundesliga – and this was impressively confirmed in the first half of the season – anyone can beat anyone, anyone can become a stumbling block and long series are unlikely(er). Bayern will sprinkle in a draw here and there, less often a loss. The others do it with a slightly higher frequency. The reason: Bayern are simply better. And not the others stupid.
Dortmund’s exorbitant score of 43 points still means that everyone else has to get in line. Nevertheless, the weekend’s defeat has brought the hoped-for movement, the extent of which can be seen below.
The distribution of chances to win the 2011 title after matchday 17
Team Number of German champions in 5000 simulations Championships in percent Fair odds as reciprocal of probabilities
Borussia Dortmund 4513 90.26% 1.1
FC Bayern Munich 236 4.72% 21.0
Bayer Leverkusen 210 4.20% 23.8
FSV Mainz 05 20 0.40% 250
Hannover 96 7 0.14% 714
FC Schalke 04 5 0.10%
TSG Hoffenheim 4 0.08% 1250
Eintracht Frankfurt 2 0.04%
Hamburger SV 2 0.04% 2500
SC Freiburg 1 0.02% 5000
1.FC Cologne 0 0.00%
1.FC Kaiserslautern 0 0.00%
VfB Stuttgart 0 0.00%
Werder Bremen 0 0.00%
FC St. Pauli 0 0.00%
Borussia Mönchengladbach 0 0.00%
1.FC Nuremberg 0 0.00%
VfL Wolfsburg 0 0.00%
5000 100.00%
It remains the case that the (insightful) 90% is still gigantic. Whether coach Klopp would show this to his players or whether it could have any meaningful or noteworthy influence at all is open to doubt – also on the part of the authors. Nevertheless, it would be kind of exciting to hear what those concerned would say about it. “Yes, we have 90%. But only if we keep doing everything the way we’ve been doing it.” As a possible reaction?!
Besides, when it comes to probability considerations, it basically remains a bit philosophical. “It seems true?” “How true does it seem?” “Exactly. Namely 90%.” But it only seems true. They will or they won’t. You don’t know anything for sure. What good is 90% if it is not realised?
Or, to put it another way, “To get from 90% to 100%, you need luck for the remaining 10%.”
And while that’s really true, it’s hard to believe. It sounds absurd somehow. It only becomes insightful when you think about how else the increase to occur should happen? 90% are 90% precisely because they are opposed by 10%. If one needed less than 10% “luck” (instead suggested or often quoted: ability), then the original assessment would be wrong. Then it would be 95%. And one would only need 5% luck. But then this is guaranteed.
The reason why it is considered nonsensical and illogical to need luck for the remaining percentages is that one knows that the competition requires a considerably greater degree of luck – and that this would then be interpreted, at least perceived, in this way. The curious thing is that although you need 100% of the luck for the remaining 10% (this also applies to any other favourite position, of course), the opponent or opponents with the much lower percentage chances who then step in, i.e. catch the favourite, naturally need a considerably greater measure of luck. In this respect, instead of describing this residual increase as luck, one would regard it as the absence of bad luck, thus leaving it uncommented on, since the “normal case” has occurred.
It is perceived as follows: “Since the chance is so great that the favourite will win the race, all they really need is no bad luck and they will. But this is not felt at all. It only deserves attention if the victory effect fails to materialise, after which the great misfortune has occurred (for the favourite) or the great good fortune (for the one to whom all the percentages have flown).
Although the observed, stated luck effect is essentially absent in this country with regard to football on the media side: Should Bayern really make up the 9-point deficit plus 12-goal difference that existed shortly before with three final victories against three Dortmund defeats (let’s assume that the computer would have determined 99.96% after the 31st matchday), then the result would have been a victory. If the computer had calculated 99.96% after the 31st matchday), then we would not be talking about “an incredibly happy ending for Bayern” but about a “Dortmund team that, due to its youth, was not up to the gigantic pressure and therefore simply collapsed”, if one did not simply attribute to them a “they were too stupid”.
