1) Review of the matches
Results of the 27th matchday
Borussia Mönchengladbach – 1.FC Kaiserslautern 0:1 (0:0)
SC Freiburg – FC Bayern Munich 1:2 (1:1)
- FC Nuremberg – Werder Bremen 1:3 (1:1)
Eintracht Frankfurt – FC St. Pauli 2:1 (1:1)
Hannover 96 – TSG Hoffenheim 2:0 (1:0)
Hamburger SV – 1. FC Cologne 6:2 (4:0)
Borussia Dortmund – FSV Mainz 05 1:1 (1:0)
Bayer Leverkusen – FC Schalke 04 2:0 (2:0)
VfB Stuttgart – VfL Wolfsburg 1:1 (0:1)
General assessment:
Well, the coaching changes that have been made are somehow reminiscent of playing roulette, far removed from the “Russian” variant. You hire a coach and have him sign a contract for 2 or 3 years. The coach agrees to it, knowing full well that the first small series of unsuccessful games will bring an unconditional end. However, he has already found out in permanent parallel negotiations that another coach is sitting in a similarly shaky position elsewhere and jumps onto the same firestool there, always hoping for the miracle of suddenly achieving a series of positive results and ascending to the coaching Olympus, from which he will of course be brought down again the next season. The word “long-term” does not exist. Least of all in the context of “thinking”.
It is a pure results sport. The results, however, do not follow any inevitability – as recorded and elaborated in these documents here, among others. Almost all games are on a knife-edge and decided with one goal situation here being thwarted and another there seeing the ball behind the line. Even more so by the referee’s decisions. You can’t tell how well a coach works by anything, because he doesn’t even get the chance to implement any kind of “concept” at the club he’s hired. A Thomas Schaaf (and with him SV Werder) is ridiculed because the “rip cord” is not pulled. Ridiculous. But only the comments from the media side, who intend to force the change, only to be able to announce a sensation and hunt for the next scalp from next week. Embarrassing. Clueless. Stupid. The idea that the spectator will go along with this is deceptive. Because: just because not all clubs are broke or there are still many, many fans running to the stadiums does not prove that the policies applied are good.
The measures may just not have been enough to scare away the spectators for good. There is certainly something to the thesis that the spectator not only continues to watch football, but is just as keen to consume the inane media reports in order to be put on the spot with them once again. “What’s that bubblehead talking about? What nonsense!”
Apart from that, there is the assertion that the reporters no longer enjoy football and what happens on the pitch. It’s all about the stories on the sidelines. To simply marvel at successful, great actions like a circus act is “out”. The fault is sought. And the emotions are suppressed anyway. At least the positive ones. A commentator who would talk about a fantastic cross that does NOT lead to a goal would have to fear that from next week onwards he will be able to watch the game from the stands at best. Because: another smart-ass would have been there a long time ago, who would have said: “But the opponent must have prevented the cross. He’s only providing security” or “he’s just watching”. And if it did lead to a goal, he would have preferred not to use the word “fantastic”. Because he should have realised – according to the smart-ass – “that the goalkeeper was stuck on the line for far too long” and “the ball was forever in the air” and “the defenders were collectively sleeping”.
Since there are no successful, good actions and every game outcome is deserved because of the universally accepted rule that “goals count”, people pounce on marginal events. Rolling coaches’ heads are very popular. The executioners saw them, the fan who can’t avoid the media does the rest. “Magath out.” Or whoever.
The second part of the general assessment now briefly goes into the Dortmund goal against, which is supposedly debatable.
The attention for such a scene is heightened by the accident in the 2nd division the previous weekend. The Osnabrück player who was seriously injured and stood between life and death for 12 minutes ensured that people were once again reminded that there could be more important things than just winning or losing.
Now the discussion is to turn to whether the referee is obliged to stop the game as soon as a player is lying injured on the ground. Here is the old familiar little story:
There was once the boy who called out twice that the wolf was coming – and everyone rushed to help. The third time the wolf actually came. The boy called out again – and no one came.
Of course, the game is supposed to be stopped when a player is lying injured on the ground. Only the players found out that an injury is not verifiable. So they simply began to roll on the ground after stupid ball losses in order to prevent a dangerous counterattack situation in this way, at the same time concealing their own stupidity, since they could not be checked for “having done something”, possibly even for having been fouled.
This observation is much more important than the other. Because: the game lacks moments of tension. And more and more people are thinking and working in the wrong direction. If you have to interrupt here and there and in this way the action can be stopped and in that way, then soon nothing happens on the pitch. With the exception of perhaps a few genuine fans of a team (many of whom are simply there to celebrate), nobody really watches a football match for 90 minutes any more. That is what should cause concern. You have to provide moments of suspense. This problem has not yet been recognised. The many who turn away shaking their heads simply claim: “Nah, football is not my game.” But they don’t even know yet how much it could be their game if it were exciting – and fair.
A defender always has one last option before the striker gets free to shoot. He falls down. The referee now gives a striker’s foul just like that in 90% of cases (this is especially the case with cross-balls, where there is virtually always a scramble) and is not under any pressure to justify the decision. This decision is (wrongly) always accepted. A falling attacker, on the other hand, must immediately expect a warning because he is accused of attempting to deceive. Simply falling down does not work.
