1) The 1st Bundesliga
a. Review of the Matches
Results of the 29th Matchday
Eintracht Frankfurt – Werder Bremen 1:1 (0:0)
Hamburger SV – Borussia Dortmund 1:1 (1:0)
FC Schalke 04 – VfL Wolfsburg 1:0 (0:0)
- FC Nuremberg – FC Bayern Munich 1:1 (0:1)
Hannover 96 – FSV Mainz 05 3:2 (1:2)
SC Freiburg – TSG Hoffenheim 3:2 (1:2)
VfB Stuttgart – 1.FC Kaiserslautern 2:4 (2:1)
Borussia Mönchengladbach – 1.FC Köln 5:1 (3:0)
Bayer Leverkusen – FC St. Pauli 2:1 (0:0)
General assessment:
Well, if you still have the admonishing words of the previous week in your ears, then that leads to the conclusion that they were either heard by officials or that the admonitions were nonsensical. There was quite a lot of turned play and some goal spectacle, as well as a few penalties that were “courageously” awarded, as called for. On the other hand, there was of course the scene when Ibisevic, the Hoffenheim attacker, was fouled so clearly in the penalty area that there are no two opinions: That was a penalty kick. However, it was not awarded. Should we now once again say: “He didn’t see that”? No, that would be just as much nonsense. Because: why does he (the referee) see a foul from the striker’s side blindfolded from the other half of the pitch? That makes the decision easy. There is the shadow of a doubt when receiving the ball? Well, then it was surely handball or a push or a…. or…or… or. No matter: there I whistle, against the attacker. And I don’t even need a justification. For the attacker? Never!
Well, that was far from the peak of injustice in this scene. Because: when Ibisevic indignantly wanted to draw attention to the irregularity committed against him – which really everyone in the stadium except one (up to three, because what would the assistants and the radio link be for if they weren’t allowed to draw attention to it?) – this verdict was again unanimous and without contradiction: for such unsportsmanlike conduct, such impropriety, there is neither tact nor flexibility in the penalty: yellow card. And woe betide him if he dared to remain indignant in the face of this heightened injustice. Then he would have been shown a yellow card in no time.
Now one wonders whether, in general, never having a yellow card for bleating has any bearing on whether bleating has any justification. So if after the game the officials clearly come to the conclusion that it was a crystal-clear penalty, then surely the yellow card could at least be deleted again, just to document that this indignation could be understood? For that you would actually have to apologise to the striker? No, that’s just it. It is a goal (or “almost-goal”) that was not given. There is not even a tiny ripple over the edge of the water glass, which was caused by the storm inside. But woe betide him if he had given a penalty and it had been found to be wrong, had resulted in such an “illegal” goal. That would have caused a veritable (oh, no, the unword, but used…) tsunami.
Just a form of evidence that there is a definite tendency to lash out against strikers. However, as much as it may be psychologically understandable, it is damaging to football. The media contribute significantly to this with their form of dissemination. Here, it could very well be brought about that a (wrongly) not given goal can cause just as much damage as a wrongly recognised one.
Otherwise, it was a matchday without any particular complaints as far as the suspense content and the development of the table situation (with the upcoming decisions) are concerned. Dortmund may have produced a boring result (which 1:1 clearly is), but the game itself and the way the result came about was anything but boring. There were a number of top-class goals and Klopp got to the heart of the matter when he said that he would have found a 0:1 extremely unfair, but that the 1:1 was acceptable again (of course, especially due to the timing, namely deep in injury time).
Bayern’s 1:1 immediately cost the coach his head, which should only be commented on here insofar as football has mutated into a pure results sport, as recognised by the bosses. Whether the spectators still enjoy it, whether it is played well, none of this matters any more. Results are the order of the day, no matter what. However, it should be borne in mind that the neutral spectator has long since been lost (as has been emphasised here many times), because he no longer buys this cheating package. They want to see an exciting, fair football match (who is that supposed to be? Exactly, they don’t exist any more…) with as many goal scenes and goals as possible and, best of all, a fair winner at the end. If that doesn’t exist, then they would like to be allowed to feel sadness instead of blame and fault-finding — to see coaches’ heads roll.