There was only one team that was once 100% (perceived) champion – and yet didn’t make it. Never forget: Schalke 2001. However, it is speculative how many percent they really were at that moment, but it must have been as high as a tower in the 90s. You have to consider that it was the last action of the game, the indirect free kick after the back pass didn’t even have to happen and the referee could have let it go on (a view that is often held here, by the way: if it was the only penalty for the back pass of the entire season, then the whistle came as a surprise to all Hamburg players, had nothing to do with “stupidity” and should have been let off, not because the action did not warrant it, but because it should not/should not be interpreted as the only decisive action of the entire championship season).
So: If the numbers here are correct (and we have long been in the field of philosophy: how can a probability be correct? It will come or it will not! It becomes true or it becomes false. It comes or it does not come. Percentages? For the backside… It is the endeavour of these texts to show that it could be different, that a probability does yield something).
After so much Osophie, it only gets really exciting when you look at the gains and losses. What did Dortmund’s defeat cost them and who benefited from it and how much?
Changes in chances compared to the previous week due to the matchday 17 results
Team Changes absolute compared to the previous week Championships in per cent
FC Bayern Munich 166 3.32%
Bayer Leverkusen 28 0.56%
FSV Mainz 05 9 0.18%
FC Schalke 04 5 0.10%
Eintracht Frankfurt 2 0.04%
TSG Hoffenheim 2 0.04%
Hamburger SV 1 0.02%
1.FC Kaiserslautern 0 0.00%
1.FC Cologne 0 0.00%
1.FC Nuremberg 0 0.00%
Borussia Mönchengladbach 0 0.00%
FC St. Pauli 0 0.00%
VfB Stuttgart 0 0.00%
Werder Bremen 0 0.00%
Hannover 96 -1 -0.02%
SC Freiburg -1 -0.02%
VfL Wolfsburg -1 -0.02%
Borussia Dortmund -210 -4.20%
0 0.00%
Fact: for the first time we see Dortmund properly in a last place. And this without any of the artifice required before. They have forfeited chances. Of course they lost chances. However, the lead was still too big to make it look really gigantic. 4.2% is something, but they had quite a considerable amount at their disposal.
The main gain – how could it be otherwise – was made by Bayern. They had the relatively difficult task in Stuttgart and mastered it. At the same time, the previous main rival missed out on two points at home (Leverkusen against Freiburg). Of course, other teams must have benefited from Dortmund’s defeat. Leverkusen, however, not to the desired extent, while Mainz’s chances were already somewhat too small, so that their gain is also moderate (despite victory).
4) Direct Champions League qualification via 2nd place
The probability distribution for 2nd place
Team Number of 2nd places 2nd place in percent Fair odds as reciprocal of probabilities
FC Bayern Munich 1971 39.42% 2.54
Bayer Leverkusen 1641 32.82% 3.05
FSV Mainz 05 471 9.42% 10.62
Borussia Dortmund 388 7.76% 12.89
TSG Hoffenheim 147 2.94% 34.01
Hannover 96 109 2.18% 45.87
SC Freiburg 89 1.78% 56.18
Hamburger SV 49 0.98% 102.04
VfL Wolfsburg 18 0.36% 277.78
1.FC Kaiserslautern 1 0.02% 5000.00
1.FC Cologne 0 0.00%
Eintracht Frankfurt 34 0.68%
VfB Stuttgart 0 0.00%
Werder Bremen 6 0.12%
FC St. Pauli 0 0.00%
Borussia Mönchengladbach 0 0.00%
1.FC Nuremberg 2 0.04%
FC Schalke 04 74 1.48%
5000 100.00%
Here, Bayern actually earned the top position. Leverkusen failed, Bayern won and Dortmund’s chances of taking second place have also increased because those in first place have declined. In any case, it makes sense and everyone will believe it of Bayern, if not even more…
The changes compared to the previous week:
Team Win/Loss absolute Win/Loss in per cent
FC Bayern Munich 430 8.60%
Borussia Dortmund 163 3.26%
FSV Mainz 05 133 2.66%
FC Schalke 04 30 0.60%
Eintracht Frankfurt 23 0.46%
1.FC Nuremberg 2 0.04%
1.FC Kaiserslautern 1 0.02%
1.FC Cologne 0 0.00%
Borussia Mönchengladbach 0 0.00%
FC St. Pauli 0 0.00%
VfB Stuttgart 0 0.00%
Hamburger SV -1 -0.02%
SC Freiburg -3 -0.06%
VfL Wolfsburg -11 -0.22%
Werder Bremen -22 -0.44%
TSG Hoffenheim -42 -0.84%
Hannover 96 -95 -1.90%
Bayer Leverkusen -608 -12.16%
0 0.00%
Bayern with the big gain, that is logical. Leverkusen’s chances have worsened (so much) because they had to give something to all their competitors (including Dortmund).