If, on the other hand, the defenders do it, then they either get the whistle directly or, in rare cases, the referee graciously allows them to continue. Of course, this only happens if the referee believes that the action cannot result in a goal. A caution for attempted deception by a defender is never given – despite the much higher frequency. Yet this is the action that should cause much more concern. Since it is directed against the goal action – and thus against the tension felt in the game on the part of the neutral spectator (who therefore hardly exists).
Otherwise, the match day brought a few surprises as usual, but also a few favourite events, the ratio of which can be read off in later figures. Werder can be expressly congratulated on winning another game. As mentioned above, the hectic activity of many club officials is ridiculous. It is perhaps surprising, but on the other hand even more logical, that Werder should win at Nuremberg, which is in such good form. Nuremberg perhaps a bit “laid back”, as they are very satisfied with the results so far.
HSV with a clear victory after the change of coach. Well, but at least it was Cologne who were in almost the same situation as Nuremberg: so many good results, the relegation places far behind them, you can expect a more relaxed performance. Especially as HSV certainly have high quality in their ranks.
Bayern with an almost last-minute victory. Well, it’s always to be expected of them. And the way Ribery sank the ball was a feast for the eyes. Leverkusen’s run continues and Schalke could not offer enough resistance despite(?!) Magath’s dismissal.
Remarkable was the equaliser in injury time from VfB Stuttgart. Wolfsburg had already had a few chances to decide the game and would have liked to get back on track. A game like that, a goal like that can trigger everything – and decide in connection with relegation.
Frankfurt finally wins again. At the expense of St. Pauli, who seem to be running out of steam. Or is it all just a coincidence?
Gladbach’s defeat against a direct competitor will of course also have a considerable influence on the distribution of chances in the relegation battle, as can be seen in the corresponding chapter.
Hannover stays in it with a victory over Hoffenheim, who have weakened considerably in the second half of the season despite their win against Dortmund.
2) The standings
Sp S U N Pkt T GT Diff
1 Borussia Dortmund 27 19 5 3 62 54 – 16 +38
2 Bayer Leverkusen 27 16 7 4 55 56 – 34 +22
3 Hannover 96 27 16 2 9 50 39 – 36 +3
4 FC Bayern Munich 27 14 6 7 48 59 – 34 +25
5 FSV Mainz 05 27 14 2 11 44 42 – 34 +8
6 1.FC Nürnberg 27 12 6 9 42 42 – 36 +6
7 Hamburger SV 27 12 4 11 40 43 – 44 -1
8 SC Freiburg 27 11 4 12 37 34 – 38 -4
9 TSG Hoffenheim 27 9 9 36 42 – 39 +3
10 FC Schalke 04 27 9 6 12 33 31 – 33 -2
11 1.FC Köln 27 9 5 13 32 37 – 49 -12
12 Werder Bremen 27 8 8 11 32 37 – 53 -16
13 1.FC Kaiserslautern 27 8 7 12 31 36 – 43 -7
14 Eintracht Frankfurt 27 9 4 14 31 27 – 37 -10
15 VfB Stuttgart 27 8 5 14 29 46 – 49 -3
16 FC St. Pauli 27 8 4 15 28 29 – 47 -18
17 VfL Wolfsburg 27 6 9 12 27 31 – 40 -9
18 Borussia Mönchengladbach 27 6 5 16 23 38 – 61 -23
723 723 0
Total number of games 243
Goals ø 2.98
Dortmund’s lead is melting away. Even if the loss of points was doubtful, debatable or even unfortunate. It reminds one a little of the soft arm of a tennis player who has three match points. One is missed, the second the first serve is in the net. The effects can be read in the title chances section.
The usual, no longer totally astonishing, picture with Hanover, Mainz, Nuremberg at the top. Now one may no longer speak of an expected correction. A shift here or there, perhaps.
Above all, this concerns the bottom of the table. After all, first Schalke and then Werder and Stuttgart have pretty much “made a run for it”, no matter how the successes partly came about (Werder, for example, with victory in Freiburg, after the regular 2:1 was disallowed, Stuttgart last with equalisation in the last second), the heavyweights possibly have those few percent more class, so that they can at least still avoid relegation with aplomb. Only Wolfsburg is still waiting…
3) The title question
Explanation: these figures 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 probabilities
1 Borussia Dortmund 4815 96.30% 1.04
2 Bayer Leverkusen 177 3.54% 28
3 FC Bayern Munich 7 0.14% 714
4 Hannover 96 1 0.02% 5000
5000 100.00%
Hannover also has another title win in 5000 tries! Bayern also only with extremely blatant outsider chances. But Leverkusen is working on the miracle. 3.54% are more than hitting a number exactly in roulette.
Change in chances compared to the previous week due to the results of Matchday 27
Team Changes absolute compared to the previous week Championship Percentage
Bayer Leverkusen 118 2.36%
Hannover 96 1 0.02%
Borussia Dortmund -119 -2.38%
0 0.00%
As you can see Dortmund with a considerable loss of more than 2%, although the grapes were already so close! Leverkusen almost completely steals the chances. Bayern not represented, as they had exactly the same chance in the simulation of the previous week. The problem for them: Leverkusen also won and thus skimmed off the chances that Bayern would have made good in itself.