The fact that Stuttgart lost at home would certainly not have been thought possible, but the view is expressed here that Kaiserslautern did not always get their just rewards from their many good performances, insofar as they were once again entitled to a real sense of achievement.
Frankfurt, too, showed the great football of the first half of the season, but did not quite take the spoils. At least it was enough for a 1-1 draw against Werder, who are probably saying goodbye to the relegation race point by point.
The matches between Hannover and Mainz and Freiburg and Hoffenheim were almost identical, with the visitors leading at half-time (2:1) and the home team winning 3:2. Nevertheless, it may be noted here that all teams do not play for that much. Hanover certainly have the chance, and Mainz might have had it too, to reach Europe, but the demands are not there, so that the tension can still decrease. This slackening of tension can then sometimes lead to a few surprising or high-scoring results. The opposite, “tension”, is usually reflected in attentive defending…
Gladbach’s result against Cologne also falls into this category. Even if it should only concern the away team here, which already felt on the safe shore after the very good series. Gladbach, on the other hand, is playing with a bit of desperation. They know they need a (small) miracle and are playing fresh, cheerful and free forward. What, please, is supposed to go sour about vinegar?
Certainly a little explosiveness in the game between Schalke and Wolfsburg due to the change(s) of coach. Schalke have stabilised and Rangnick is reportedly aiming for even more. Worry child Wolfsburg at least managed to hold on to 16th place thanks to Leverkusen’s continued turnaround against St. Pauli. At least St. Pauli did their best to make life difficult for the top favourites and showed that they are still a force to be reckoned with, even if their tough remaining programme leaves them with little hope.
b. The standings
Sp S U N Pkt T GT Diff1 Borussia Dortmund 29 20 6 3 66 59 – 18 +41
2 Bayer Leverkusen 29 18 7 4 61 59 – 35 +24
3 Hannover 96 29 17 2 10 53 43 – 42 +1
4 FC Bayern Munich 29 15 7 7 52 61 – 35 +26
5 FSV Mainz 05 29 14 3 12 45 45 – 38 +7
6 1.FC Nürnberg 29 12 7 10 43 43 – 38 +5
7 Hamburger SV 29 12 6 11 42 44 – 45 -1
8 SC Freiburg 29 12 5 12 41 38 – 41 -3
9 FC Schalke 04 29 11 6 12 39 34 – 33 +1
10 TSG Hoffenheim 29 9 10 37 44 – 42 +2
11 1.FC Köln 29 10 5 14 35 39 – 54 -15
12 1.FC Kaiserslautern 29 9 7 13 34 40 – 46 -6
13 Werder Bremen 29 8 10 11 34 39 – 55 -17
14 Eintracht Frankfurt 29 9 6 14 33 29 – 39 -10
15 VfB Stuttgart 29 8 6 15 30 49 – 54 -5
16 VfL Wolfsburg 29 6 10 13 28 32 – 42 -10
17 FC St. Pauli 29 8 4 17 28 30 – 51 -21
18 Borussia Mönchengladbach 29 7 5 17 26 43 – 63 -20
771 771 -1
Total number of games 261
Goals ø 2.95
Bayern falls back, so that Hannover again takes the place in the potential Champions League sun, which still seems a bit absurd in view of the goal differences (and also does not correspond to the performances shown). Bayern still have a little time… On Saturday against Leverkusen, “the new guy” can shine right away (or be labelled an “interim solution”). A victory, on the other hand — which the team could of course achieve without his help — and a new star has appeared in the coaching sky. If the media are to be believed.
The relegation battle remains exciting, but there is this gap between 14 and 15 that would first have to be closed to speak of true drama. The back 4 are settling a bit too much….
c. The title question
Team Number of German champions in 5000 simulations Championships in percent Fair odds as reciprocal of probabilities
1 Borussia Dortmund 4798 95.96% 1.04
2 Bayer Leverkusen 202 4.04% 25
5000 100.00%
There are two candidates left. The heavy legs comparable to tennis elbow were not evident at Dortmund. Nevertheless, it feels like tension. Clearly, a lot now depends on Saturday, when Leverkusen could receive the accolade. It looks a bit like a distortion of competition that the teams on 1 and 2 may/must play on different days. Consider: Leverkusen loses in Munich, but learns the next day that Dortmund also loses. But suppose they knew during the game in Munich that Dortmund was behind? Wouldn’t this be able to release forces? Or even more so: they get to play on Sunday and already know that Dortmund has lost? Surely that must be an advantage? Has this been considered by the officials?