5) The relegation question
Here one should not expect excessive tension (at least temporarily). All the teams in the relegation places have lost, so their chances of relegation are increasing all over the place. And, as elaborated last week, this does not increase the perceived tension. One might say to oneself: “Let’s wait for a matchday when the teams at the bottom score. And then we’ll look up here again.”
(Note: It might be interesting to show the developments graphically over longer periods of time. This idea will certainly be taken up in a later text).
Related to this, for example: Will we see Gladbach’s chances of staying in the class rise again?
The disdainful percentages
Team Direct relegation (17th or 18th place) Relegation Total
Borussia Mönchengladbach 83.88% 2.99% 86.87%
FC St. Pauli 46.28% 7.53% 53.81%
1.FC Köln 39.30% 7.75% 47.05%
VfB Stuttgart 17.42% 5.78% 23.20%
1.FC Nürnberg 5.48% 3.33% 8.81%
1.FC Kaiserslautern 4.14% 2.85% 6.99%
Werder Bremen 1.84% 1.37% 3.21%
VfL Wolfsburg 0.66% 0.61% 1.27%
Eintracht Frankfurt 0.38% 0.43% 0.81%
Hamburger SV 0.22% 0.23% 0.45%
FC Schalke 04 0.20% 0.15% 0.35%
SC Freiburg 0.16% 0.16% 0.32%
Hannover 96 0.00% 0.08% 0.08%
TSG Hoffenheim 0.02% 0.06% 0.08%
FSV Mainz 05 0.02% 0.01% 0.03%
FC Bayern Munich 0.00% 0.00% 0.00%
Bayer Leverkusen 0.00% 0.00% 0.00%
Borussia Dortmund 0.00% 0.00% 0.00%
200.00% 33.33% 233.33%
So Gladbach are way ahead and huge favourites to be relegated. At least their chances of being saved are greater than Dortmund’s chances of being caught. Stuttgart is also climbing up the rankings.
The change in chances from matchday 16 to matchday 17 with regard to relegation
Team Change in chances
1.FC Nuremberg -11.65
1.FC Kaiserslautern -10.16%
Eintracht Frankfurt -1.54%
VfL Wolfsburg -0.77%
FC Schalke 04 -0.67%
Hamburger SV -0.46%
SC Freiburg -0.09%
TSG Hoffenheim -0.07%
FSV Mainz 05 -0.02%
FC Bayern Munich 0.00%
Borussia Dortmund 0.00%
Bayer Leverkusen 0.00%
Hannover 96 0.05%
Werder Bremen 1.69%
VfB Stuttgart 3.77%
Borussia Mönchengladbach 3.96%
FC St. Pauli 7.25%
1.FC Cologne 8.71%
0.00%
You can see here how good the Nuremberg victory did them. A so-called “important home victory”. Kaiserslautern, of course, also catapulted up, so away from the danger of relegation.
At the bottom, the three candidates have all lost, making their relegation more certain (St. Pauli joins them, so we would currently have to talk about four candidates for the aforementioned 21/3 places).
6) The points expectations and the deviations.
These values should only be mentioned as a matter of routine. Major surprises are hardly to be expected.