4) The title chances as they develop
Surely it is exciting when there is a regression of the winner who seems so certain. You involuntarily think: “Well, as you can see it’s not through yet. Let’s see what happens next week.”
Compare this with the situation three weeks ago when Leverkusen and Dortmund were level on points and Leverkusen had only picked up one point compared to Dortmund’s three victories. In that case, the situation in the standings would be absolutely identical (in this theory of origins), except that we would then be talking about “boredom finally setting in”, and this only because of the origins.
This is not to say that the human mind is simple-minded. It is merely a way of understanding how irrational such feelings are. A chance of 3.6% is once perceived as gigantically large, due to the unexpected increase in the chance, while when reduced to this value it is perceived as tiny, hardly worth mentioning. This phenomenon is exactly analogous to an optical illusion (or any other sensory illusion). Only it is unusual to think about it in the case of probabilities.
5) Direct Champions League qualification via 2nd place
The probability distribution for 2nd place after the 27th matchday
Team Number 2nd place 2nd place in percent Fair odds as inverse of probabilities1 Bayer Leverkusen 3872 77.44% 1.29
2 FC Bayern Munich 836 16.72% 5.98
3 Borussia Dortmund 182 3.64% 27.47
4 Hannover 96 104 2.08% 48.08
5 FSV Mainz 05 5 0.10% 1000.00
6 Hamburger SV 1 0.02% 5000.00
5000 100.00%
It’s clear that Leverkusen are ahead now. They consistently win their games and even if Bayern wins at the same time, the shortening of the duration speaks for Leverkusen. Hanover is holding its own.
The changes compared to the previous week:
Team Win/Loss absolute Win/Loss in per cent.
1 Bayer Leverkusen 140 2.80%
2 Borussia Dortmund 118 2.36%
3 Hamburger SV 1 0.02%
15 Hannover 96 -9 -0.18%
16 1.FC Nuremberg -13 -0.26%
17 FSV Mainz 05 -23 -0.46%
18 FC Bayern Munich -214 -4.28%
0 0.00%
As you can see Bayern with the biggest loss despite their away win. Their chances dwindle the most with Leverkusen wins. The flame of hope is fed by their failure.
6) The relegation question
The distribution of relegation percentages
Note: There would also be a detailed breakdown across the individual places. Here, places 17 and 18 count as fully relegated (i.e. as 1, for relegated, otherwise the term is “direct relegation”), and a further third of relegated teams are added due to the relegation, whereby the first division team is generally rated as 2/3 to 1/3 favourite over the second division team. This makes the total number of relegated teams equal to 233.33%. In individual cases, of course, it would be different in reality. So if, for example, Hertha entered in 3rd place and St. Pauli in 16th, one could perhaps speak of a balanced pairing.
Team Direct relegation (17th or 18th place) Relegation by relegation Total
1 Borussia Mönchengladbach 93.54% 1.28% 94.82%
2 FC St. Pauli 54.40% 6.67% 61.07%
3 VfL Wolfsburg 19.56% 5.91% 25.47%
4 Eintracht Frankfurt 10.90% 6.58% 17.48%
5 VfB Stuttgart 9.50% 5.05% 14.55%
6 1.FC Kaiserslautern 7.04% 3.95% 10.99%
7 1.FC Cologne 2.86% 2.13% 4.99%
8 Werder Bremen 1.88% 1.33% 3.21%
9 FC Schalke 04 0.30% 0.33% 0.63%
10 TSG Hoffenheim 0.02% 0.05% 0.07%
11 SC Freiburg 0.00% 0.05% 0.05%
200.00% 33.33% 233.33%
Still eleven teams in the relegation race, which is quite a lot. Whereby the teams behind Werder don’t really count anymore. Nevertheless, one must still speak of a tight race and an exciting battle.
Logically, Gladbach and Pauli are far ahead. Wolfsburg still insists on its potential. Whether that really plays the decisive role in the relegation battle or fear paralyses the legs of the favourites in crucial situations? We shall see…
The change in chances from the 26th to the 27th matchday with regard to relegation
Team Change in chances
1 Eintracht Frankfurt -17.66%
2 1.FC Kaiserslautern -11.52%
3 Werder Bremen -7.30%
4 Hamburger SV -0.01%
11 SC Freiburg 0.03%
12 TSG Hoffenheim 0.05%
13 FC Schalke 04 0.21%
14 VfL Wolfsburg 1.75%
15 VfB Stuttgart 2.46%
16 1.FC Cologne 2.69%
17 Borussia Mönchengladbach 9.21%
18 FC St. Pauli 20.09%
0.00%
Frankfurt top the table with an enormously important win against their direct rivals. That Lautern are behind, despite winning away at another rival, in improving their chances of avoiding relegation, perhaps becomes clear like this: they could not gain as many percentages from Gladbach as Frankfurt could from Pauli, since Gladbach were already very far behind anyway as far as the danger of relegation was concerned. Frankfurt, on the other hand, was able to help itself brilliantly to Pauli. As you can see, the Pauli loss is also much greater than that of Gladbach. (And, believe it or not: the text part before was written before your own gaze wandered downwards).