Changes in chances compared to the previous week due to the results of Matchday 29
Team Changes absolute compared to previous week Championship Percentage
Bayer Leverkusen 90 1.80%
FC Bayern Munich -1 -0.02%
Borussia Dortmund -89 -1.78%
0 0.00%
Bayern lost its last 1/5000th. But Dortmund also lost an impressive 1.78%. Feels like more? You should probably ask the betting market if they see it that way….
d. The title chances in the development
You can’t expect excitement from the curve. It is just curious that Dortmund simply cannot bag the missing few percentages. One should know that consistency in the development of chances is rather unusual. Especially when the chances are already very high. Then it either goes rapidly towards 100% – or crashes brutally all at once. Here it is actually the case that Dortmund keeps the chances very close to 1 in an amazing way, but cannot close the gap. The results are actually good — the games too, of course — but the competition is winning consistently.
e. Direct Champions League qualification via 2nd place
The probability distribution for 2nd place after the 29th matchday
Team Number 2nd place 2nd place in percent Fair odds as inverse of probabilities1 Bayer Leverkusen 4502 90.04% 1.11
2 FC Bayern Munich 268 5.36% 18.66
3 Borussia Dortmund 202 4.04% 24.75
4 Hannover 96 28 0.56% 178.57
5000 100.00%
It’s clear: Leverkusen are firm favourites. Bayern can only increase its remaining percentage with a win on Saturday. But that would probably destroy Dortmund’s dubious “chances”.
The changes compared to the previous week:
Team Win/loss absolute Win/loss in per cent
1 Bayer Leverkusen 303 6.06%
2 Borussia Dortmund 89 1.78%
3 Hannover 96 7 0.14%
18 FC Bayern Munich -399 -7.98%
0 0.00%
Bayern with a huge slump. Only a win in Nuremberg would have helped. That was clear – and was missed. The panic of the bosses has already been commented on, and is of course related to their perceived (and not “calculated”) loss of chances. Otherwise, Dortmund “created” a few chances again.
f. 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. in total as 1, for relegated in each case, 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 compared to 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 Liga 2 in 3rd place and St. Pauli in 16th place, one could perhaps speak of a balanced pairing.
Team Direct relegation (17th or 18th place) Relegation by relegation Total
1 Borussia Mönchengladbach 83.44% 3.25% 86.69%
2 FC St. Pauli 70.88% 5.24% 76.12%
3 VfL Wolfsburg 25.26% 8.50% 33.76%
4 VfB Stuttgart 13.42% 7.50% 20.92%
5 Eintracht Frankfurt 4.52% 5.10% 9.62%
6 1.FC Köln 0.78% 1.51% 2.29%
7 Werder Bremen 0.92% 1.09% 2.01%
8 1.FC Kaiserslautern 0.78% 1.10% 1.88%
9 TSG Hoffenheim 0.00% 0.05% 0.05%
200.00% 33.33% 233.33%
Even if there are still 9 teams listed here, you can see the big jump from Stuttgart to Frankfurt. The other teams just shouldn’t feel safe yet.
The change in chances from the 28th to the 29th matchday in terms of relegation
Team Change in chances1 1.FC Kaiserslautern -11.44%
2 Borussia Mönchengladbach -9.21%
3 Eintracht Frankfurt -6.11%
4 Werder Bremen -0.74%
5 FC Schalke 04 -0.67%
15 1.FC Cologne 1.33%
16 VfL Wolfsburg 3.85%
17 VfB Stuttgart 7.99%
18 FC St. Pauli 15.01%
0.00%
Winner of the matchday, of course, Kaiserslautern with a great away win at a direct rival. Frankfurt also “wins”, despite the 1:1 at home. The reason here: the competition at the back (Pauli and Stuttgart) both lost, which benefits them. St. Pauli was also only beaten so badly because the competition played against them, because a defeat in Leverkusen was, so to speak, also “expected” by the computer (if one may understand 75% in this way).