Expected points and deviations from them sorted by size of deviation, from positive to negative
Team Name Points expected Points scored Deviation Deviation absolute1 Borussia Dortmund 29.76 43 13.24 13.24
2 Hannover 96 19.46 31 11.54 11.54
3 FSV Mainz 05 23.20 33 9.80 9.80
4 SC Freiburg 19.92 28 8.08 8.08
5 Eintracht Frankfurt 20.80 26 5.20 5.20
6 Bayer Leverkusen 28.40 33 4.60 4.60
7 1.FC Nuremberg 18.12 22 3.88 3.88
8 1.FC Kaiserslautern 19.23 21 1.77 1.77
9 TSG Hoffenheim 25.19 25 -0.19 0.19
10 FC St. Pauli 17.68 17 -0.68 0.68
11 Hamburger SV 26.28 24 -2.28 2.28
12 1.FC Köln 17.91 15 -2.91 2.91
13 FC Bayern Munich 33.17 29 -4.17 4.17
14 FC Schalke 04 26.51 22 -4.51 4.51
15 VfL Wolfsburg 26.09 19 -7.09 7.09
16 Werder Bremen 26.86 19 -7.86 7.86
17 Borussia Mönchengladbach 18.52 10 -8.52 8.52
18 VfB Stuttgart 25.61 12 -13.61 13.61
6.27 109.93
ø Deviation 6.11Dortmund, of course, remains the first-round sensation. Hannover’s second place is surprising at most because of the last defeat at the moment. Mainz and Freiburg are also clear.
At the back, it’s VfB Stuttgart after all, and even by some distance. Well, if you consider that 12 points are really extremely few and they actually intended to play at the top, it becomes understandable. Gladbach and Werder need no further comment.
The average deviation has risen again (and more than before), which ultimately only means that there were some surprises again. You can see and feel it that way, but here you can also see the figures. 6.11 are a lot (also in comparison with other countries, which is not the case today). The German league is alive. Above all, thanks to the “unpredictability”, which automatically creates tension.
7) Goal expectations and their deviations
This statistic is also given for the sake of completeness.
Team Name Goal expectation Goals scored Goals conceded Goals expected Goals conceded Total deviation
Borussia Dortmund 29.67 39 19.64 10 18.96
FSV Mainz 05 24.04 30 24.63 19 11.59
TSG Hoffenheim 26.25 32 23.29 22 7.05
Eintracht Frankfurt 22.18 24 26.21 21 7.03
1.FC Kaiserslautern 21.50 27 28.18 27 6.68
SC Freiburg 22.25 25 27.91 25 5.66
Hannover 96 21.41 25 27.84 27 4.43
1.FC Nuremberg 19.98 22 28.55 28 2.57
Bayer Leverkusen 29.53 35 21.64 25 2.11
FC Schalke 04 27.03 25 21.99 24 -4.04
FC Bayern Munich 31.30 31 16.01 20 -4.29
FC St. Pauli 19.35 16 28.32 30 -5.04
VfL Wolfsburg 27.09 24 22.93 25 -5.16
Hamburger SV 26.92 27 22.44 28 -5.48
1.FC Köln 20.52 18 29.67 33 -5.85
VfB Stuttgart 27.53 32 24.05 35 -6.48
Borussia Monche 22.74 26 31.39 47 -12.35
Werder Bremen 28.88 23 23.48 35 -17.40
0.00
Dortmund remains on 1, Mainz moves up to 2, as their goal ratio is also that of a top team.Hoffenheim has had some bad luck as far as the points yield is concerned, but in the goal ratio it looks much better, which somehow translates to: Actually, the potential is actually higher. But they have distributed their goals somewhat unfavourably. Intuitively, this corresponds to observations made of their performances: There’s still room for improvement.
Right at the back here, of course, not Stuttgart, since their goal ratio is still decent, but Werder, who have surpassed best marks with the gigantic flood of goals conceded, which should actually be called “worst marks” as a result.
Gladbach right in front of them, this is also clear.