7) The relegation question in development
It jags on beautifully. However, Gladbach and St. Pauli have seen a sensitive jagging upwards. At Pauli continuously, at Gladbach only now again, after they were once at over 90%.
The rest is still in the race, but Frankfurt (as the remaining team) has taken a good step.
8) The points 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 match according to the formula probability of victory * 3 points + probability of draw * 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 those that have occurred, but an imbalance is forced by the three-point rule. Too many points scored means that there were too few draws.
Team Name Points scored Deviation Deviation absolute
1 Hannover 96 32.41 50 17.59 17.59
2 Borussia Dortmund 49.48 62 12.52 12.52
3 1.FC Nürnberg 31.70 42 10.30 10.30
4 Bayer Leverkusen 46.25 55 8.75 8.75
5 FSV Mainz 05 35.28 44 8.72 8.72
6 1.FC Köln 28.89 32 3.11 3.11
7 SC Freiburg 33.92 37 3.08 3.08
8 1.FC Kaiserslautern 30.27 31 0.73 0.73
9 FC St. Pauli 28.32 28 -0.32 0.32
10 Hamburger SV 41.53 40 -1.53 1.53
11 Eintracht Frankfurt 33.35 31 -2.35 2.35
12 TSG Hoffenheim 39.26 36 -3.26 3.26
13 FC Bayern Munich 52.26 48 -4.26 4.26
14 Borussia Mönchengladbach 29.31 23 -6.31 6.31
15 Werder Bremen 39.58 32 -7.58 7.58
16 FC Schalke 04 41.91 33 -8.91 8.91
17 VfB Stuttgart 39.34 29 -10.34 10.34
18 VfL Wolfsburg 38.59 27 -11.59 11.59
8.34 121.25
ø Deviation 6.74Hannover still increases its lead at the top as they won and Dortmund lost. As you can see, for example, Freiburg is “only” one win above expectation, as is Cologne. St. Pauli has only a minimal deficit, which shows how little the computer expected from them. After all, with this yield they are in the relegation place, which would still offer chances if achieved in the final standings. And that would be an acceptable goal.
The “big disappointments” remain quite clearly behind, even behind the actual bottom of the table, Mönchengladbach. If you look at the expected points, you can see why. Gladbach should only have 29, while Schalke should have almost 42. Sure, in Schalke’s case it’s because they kept getting into some kind of upward trend, whereupon the computer trusted them to do more again, while Werder, Stuttgart and Wolfsburg consistently underperformed over the season, so the expectation adjusted more quickly. This is only to explain why Schalke should have scored (significantly) more points than the others, as they were not originally rated stronger than these “competitors”.
The foreign comparison for the average point deviation
Note: the theory is that the German Bundesliga is the most exciting among Europe’s top leagues. This finding is rather intuitively derived, but so far “accepted” both in this country and abroad. Of course, the higher goal average is an indication of this, as well as the(perceived) lower predictability when it comes to the title, relegation, but also other issues. Balance is a criterion and possibly the main reason for this.
The measure used here for the deviation in average points expectation provides measurable information about this, but it is probably a “problem” specific to this season (the fan thanks) that the Bundesliga has produced a particularly large number of surprises. This can be seen in figures.
League 1 ø Deviation Change from previous week
Germany 6.74 -0.24
Italy 4.92 -0.11
Spain 3.33 0.05
France 3.56 0.05
England 2.39 0.06
Germany remains far ahead, yet the matchday has corrected a little. “Correction”, when looked at closely, means that the teams that had underperformed their expectation so far have scored more than those that were previously above expectation. If you look at the results, you can certainly see it. Especially Freiburg – Bayern and Nürnberg – Werder are the clear pairings with the trend, also HSV – Köln. There was not much movement abroad, and not specifically in one direction.
Mathematically, one should not expect an equaliser. If one does feel that way, then it is more of a philosophical consideration that cannot necessarily be represented in numbers. Nevertheless, it is more likely to “wait” for a trend towards equalisation, author-wise.
9) Goal expectations and their deviations
Explanation: Almost the same applies to goals as to 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. However, the goal average may show a deviation.
Team Name Goal expectation Goals scored Goals conceded expected Goals conceded Total deviation
1 Borussia Dortmund 48.44 54 29.10 16 18.66
2 1.FC Nürnberg 34.01 42 42.88 36 14.86
3 FSV Mainz 05 37.07 42 40.26 34 11.20
4 Hannover 96 35.01 39 42.73 36 10.72
5 Bayer Leverkusen 48.18 56 33.98 34 7.80
6 1.FC Kaiserslautern 33.71 36 45.02 43 4.31
7 1.FC Köln 32.65 37 46.40 49 1.75
8 SC Freiburg 36.02 34 41.39 38 1.37
9 FC Bayern Munich 50.55 59 26.87 34 1.32
10 TSG Hoffenheim 41.80 42 38.52 39 -0.28
11 FC St. Pauli 30.99 29 45.00 47 -3.99
12 Eintracht Frankfurt 34.48 27 40.18 37 -4.30
13 VfB Stuttgart 43.08 46 40.06 49 -6.02
14 Hamburger SV 42.58 43 35.99 44 -7.58
15 Borussia Mönchengladbach 36.87 38 50.58 61 -9.29
16 FC Schalke 04 41.60 31 34.21 33 -9.39
17 VfL Wolfsburg 39.99 31 37.64 40 -11.35
18 Werder Bremen 43.23 37 39.45 53 -19.78
710.24 723 0.00
Goals ø expected: Goals ø scored: ø Deviation 8.00
2.92 2.98 Here Dortmund still in front and Hannover, due to the not too favourable goal ratio on 4 back. Bayern is even up in this statistic, whereas Werder slips significantly to 18 with the disastrous ratio.