g. The relegation question in the development
Gladbach remains constant. Namely, constantly fluctuating. Again and again the line points upwards, but jags down again. St. Pauli with some very energetic upward movements, as you can see nicely. Whether they can tip this over again? (and even a win would be enough for that, just for the curve to move down once more). Stuttgart once again with an “uppercut” as well.
h. 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 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 absolute1 Hannover 96 34.59 53 18.41 18.41
2 Borussia Dortmund 53.39 66 12.61 12.61
3 Bayer Leverkusen 50.50 61 10.50 10.50
4 1.FC Nürnberg 34.10 43 8.90 8.90
5 FSV Mainz 05 38.17 45 6.83 6.83
6 SC Freiburg 36.50 41 4.50 4.50
7 1.FC Köln 31.72 35 3.28 3.28
8 1.FC Kaiserslautern 32.11 34 1.89 1.89
9 Hamburger SV 43.72 42 -1.72 1.72
10 FC St. Pauli 29.98 28 -1.98 1.98
11 Eintracht Frankfurt 35.75 33 -2.75 2.75
12 FC Bayern Munich 56.51 52 -4.51 4.51
13 Borussia Mönchengladbach 31.03 26 -5.03 5.03
14 TSG Hoffenheim 42.05 37 -5.05 5.05
15 FC Schalke 04 45.27 39 -6.27 6.27
16 Werder Bremen 42.59 34 -8.59 8.59
17 VfB Stuttgart 42.37 30 -12.37 12.37
18 VfL Wolfsburg 41.15 28 -13.15 13.15
5.52 128.32
ø Deviation 7.13Hanover continues to drift. And has even widened the gap again. 18.4 points above expectations. Coincidence or does the computer simply have “no idea”?
As you can see, St. Pauli, for example, have hardly disappointed. They are playing within their means. One win and they would be out of the red. At the back, the four already described as “problem children” since Matchday 14 remain. None of them can really break free. Hoffenheim, who have done nothing good since the winter break, are slipping in a bit. The “squad thinning”, the change of coach?
The foreign comparison for the average point differential.
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 is reflected in the figures.
League 1 ø Deviation Change from previous week
Germany 7.13 0.25
Italy 5.49 0.58
Spain 3.94 0.32
France 3.61 0.05
England 2.24 0.09
Germany right in front, as they have been for a long time. Italy, however, is somehow starting to compete with them. The number of measurable surprises in all the top leagues has increased. What does that mean? But this, that short-term trends are gaining in significance over long-term forecasts?
i. 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 deviation1 Borussia Dortmund 51.93 59 30.92 18 19.99
2 1.FC Nürnberg 36.80 43 46.23 38 14.43
3 FSV Mainz 05 39.88 45 42.91 38 10.03
4 Hannover 96 37.29 43 45.84 42 9.55
5 Bayer Leverkusen 52.55 59 35.90 35 7.35
6 1.FC Kaiserslautern 36.01 40 48.78 46 6.77
7 SC Freiburg 38.45 38 44.03 41 2.58
8 FC Bayern Munich 55.64 61 29.12 35 -0.53
9 1.FC Köln 35.79 39 49.43 54 -1.36
10 TSG Hoffenheim 44.64 44 41.28 42 -1.36
11 Eintracht Frankfurt 36.73 29 42.90 39 -3.83
12 Borussia Mönchengladbach 39.36 43 55.46 63 -3.90
13 FC St. Pauli 32.87 30 48.82 51 -5.04
14 Hamburger SV 45.08 44 39.38 45 -6.71
15 FC Schalke 04 44.34 34 36.08 33 -7.26
16 VfB Stuttgart 46.54 49 43.13 54 -8.41
17 VfL Wolfsburg 42.20 32 40.09 42 -12.11
18 Werder Bremen 46.43 39 42.24 55 -20.19
762.54 771 0.00
Goals ø expected: Goals ø scored: ø Deviation 7.86
2.92 2.95 If you consider how many goals against the post (and other great chances) Dortmund “missed” – Barrios alone with 10 aluminium goals – then you could come to the conclusion that Dortmund were not even sufficiently rewarded for the performance they showed. Although 20 goals better than expected are quite impressive?