8) The playing strength ranking
Goal expectations
Team For Against Quotient For/Again Shift1 Borussia Dortmund 1.87 0.97 1.93 +0
2 FC Bayern Munich 1.94 1.05 1.85 +0
3 Bayer Leverkusen 1.84 1.32 1.39 +0
4 FC Schalke 04 1.61 1.23 1.31 +0
5 VfL Wolfsburg 1.56 1.28 1.22 +0
6 TSG Hoffenheim 1.65 1.36 1.21 +0
7 Hamburger SV 1.61 1.45 1.11 +1
8 Werder Bremen 1.59 1.44 1.10 -1
9 VfB Stuttgart 1.67 1.66 1.01 +0
10 FSV Mainz 05 1.43 1.44 0.99 +0
11 SC Freiburg 1.38 1.49 0.93 +0
12 Eintracht Frankfurt 1.3 1.44 0.90 +0
13 Hannover 96 1.33 1.64 0.81 +0
14 1.FC Kaiserslautern 1.31 1.65 0.79 +0
15 1.FC Nürnberg 1.21 1.71 0.71 +1
16 1.FC Köln 1.18 1.72 0.69 -1
17 Borussia Mönchengladbach 1.31 2.15 0.61 +0
18 FC St. Pauli 1.02 1.8 0.57 +0
26.81 26.8
There were only minimal shifts as you can see, all plausible (HSV swaps with Werder and Nuremberg with Cologne). However, you can see that Bayern is really closing in on Dortmund again. Apart from that, it’s still a little surprising that the order is still based on original estimates, but you can’t think of a more reliable order right away. Should Hanover really be ahead of Stuttgart?
Whether this somehow conservative (but long since mathematically verified) procedure is sensible, at least for this curious season, remains to be seen. Possibly, however, it will also set a trend pointing in the right direction.
9) The mathematical review of the results of matchday 17
These results with their deviations also show the number of surprises. The 36 goals compared to only 26.5 expected alone provides enough variety, but also in terms of tendencies. A 3:5 is already obvious that it is not a normal result. So logically, it is ahead in the deviation.
Goal expectation
Home Away Result DeviationGladbach HSV 1.53 1.90 1 2 -0.53 0.10
Bremen Kaiserslautern 2.13 1.05 1 2 -1.13 0.95
Wolfsburg Hoffenheim 1.53 1.32 2 2 0.47 0.68
Frankfurt Dortmund 0.92 1.85 1 0 0.08 -1.85
Nuremberg Hanover 1.37 1.35 3 1 1.63 -0.35
Schalke 04 FC Cologne 2.09 0.92 3 0 0.91 -0.92
St. Pauli Mainz 1.12 1.42 2 4 0.88 2.58
Leverkusen Freiburg 2.04 1.08 2 2 -0.04 0.92
Stuttgart FC Bayern 1.26 1.61 3 5 1.74 3.39
13.98 12.51 18 18 4.02 5.49
Expected goal total Expected goal average: Goal total: 36 Goal average achieved
26.48 2.94 4 Just a reminder of the estimates for this matchday’s games in advance, in computer view:
The probabilities for the outcomes of the Matchday 17 matches.
Pairing 1 X 2
Gladbach HSV 31.15% 22.33% 46.53% Bremen Kaislautern
Bremen Kaiserslautern 62.01% 20.26% 17.73%
Wolfsburg Hoffenheim 41.94% 25.11% 32.94%
Frankfurt Dortmund 18.27% 22.53% 59.20%
Nuremberg Hanover 37.38% 25.97% 36.65%
Schalke 04 FC Cologne 64.24% 20.17% 15.59%
St. Pauli Mainz 29.52% 26.60% 43.88%
Leverkusen Freiburg 59.48% 21.11% 19.40%
Stuttgart FC Bayern 29.92% 24.72% 45.36%
3.74 2.09 3.17
The events of matchday 17 that occurred
Pairing 1 X 2
Gladbach HSV 46.53%
Bremen Kaiserslautern 17.73%
Wolfsburg Hoffenheim 25.11%
Frankfurt Dortmund 18.27%
Nuremberg Hanover 37.38%
Schalke 04 FC Cologne 64.24%
St. Pauli Mainz 43.88%
Leverkusen Freiburg 21.11%
Stuttgart FC Bayern 45.36%
3 2 4
Almost an entire home win is missing from the visitors (and not the draws) again. We can see that the Lauter away win was the bigger surprise compared to the Frankfurt home win over Dortmund, but that the two draws were also quite unlikely, and yet exactly the two expected (in total) occurred.