Also for this statistic the foreign comparison:
Rank Country League 1 ø Goal difference Change from previous week.
1 Germany 8.00 -0.36
2 Italy 5.59 -0.05
3 Spain 4.57 0.29
4 England 5.15 0.12
5 France 4.36 -0.18
Germany far ahead, despite the correction that has occurred. Confirmed again and again: this is a season of surprises, much more than usual and elsewhere. The overall trend here already points rather downwards, as the buzzer of changes has a value of -0.18. Here, too, it would be worth waiting to see whether it is confirmed as a trend.
10) The playing strength ranking
Note: Playing strength is measured in goals expected against the average team (which does not exist in practice). There is offensive strength, which is measured in expected goals scored, and defensive strength, which is measured in expected goals conceded. The quotient of these two values is the measure of playing strength. The more expected goals scored, the higher the value; the fewer expected goals conceded, the higher the value.
Goal expectations
Team For Against Quotient For/Counter Shift
1 Borussia Dortmund 1.75 0.85 2.06 +0
2 FC Bayern Munich 2.21 1.15 1.92 +0
3 Bayer Leverkusen 1.93 1.20 1.61 +0
4 FC Schalke 04 1.29 1.16 1.11 +0
5 Hamburger SV 1.64 1.48 1.11 +1
6 1.FC Nürnberg 1.48 1.40 1.06 -1
7 FSV Mainz 05 1.44 1.39 1.04 +0
8 Hannover 96 1.38 1.38 1.00 +1
9 Werder Bremen 1.53 1.56 0.98 +1
10 TSG Hoffenheim 1.42 1.46 0.97 -2
11 VfB Stuttgart 1.53 1.68 0.91 +0
12 SC Freiburg 1.25 1.44 0.87 +1
13 VfL Wolfsburg 1.22 1.44 0.85 +1
14 1.FC Köln 1.39 1.69 0.82 -2
15 1.FC Kaiserslautern 1.22 1.61 0.76 +0
16 Borussia Mönchengladbach 1.30 1.92 0.68 +0
17 Eintracht Frankfurt 1.00 1.50 0.67 +0
18 FC St. Pauli 1.09 1.76 0.62 +0
26.07 26.07 +0
Goals ø expected
2.897 As always, a few minor shifts. Bayern “robb(en)t” their way back up, a few more bad results from Dortmund and they’ll be caught up. Hoffenheim with a fall by 2 places due to the 0:2 in Hannover and also Werder passes with the 3:1 away win.
Also Cologne with a fall by 2 places with the 2:6. Wolfsburg got a good result despite the late equaliser and also Freiburg with the 1:2 against Bayern did not disappoint directly (from the computer’s point of view).
11) The frequency of tendency changes
Note: a “change of tendency” is considered to be a goal that equalises a lead or scores a lead. The 1:0 is not counted, because without this goal it would not even begin to have anything to do with tension in the goal sequence. Every now and then, a statistical comparison is made here with other countries. This shows that there are more changes of tendency in Germany than elsewhere, which on the one hand points to perceived tension in the Bundesliga – which is possibly envied abroad – and on the other hand points to possible tactical deficiencies, which, following an old tradition, make one advise to urgently go for a second goal after a 1:0 – and not to dull and insipidly, as is usual abroad, rock this goal over time. More information about the effectiveness or weakness of the German behaviour can be found in the international comparisons.
There were a total of 8 changes of tendency on this matchday, which is exactly in line with the season average of 0.89 (and still too little in terms of genuine excitement generated by it, even if it is the highest value in Europe).
These were:
Freiburg vs Bayern, equaliser Freiburg, winning goal Bayern = 2.
Nürnberg – Werder, equaliser Nürnberg, lead and win Werder = 2.
Frankfurt – St. Pauli, equaliser St. Pauli, winning goal Frankfurt = 2.
Dortmund – Mainz the equaliser = 1.
Stuttgart – Wolfsburg the equaliser =1.
Again, the call to rethink and think in terms of more goals made possible purely by applying existing rules. There would be pleasing movements in this category here.