As you can see: Hanover’s performance is somewhat put into perspective, but also that of Bayern: the goal ratio “almost fits” in any case. In this respect, the change of coach is proven to be completely nonsensical, if you like: Bayern has achieved a goal ratio that matches their expectation. They have scored the goals somewhat unfavourably, so that a total of 4.5 points are missing. This equates to just one game turned around (a win instead of a defeat) plus a draw instead of a defeat. And this seems very easily conceivable when looking back at the many superiorly fought games.
Also for this statistic the foreign comparison:
Place Country League 1 ø Goal difference Change from previous week.
1 Germany 7.86 0.01
2 Italy 6.22 0.63
3 Spain 5.15 0.05
4 England 4.55 -0.57
5 France 4.55 0.23
The lead of the German league is still quite clear. However, Italy has made up considerable ground in the last two weeks. A correction towards more balance was only seen in England.
j. The strength of play 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 1.80 0.85 2.11 +0
2 FC Bayern Munich 2.10 1.11 1.89 +0
3 Bayer Leverkusen 1.88 1.17 1.60 +0
4 FC Schalke 04 1.29 1.09 1.18 +1
5 Hamburger SV 1.59 1.41 1.13 -1
6 1.FC Nürnberg 1.42 1.36 1.05 +0
7 FSV Mainz 05 1.44 1.44 1.01 +0
8 Werder Bremen 1.49 1.53 0.98 +0
9 Hannover 96 1.44 1.48 0.98 +1
10 TSG Hoffenheim 1.39 1.48 0.94 -1
11 SC Freiburg 1.29 1.46 0.89 +1
12 VfB Stuttgart 1.52 1.74 0.88 -1
13 VfL Wolfsburg 1.18 1.43 0.82 +0
14 1.FC Kaiserslautern 1.27 1.59 0.80 +1
15 1.FC Köln 1.35 1.76 0.77 -1
16 Borussia Mönchengladbach 1.38 1.82 0.76 +0
17 Eintracht Frankfurt 1.00 1.48 0.67 +0
18 FC St. Pauli 1.06 1.77 0.60 +0
25.935 25.93 +0
Goals ø expected
2.882 Despite the fantastic series, Leverkusen still can’t really come close to Bayern. But would it, despite almost securing 2nd place, be realistic?
Gladbach’s 5:1 win has put them quite clearly away from the bottom, even from Frankfurt. They almost overtook their previously stable Rhineland neighbours. But surely a 5:1 is also a result to which one attaches a certain importance?
k. 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. International comparisons provide more information about the effectiveness or weakness of German behaviour.
Here, too, the foreign comparison:
Top league in.. Matches Equalising goals Leads Home Leads Away Trend changes total Trend changes per match
Germany 251 130 50 39 219 0.873
England 308 160 51 39 250 0.812
Italy 310 129 47 31 207 0.668
France 290 123 33 30 186 0.641
Spain 300 114 34 38 186 0.620
The foreign comparison was taken from the previous week and has not yet been adjusted. Here is just a brief review of the matches shot in the individual leagues, starting with the German one:
Frankfurt – Werder had 1, the equaliser.
HSV – Dortmund also this equaliser, so 1 more.
Schalke – Wolfsburg without, 0.
Nürnberg – Bayern again with 1, Nürnberg’s equalising goal.
Hannover against Mainz the spectacle begins: lead, equaliser, behind, equaliser, lead. That makes 4 changes of tendency.
Identical the course Freiburg – Hoffenheim. 4.
The same goes for Stuttgart against Kaiserslautern. Lautern leads, Stuttgart turns, Lautern turns back. 4 changes of tendency.
Gladbach – Cologne was a one-way street, so 0.
But Leverkusen turn the game around after 0:1. Another 2.
So the sum of all tendency changes is 1 + 1 + 1 + 0 + 4 + 4 + 0 + 2 = 17.
17 “exciting goals” that promised at least one of the parties an improvement in the points tally (even if only temporary for some). That is already very stately. In the statistics it would mean that there are now 236 in 262 (Schalke against St. Pauli, which was missing last week, was recorded as 0:2, i.e. without a change in tendency). So there is an increase to 236/262 = 0.9.
In England there were 5 in 10 games, so below average.
In France there were 9 in 10 games, as above average.
In Italy there were also 9 in 10 games, also a lot of action.
In Spain there were 6 in 10 games, so almost “normal”, given the 0.62 so far this season.