This graph could also be supplemented by the ranking positions of the events that occurred:
1 3 3 3 1 1 1 2 1
1 means that the most likely event occurred, two means the second most likely, etc. Accordingly, there were three real surprises, one half, and five times “normality”. Such a distribution, depending on the size of the probabilities, is of course not completely abnormal, but neither is it suitable for establishing the order one might still be waiting for.
In their view, understanding and interpretation, another figure could bring a further form of enlightenment. For this purpose, all the probabilities of the events that have occurred are added up, i.e. ultimately the numerical entries from the last graph.
The sum of these numbers (25.11% + 18.27% + 37.38% + 64.24% + 43.88% + 21.11% + 45.36% =) is 3.2. Now one only has to understand and interpret this number: Absolute unpredictability would mean that one should expect a 3.0. One would have no clues whatsoever as to how a game could turn out. A Martian who first goes to the stadium and is told, “There are three possible outcomes. What’s the outcome?” could only throw one die to decide. 1 or 2 for a home win, 3 or 4 for a draw, 5 or 6 for an away win. So the chance would be 1/3, for each game outcome – at least from his point of view. For all games, he sees a 1/3 chance for all outcomes, which results in 9 * 1/3 = 3.0. There would still be 9 games, he would have estimated each with 1/3 1/3 1/3, and the 1/3 chance would have occurred in each case (analogous to the graph above), since there would be no deviating entry.
As soon as one begins to know football, to “commit” oneself to favourites here or there – all measured in probabilities — one should succeed in surpassing this 3.0. Not for each individual matchday, of course, but overall, for all matches. Now, on this match day, this did indeed happen with the 3.2 determined, but perhaps not to the extent expected. Somehow favourites have been identified and somehow they have prevailed, but was it sufficiently strong? Or should there have been more favourite events?
Well, this can also be determined and it should be briefly presented, or at least calculated, as the last thing for today. To do this, you have to square all the odds in the original graph and then add them up. This would then look like this:
The expected “determination” for the 17th matchday
Pairing 1 X 2 Squares added up
Gladbach HSV 31.15% 22.33% 46.53% 36.33%
Bremen Kaiserslautern 62.01% 20.26% 17.73% 45.70%
Wolfsburg Hoffenheim 41.94% 25.11% 32.94% 34.75%
Frankfurt Dortmund 18.27% 22.53% 59.20% 43.46%
Nuremberg Hanover 37.38% 25.97% 36.65% 34.15%
Schalke 04 FC Cologne 64.24% 20.17% 15.59% 47.77%
St. Pauli Mainz 29.52% 26.60% 43.88% 35.04%
Leverkusen Freiburg 59.48% 21.11% 19.40% 43.60%
Stuttgart FC Bayern 29.92% 24.72% 45.36% 35.64%
3.74 2.09 3.17 3.56
(Note: the 36.33% for “squares added up” for game 1 is calculated as 31.15% * 31.15* + 22.33% * 22.33% + 46.53% * 46.53%. The higher the sum of the squares, the higher the fixing, thus the higher a favourite position in the game. Very balanced games allow no or only a very low determination.
Furthermore, it is immediately mathematically obvious: the sum of the squares is always greater than or equal to 33.33%. This value would correspond to the minimum, i.e. no fixing at all, where all chances are 33.33%. A precise mathematical explanation perhaps elsewhere).
Overall, this number, the 3.2 that actually occurred, would have had to be a 3.56 for favourites and outsiders events to have occurred in the correct proportion.
Why the squares have to be added up should not be explained too deeply, at least here this much, intuitively: a 62% event occurs 62% of the time. So one calculates the expected value accordingly (only mentioned here for petty mathematicians).
The fact that a certain determination occurred on matchday 17 shows that the favourites were (presumably) correctly identified, but that the number that occurred is only 3.2 and not 3.56 indicates for this matchday that there were too many outsider events, i.e. too many surprises, mathematically speaking. The fan could continue to be enraptured by this.
10) The preview of matchday 18
Of course, the preview must not be missing, even though the matchday does not take place until mid-January. On the betting market, one would probably still have little orientation.