12) The mathematical review of the results of the 27th matchday
Goal expectation
Home Away Total DeviationGladbach Kaiserslautern 1.79 1.47 3.26 0 1 -1.79 -0.47
Freiburg FC Bayern 1.15 1.91 3.06 1 2 -0.15 0.09
Nuremberg Bremen 1.92 1.15 3.07 1 3 -0.92 1.85
Frankfurt St. Pauli 1.25 0.97 2.22 2 1 0.75 0.03
Hannover Hoffenheim 1.64 1.21 2.84 2 0 0.36 -1.21
HSV FC Cologne 1.83 1.17 3.00 6 2 4.17 0.83
Dortmund Mainz 1.87 0.80 2.67 1 1 -0.87 0.20
Leverkusen Schalke 04 1.73 1.01 2.74 2 0 0.27 -1.01
Stuttgart Wolfsburg 1.74 1.18 2.92 1 1 -0.74 -0.18
14.91 10.86 25.77 16 11 1.09 0.14
Expected goal total Expected goal average Scored goal average
25.77 2.86 3.00 ø expected goal deviation 1.87 ø goal deviation 1.77
The goal expectation was slightly exceeded, which on the one hand is pleasing, on the other hand may be due to the outbreak of spring, but also due to a single 6:2. Nevertheless, it is in line with a long-term observation that from this time of year or phase of the season onwards, more goals are scored again. And a 6:2 for these two teams, who are temporarily in no-man’s land, may have something to do with the fact that they play a little more relaxed.
The home teams converted their advantage as expected. The average goal difference even smaller than expected (despite this 6:2), which gives this matchday an attribute of “completely normal”. Perhaps also confirmed in the next statistics?
The determination
Note: The fixing is calculated for each match 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 the favourite position, the higher the sum of the squares, but also the more “certain” the occurrence of the (favourite) 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 of the estimates made here in the long term by comparing expected/occurred. This is done week by week, but of course also overall.
The determination expected
Pairing 1 X 2
Gladbach Kaiserslautern 45.38% 22.75% 31.86% 35.93%
Freiburg FC Bayern 22.74% 22.12% 55.13% 40.46%
Nuremberg Bremen 55.42% 22.04% 22.54% 40.65%
Frankfurt St. Pauli 42.93% 28.46% 28.62% 34.71%
Hanover Hoffenheim 47.55% 24.25% 28.21% 36.44%
HSV FC Cologne 52.73% 22.81% 24.46% 38.99%
Dortmund Mainz 62.77% 21.77% 15.46% 46.53%
Leverkusen Schalke 04 54.40% 23.61% 21.99% 40.00%
Stuttgart Wolfsburg 50.56% 23.50% 25.94% 37.82%
4.34 2.11 2.54 3.52
Average expected commitment: 39.06%
The determination arrived Pairing 1 X 2
Gladbach Kaiserslautern 45.38% 22.75% 31.86% 31.86%
Freiburg FC Bayern 22.74% 22.12% 55.13% 55.13%
Nuremberg Bremen 55.42% 22.04% 22.54% 22.54%
Frankfurt St. Pauli 42.93% 28.46% 28.62% 42.93%
Hanover Hoffenheim 47.55% 24.25% 28.21% 47.55%
HSV FC Cologne 52.73% 22.81% 24.46% 52.73%
Dortmund Mainz 62.77% 21.77% 15.46% 21.77%
Leverkusen Schalke 04 54.40% 23.61% 21.99% 54.40%
Stuttgart Wolfsburg 50.56% 23.50% 25.94% 23.50%
4.34 2.11 2.54 3.52
average commitment received: 39.16%As you can see, surprises and “normal” results were exactly in line with expectations. The average determination was almost exactly the same as the expected one. In this sense, a “picture book match day”. As one learns on closer inspection, some clear favourites prevailed (Bayern, Frankfurt, Hannover, HSV, Leverkusen), five in total, three times the second most likely (Gladbach, Nürnberg, Dortmund) and once the least likely (Stuttgart). So to speak, “ideal” for these few games. But somehow it also illustrates what this determination achieves?!?
Note: No comparable model has yet been discovered in mathematics. Not even by a mathematician who had set himself the task of proving to the author that there would definitely be nothing new.
13) League statistics
Note: such a statistic is regularly produced by the computer. It is generally used for quality control of the individual figures, Each figure has its meaning and is explained in more detail. The goal average is not repeated here. The home advantage is calculated by dividing the goals scored by the home team by half of the total goals. In this way, you can see how many more goals the home teams score than they would score without home advantage. 1,116 is 11.6% more for the home team, 11.6% less for the away team.
1st Football Bundesliga 2010/2011
Statistics of the actual results Matches Home wins Draws Away wins Goals conceded Home advantage
234 111 49 83 408 315 1.129
Statistics of expected results Matches Home wins Draws Away wins Goals Conceded Home advantage
234 110.67 57.33 74.98 398.0 312.2 1.121
Statistics of absolute deviations Matches Home wins Draws Away wins Goals Conceded Home advantage
0 0.33 -8.33 8.02 10 2.8 0.00782
Statistics of percentage deviationsMatches Home wins Draws Away wins Goals Conceded Home advantage
0 0.30% -17.00% 9.66% 2.45% 0.89% 0.69%
Determination expected Determination arrived
39.33% 37.87%
ø Goal difference ø Goal difference expected
1.97 1.91 All values here halfway within the range. Of course, the low number of draws that occurred is striking. It’s just that it’s probably a coincidence, although there is no trend at present to suggest that it could even out again. However, a new season could provide some information. Incidentally, the computer regularly adjusts the so-called “draw factor” – which proved to be indispensable – so that the percentage of expected draws gradually decreases.