Overall, the foreign leagues have had a little more than average number of changes of tendency, but only by their standard. The Bundesliga has once again taken the cake. By the way, here is the value of the 2nd Bundesliga very briefly (which will also be included in the future):
2nd division: 260 games, 121 equalising goals, 47 home leading goals, 35 away leading goals. In total, 203/260 = 0.78.
The 2nd division is therefore still behind England, but ahead of the other three top leagues.
l. The mathematical review of the results of the 29th matchday
Goal expectation
Home Away Total Deviation
Frankfurt Bremen 1.26 1.32 2.58 1 1 -0.26 -0.32
HSV Dortmund 1.15 1.73 2.88 1 1 -0.15 -0.73
Schalke 04 Wolfsburg 1.47 0.81 2.28 1 0 -0.47 -0.81
Nuremberg FC Bayern 1.37 1.76 3.14 1 1 -0.37 -0.76
Hannover Mainz 1.61 1.36 2.97 3 2 1.39 0.64
Freiburg Hoffenheim 1.40 1.19 2.59 3 2 1.60 0.81
Stuttgart Kaiserslautern 1.95 1.19 3.14 2 4 0.05 2.81
Gladbach FC Cologne 1.62 1.55 3.16 5 1 3.38 -0.55
Leverkusen St. Pauli 2.56 0.81 3.37 2 1 -0.56 0.19
14.38 11.73 26.11 19 13 4.62 1.27
Expected goal total Expected goal average Scored goal average
26.11 2.90 3.56 ø expected goal difference 1.92 ø goal difference 1.98
Plenty of goals then, with a fairly normal home advantage at 19:13 (compared to 14.38:11.73 expected). The average goal deviation in high-scoring games is usually above expectation, which is confirmed here (1.98 vs. 1.92), yet not exorbitantly high. One could put it this way: The computer also considers such results (well) possible.
m. The determination
Note: The determination is calculated for each game 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
Frankfurt Bremen 35.42% 26.60% 37.98% 34.05%
HSV Dortmund 25.18% 23.77% 51.05% 38.05%
Schalke 04 Wolfsburg 52.73% 26.60% 20.67% 39.15%
Nuremberg FC Bayern 29.96% 23.30% 46.74% 36.25%
Hanover Mainz 43.35% 24.35% 32.30% 35.15%
Freiburg Hoffenheim 41.79% 26.36% 31.86% 34.56%
Stuttgart Kaiserslautern 54.80% 22.04% 23.16% 40.25%
Gladbach FC Cologne 39.68% 23.67% 36.65% 34.78%
Leverkusen St. Pauli 75.05% 15.30% 9.65% 59.60%
3.98 2.12 2.90 3.52
Average expected commitment: 39.09%
The determination arrived Pairing 1 X 2
Frankfurt Bremen 35.42% 26.60% 37.98% 26.60%
HSV Dortmund 25.18% 23.77% 51.05% 23.77%
Schalke 04 Wolfsburg 52.73% 26.60% 20.67% 52.73%
Nuremberg FC Bayern 29.96% 23.30% 46.74% 23.30%
Hanover Mainz 43.35% 24.35% 32.30% 43.35%
Freiburg Hoffenheim 41.79% 26.36% 31.86% 41.79%
Stuttgart Kaiserslautern 54.80% 22.04% 23.16% 23.16%
Gladbach FC Cologne 39.68% 23.67% 36.65% 39.68%
Leverkusen St. Pauli 75.05% 15.30% 9.65% 75.05%
3.98 2.12 2.90 3.49
average commitment received: 38.82%No particular deviation expectation/reality in this statistic either. The favourites prevailed in the normal, expected proportion. 39.02% expected, 38.82% arrived. This is quite livable, as long as one (or: computer) tries to be a prophet. “I did my best with the possible determination. Reality confirmed for me: there was nothing more to it.”