Goal expectations for matchday 18
Goal expectation
Home AwayLeverkusen Dortmund 1.36 1.51
Bremen Hoffenheim 1.61 1.40
Nuremberg Gladbach 2.03 1.41
Stuttgart Mainz 1.81 1.56
Wolfsburg FC Bayern 1.25 1.58
St. Pauli Freiburg 1.18 1.47
Schalke 04 HSV 1.81 1.13
Frankfurt Hanover 1.51 1.10
Kaiserslautern FC Cologne 1.74 1.11
14.31 12.28
Expected goal total: 26.59.
This graph only shows in overview who is favourite, how many goals are expected in the individual match, how many are expected in total, and a little bit how the computer works. The total is under 27 expected goals, so on average less than 3 goals per game are still expected, despite the 3.14 average that has come in so far. Those who could predict better should try. The computer response to the results has been shown to be realistic in the long term and has even been verified (in advance) in a longer term analysis.
So: the person who should say that 3.14 goals are scored per match after all and that it can be assumed that it will be the same on the next matchday is probably (alternative assessments would be welcome to be investigated) making a (bigger) mistake. This would, of course, have to be proven via a practical text.
The distribution of chances of the 18th matchday for 1-X-2
Pairing 1 X 2
Leverkusen Dortmund 34.16% 25.06% 40.78% 34.58%
Bremen Hoffenheim 42.52% 24.33% 33.15% 34.99%
Nürnberg Gladbach 51.91% 21.60% 26.49% 38.63%
Stuttgart Mainz 43.85% 22.73% 33.42% 35.56%
Wolfsburg FC Bayern 30.10% 24.93% 44.97% 35.50%
St. Pauli Freiburg 30.30% 25.99% 43.71% 35.04%
Schalke 04 HSV 53.22% 23.23% 23.55% 39.26%
Frankfurt Hannover 46.49% 25.88% 27.63% 35.95%
Kaiserslautern FC Cologne 51.90% 23.86% 24.25% 38.50%
4.84 2.18 4.98 3.28
As you can see, Dortmund remain favourites despite their recent defeat. This would still have to be compared with the betting market and could be seen differently individually, especially because of the start of the second half of the season, perhaps also because of the first leg, in which Leverkusen remained the winner.
Bremen remain favourites against Hoffenheim. Yes, how else could it be?
Nuremberg are quite clear favourites against Gladbach, but you can assume that Gladbach will do everything to get something in this game. A successful start – and everything would be possible again.
Stuttgart are favourites against Mainz, but only quite tenderly with a 10% “surplus”. Mainz have earned – and deserved – respect.
Bayern are of course favourites in Wolfsburg. However, it could be that the betting market rates this chance much higher (around 50% to above even conceivable). The computer, if you like, continues to “wait” patiently for Wolfsburg’s potential to be realised. Whether it is right to do so remains to be seen. This game offers a huge opportunity. But whether Bayern will play along?
Freiburg are already bigger favourites in Pauli than Stuttgart at home against Mainz. Well, the Breisgauer’s very good results on the one hand, which don’t let up, versus a serious Pauli crisis on the other, which seriously calls into question their suitability for the league, of course, since someone has to be relegated even if they were “fit”, i.e. theoretically they wouldn’t even be replaced equally.
Schalke also clearly in the lead against HSV, which continues to be in crisis (the performance in Gladbach was no more than a first step). You have to agree with that at the moment.
Thanks to the home advantage, Frankfurt and Lautern are also somewhat clearly ahead in the probabilities against Hannover and Cologne respectively, which one is immediately prepared to sign off on. As always, the level of the odds is on trial.
And it is in this context that the newly determined figure of the “fixing” (another term for it: the average expected probability) has matured into a measure. This time, however, there are no such clear favourites overall, as can be seen from the moderate value of 3.28.
So: will the favourites show more throughput in the new year after all or will it remain a league full of surprises? The future will tell, which will ultimately turn all chances that lie between 100% into either a 0 (for what doesn’t come) or a 1 (for what does come). This increase is only achieved through coincidences, which for one side look like luck, for the other like bad luck. Even if one has the illusion of being able to influence it as a participant. But the opponent also has it, in the size of the determined chance, which defines the framework of his possibilities…
A lot of Osophie…
11)