As you can see, the home teams have already scored more of the too many goals than the away teams. Although the away teams still have too many wins. This suggests that high wins have tended to go to the home teams (proportionally too many). On the other hand, the average goal difference of 1.97 compared to 1.91 expected indicates (as there is a higher difference than in other seasons) that the surprises can be read here as well, if one only looks closely enough.
14) Preview of the 28th matchday
Note: The computer uses a specially developed algorithm – which can of course be explained and is highly logical – to calculate the goal expectations (and the individually maintained home advantage not shown here) to these goal expectations. 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 TotalSt. Pauli Schalke 04 1.06 1.27 2.33
Kaiserslautern Leverkusen 1.11 1.81 2.92
FC Bayern Gladbach 3.33 0.88 4.21
Dortmund Hanover 1.76 0.67 2.43
Bremen Stuttgart 1.88 1.52 3.40
Mainz Freiburg 1.46 1.03 2.49
Hoffenheim HSV 1.65 1.36 3.01
FC Cologne Nuremberg 1.59 1.41 3.00
Wolfsburg Frankfurt 1.40 0.98 2.38
15.23 10.95 26.18
Expected goal total Expected goal average
26.18 2.91 Without special comment. The home teams in front, as (almost) always, the expected goal average within the normal range. I wonder if there will be a surplus again, as previously indicated?
There should be many goals in Munich, very few in St. Pauli, Dortmund (!!), Wolfsburg and Mainz. Many still absolutely in Bremen.
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 events.
The determination expected
Pairing 1 X 2
St. Pauli Schalke 04 31.18% 27.76% 41.06% 34.29%
Kaiserslautern Leverkusen 23.07% 22.87% 54.06% 39.78%
FC Bayern Gladbach 83.56% 10.24% 6.20% 71.26%
Dortmund Hannover 63.54% 22.64% 13.82% 47.41%
Bremen Stuttgart 46.29% 22.14% 31.57% 36.30%
Mainz Freiburg 46.90% 26.17% 26.93% 36.10%
Hoffenheim HSV 44.47% 23.81% 31.72% 35.51%
FC Cologne Nuremberg 41.89% 23.98% 34.13% 34.95%
Wolfsburg Frankfurt 46.59% 26.88% 26.54% 35.97%
4.27 2.06 2.66 3.72
Average expected determination: 41.28With 41.28% expected a favourite matchday. Responsible for this are Bayern and a little Dortmund. The rest with pretty normal values under 40%, in that sense open pairings.
The fair odds
Note: the fair odds are just the inverse of the probabilities. However, this is how the games are offered on the betting market or traded on the betting exchanges (“betfair”). You can gladly compare what the computer guesses. The deviations will not be enormous, but theoretically every bet is a good bet (from the computer’s point of view) if the odds paid on the market are above the fair odds. “Good” is the bet insofar as it promises long-term profit. If you consistently make bets in this way, you should make a profit in the long run. Of course, there are no guarantees for this either.
Pairing 1 X 2
St. Pauli Schalke 04 3.21 3.60 2.44
Kaiserslautern Leverkusen 4.33 4.37 1.85
FC Bayern Gladbach 1.20 9.77 16.12
Dortmund Hanover 1.57 4.42 7.24
Bremen Stuttgart 2.16 4.52 3.17
Mainz Freiburg 2.13 3.82 3.71
Hoffenheim HSV 2.25 4.20 3.15
FC Cologne Nuremberg 2.39 4.17 2.93
Wolfsburg Frankfurt 2.15 3.72 3.77
The little extra service. The values are theoretically already supplied, as the fair odds are the reciprocals of the probabilities.
15) Evaluation of the 27th Second Division Matchday
Goal expectation
Home Away Total Result Deviation
Munich 1860 Karlsruhe 1.79 1.04 2.83 5 1 3.21 -0.04
Duisburg Düsseldorf 1.58 1.02 2.60 1 0 -0.58 -1.02
Ingolstad Hertha 1.04 1.73 2.77 1 1 -0.04 -0.73
Osnabrück Aachen 1.64 1.63 3.26 1 3 -0.64 1.37
Augsburg Oberhausen 2.48 0.57 3.05 2 0 -0.48 -0.57
Erzgebirge Aue Greuther Fürth 0.99 0.99 1.99 0 0.99 -0.99
Union Bielefeld 1.90 0.63 2.53 2 0.10 1.37
SC Paderborn FSV Frankfurt 1.40 1.09 2.48 2 2 0.60 0.91
Bochum Cottbus 1.79 1.20 3.00 1 0 -0.79 -1.20
14.61 9.90 24.51 15 9 0.39 -0.90
Expected Goal Total Expected Goal Total: Goal Total: Goal Total
24.51 2.72 24 2.6667 ø expected goal difference: ø arrived goal difference:
1.81 1.74
As you can see, there is quite a big gap between expectation and reality. The average goal expectation is also below the expected one, which also speaks for a “very normal”. No outliers, everything quite fitting.