Further 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 was guaranteed to be nothing new.
n. League statistics
Note: such a statistic is regularly produced by 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
261 119 56 86 436 335 1.131
Statistics of expected results Matches Home wins Draws Away wins Goals Conceded Home advantage
261 118.93 61.52 80.54 427.6 334.8 1.122
Statistics of absolute deviations Matches Home wins Draws Away wins Goals Conceded Home advantage
0 0.07 -5.52 5.46 8.4 0.2 0.00928
Percentage deviation statisticsMatches Home wins Draws Away wins Goals Conceded Home advantage
0 0.06% -9.86% 6.35% 1.93% 0.06% 0.82%
Determination expected Determination arrived
39.39% 38.07%
ø Goal difference ø Goal difference expected
1.96 1.91 The deviations remain moderate, as expected.
The computer predicted the number of home wins almost exactly. The missing draws all turned out to be away victories. In one respect it remains obvious that the predictions were not outstanding (only on the other hand: who had them?). Surprise remains surprise, even if there is no mathematical definition for it): The determination arrived is still more than 1% below the expected one, which is quite considerable.
The ø goal deviation confirms this. Also that deviation (reality/expectation) is larger than usual, but, as one surely also feels, still within the bounds. 1.96 compared to 1.91? That is still possible.
Note: For arithmetic foxes, here is a brief explanation of the calculation method for the expected goal deviation: The computer gives each result from 0:0 to 20:20 a probability (it is actually sufficient up to 10:10, as the rest has no appreciable probability). There would be a goal deviation for each result. So if you multiply the probability of, for example, a 3:4 by the deviation that would then occur (in the case of the match Mainz – Gladbach, below, with goal expectations of 1.77:1.25, this would be 3 – 1.77 = 1.23 for Mainz plus 4 – 1.25 = 2.75 for Gladbach, i.e. a total of 3.98 goal deviation) and carry out this procedure for each match result, you get the expected average goal deviation.
o. The preview of the 30th matchday
Note: The computer calculates the goal expectations (and the individually maintained home advantage not shown here) to these goal expectations 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 TotalMainz Gladbach 1.77 1.25 3.02
FC Cologne Stuttgart 1.90 1.51 3.41
Hoffenheim Frankfurt 1.54 0.94 2.48
Wolfsburg St. Pauli 1.67 0.93 2.60
HSV Hannover 1.91 1.21 3.12
Kaiserslautern Nuremberg 1.34 1.24 2.58
Bremen Schalke 04 1.32 1.12 2.44
FC Bayern Leverkusen 1.84 1.21 3.05
Dortmund Freiburg 1.93 0.65 2.58
15.22 10.05 25.27
Expected goal total Expected goal average
25.27 2.81 The home teams are normally in front, the expected goal total is “only” 25.81. Surprising at most, as the last matchday was full of goals, so an upward adjustment would be expected. The reason, recently discussed at the same place: in absolute top matches, the goal expectation is usually lower. Even if Bayern – Leverkusen are expected to score 3.05 goals, consider that the two teams, if they each had a match against an outsider, would probably both clearly exceed this value, i.e. at least one high-scoring match (in the expectation) would be missing.
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 is, 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
Mainz Gladbach 49.50% 23.50% 26.99% 37.32%
FC Cologne Stuttgart 46.85% 22.33% 30.82% 36.43%
Hoffenheim Frankfurt 51.31% 25.75% 22.94% 38.22%
Wolfsburg St. Pauli 54.77% 24.42% 20.82% 40.29%
HSV Hannover 53.73% 22.37% 23.90% 39.59%
Kaiserslautern Nuremberg 38.92% 26.69% 34.39% 34.10%
Bremen Schalke 04 41.05% 27.45% 31.50% 34.31%
FC Bayern Leverkusen 52.08% 22.95% 24.96% 38.63%
Dortmund Freiburg 67.69% 20.58% 11.73% 51.43%
4.56 2.16 2.28 3.50
Average expected determination: 38.92%The value of 38.92% rather a little below average. The reason: the (top) favourites are blocking each other. Only one clear favourite and that (once again) Dortmund. Can they do justice to this role? It would certainly be deserved, because all the recent losses of points were mostly the result of clearly superior games.