The determination (expected) Pairing 1 X 2
Munich 1860 Karlsruhe 55.00% 23.05% 21.95% 40.38%
Duisburg Düsseldorf 50.46% 24.99% 24.55% 37.73%
Ingolstad Hertha 22.89% 23.59% 53.52% 39.45%
Osnabrück Aachen 38.73% 22.96% 38.32% 34.95%
Augsburg Oberhausen 79.15% 14.22% 6.63% 65.11%
Erzgebirge Aue Greuther Fürth 34.66% 30.67% 34.66% 33.44%
Union Bielefeld 67.86% 20.64% 11.50% 51.63%
SC Paderborn FSV Frankfurt 44.18% 26.45% 29.37% 35.14%
Bochum Cottbus 51.32% 23.01% 25.67% 38.22%
4.44 2.10 2.46 3.76
Average expected commitment: 41.78%
The determination (arrived) Pairing 1 X 2
Munich 1860 Karlsruhe 55.00% 23.05% 21.95% 55.00%
Duisburg Düsseldorf 50.46% 24.99% 24.55% 50.46%
Ingolstad Hertha 22.89% 23.59% 53.52% 23.59%
Osnabrück Aachen 38.73% 22.96% 38.32% 38.32%
Augsburg Oberhausen 79.15% 14.22% 6.63% 79.15%
Erzgebirge Aue Greuther Fürth 34.66% 30.67% 34.66% 30.67%
Union Bielefeld 67.86% 20.64% 11.50% 20.64%
SC Paderborn FSV Frankfurt 44.18% 26.45% 29.37% 26.45%
Bochum Cottbus 51.32% 23.01% 25.67% 51.32%
4.44 2.10 2.46 3.76
Average number of commitments received: 41.73% Again, an amazing coverage between the expectation and the reality. This on a favourite matchday with over 41%. Sure, Augsburg, Munich 60, Bochum and Duisburg won, but there were also the surprises, this time in the form of draws (the biggest certainly Union’s draw against Bielefeld, not only in terms of the numbers).
16) Preview of the 28th Zweitliga matchday
Goal expectation
Home Away Total
Bielefeld Augsburg 0.68 2.22 2.91
Cottbus Ingolstad 1.98 1.10 3.08
Karlsruhe Osnabrück 2.07 1.38 3.45
Greuther Fürth Duisburg 1.22 0.79 2.01
Düsseldorf Erzgebirge Aue 1.50 0.81 2.32
Hertha SC Paderborn 2.08 0.74 2.82
Aachen Munich 1860 1.47 1.45 2.92
Oberhausen Union 1.02 1.09 2.11
FSV Frankfurt Bochum 1.05 1.43 2.48
13.07 11.02 24.09
Expected goal total Expected goal average
24.09 2.68 ø expected goal difference: 1.81
Without comment… If, then this: the home teams less in front than usual, despite Hertha home game. Why? Augsburg at Bielefeld makes up for it, the rest even games.
The determination (expected) Pairing 1 X 2
Bielefeld Augsburg 9.96% 17.52% 72.52% 56.66%
Cottbus Ingolstad 57.84% 21.56% 20.61% 42.35%
Karlsruhe Osnabrück 53.26% 21.20% 25.53% 39.38%
Greuther Fürth Duisburg 46.24% 29.73% 24.03% 36.00%
Düsseldorf Erzgebirge Aue 53.53% 26.13% 20.34% 39.62%
Hertha SC Paderborn 68.58% 19.31% 12.11% 52.23%
Aachen Munich 1860 38.29% 24.63% 37.08% 34.48%
Oberhausen Union 33.15% 29.79% 37.06% 33.60%
FSV Frankfurt Bochum 27.66% 26.51% 45.83% 35.68%
3.89 2.16 2.95 3.70
Average expected commitment: 41.11% Once again a favourite matchday. On this one could at least note that they can pile up towards the end of the season. The reason: at the top or at the bottom of the table, teams can clearly stand out and ensure “clear conditions” in the matches. At the beginning of the season, the gaps between the teams are smaller, and this for eminently sensible and understandable reasons. Or who would have guessed that Bielefeld would pull away so clearly at the back? It’s not even Christian Ziege’s fault that the squad has been extremely weakened. The experts, at any rate, still rated Bielefeld around 10th. Such a crash was hard to predict.
The fair odds
Pairing 1 X 2
Bielefeld Augsburg 10.04 5.71 1.38
Cottbus Ingolstad 1.73 4.64 4.85
Karlsruhe Osnabrück 1.88 4.72 3.92
Greuther Fürth Duisburg 2.16 3.36 4.16
Düsseldorf Erzgebirge Aue 1.87 3.83 4.92
Hertha SC Paderborn 1.46 5.18 8.26
Aachen Munich 1860 2.61 4.06 2.70
Oberhausen Union 3.02 3.36 2.70
FSV Frankfurt Bochum 3.61 3.77 2.18
The little special at the end.
Let’s see if there are any answers to the many unanswered questions on matchday 28. Can Dortmund finally use the remaining 96% and come decisively closer to 100? Will Gladbach catch up once again? What will happen in Wolfsburg? Magath as a relegated team? Still hard to imagine…