The fair odds
Note: the fair odds are merely 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
Mainz Gladbach 2.02 4.25 3.70
FC Cologne Stuttgart 2.13 4.48 3.24
Hoffenheim Frankfurt 1.95 3.88 4.36
Wolfsburg St. Pauli 1.83 4.10 4.80
HSV Hannover 1.86 4.47 4.18
Kaiserslautern Nuremberg 2.57 3.75 2.91
Bremen Schalke 04 2.44 3.64 3.17
FC Bayern Leverkusen 1.92 4.36 4.01
Dortmund Freiburg 1.48 4.86 8.53
2) The 2nd Bundesliga
a. The Table Situation
Sp S U N Pkt T GT
1 Hertha BSC 29 19 5 5 62 59 – 25
2 FC Augsburg 29 17 7 5 58 52 – 21
3 VfL Bochum 29 17 4 8 55 40 – 30
4 SpVgg Greuther Fürth 29 14 9 6 51 39 – 22
5 Erzgebirge Aue 28 13 7 8 46 29 – 31
6 MSV Duisburg 29 13 7 9 46 44 – 30
7 TSV 1860 Munich 29 12 9 8 45 41 – 29
8 Energie Cottbus 29 13 6 10 45 54 – 44
9 Fortuna Düsseldorf 29 13 3 13 42 38 – 35
10 Alemannia Aachen 29 11 8 10 41 49 – 50
11 Union Berlin 29 10 8 11 38 32 – 33
12 FSV Frankfurt 28 10 4 14 34 37 – 41
13 SC Paderborn 29 8 8 13 32 27 – 40
14 FC Ingolstadt 29 8 7 14 31 35 – 43
15 Karlsruhe SC 29 7 8 14 29 39 – 63
16 VfL Osnabrueck 29 7 6 16 27 37 – 53
17 Rot Weiss Oberhausen 29 6 6 17 24 23 – 50
18 Arminia Bielefeld 29 3 6 20 15 22 – 57
697 697
Total number of games 260
Goals ø 2.68
Statistics received/expected
Games HS U HN T GT
arrived: 260 126 59 75 398 299
260 122 63.4 74.8 400 292.9
Deviation 0 4.22 -4.4 0.23 -2.3 6.1
øexpected determination
39.01%
ø determination received
39.97% The league statistics have been included here at the same time. As you can see, there are only moderate deviations in this league as well. However, here the home teams have “eaten up” the missing draws. The away victories have been (almost) exactly predicted. There are also only irrelevant deviations in the goals. All in all, the computer “got it wrong” by a total of 3.8 goals.
Otherwise, the table is reasonably well sorted, in line with expectations. However, such “order” is usually at the expense of the perceived suspense: Neither in the relegation battle nor in the promotion race is there any particular spectacle. The big favourites set themselves apart. And indeed, even the computer had these three teams in 1st to 3rd place before the season. At the very back, the gaps are also a little too big to be seriously tense.
b. The chances of promotion
Note: the simulation of League 2 runs exactly like that of League 1. 5000 runs were also made. Third place logically gives a 1/3 chance of promotion, although it should still depend on the pairing. Since the top favourites are ahead here, it could well be 50% that the time league third place team has against the first league third last.
Team 1st place 2nd place 3rd place 1/3 to advance Ascent percentage
Hertha BSC 3863 1042 93 31.00 98.72%
FC Augsburg 1090 3189 643 214.33 89.87%
VfL Bochum 47 687 3032 1010.67 34.89%
SpVgg Greuther Fürth 0 82 1178 392.67 9.49%
MSV Duisburg 0 0 25 8.33 0.17%
TSV 1860 Munich 0 0 12 4.00 0.08%
Erzgebirge Aue 0 0 10 3.33 0.07%
Energie Cottbus 0 0 7 2.33 0.05%
5000 5000 5000 1666.67 2.33
This prediction table confirms the above: The first two are as good as through (the author in particular is particularly reluctant to sign such intuitive statements, and usually to make them, especially since Augsburg are still a loose 10% away from realisation, but still…), very probably Bochum will have to go into the relegation and is considered here as 1/3 outsiders in the duel. Maybe Gladbach? Possibly Wolfsburg? Well, Bochum would be the favourite neither there nor there…
c. Expected points and deviations
Team Name Points expected Points scored Deviation Deviation absolute1 Hertha BSC 51.73 62 10.27 10.27
2 Erzgebirge Aue 35.97 46 10.03 10.03
3 VfL Bochum 46.84 55 8.16 8.16
4 SpVgg Greuther Fürth 43.90 51 7.10 7.10
5 FC Augsburg 51.92 58 6.08 6.08
6 TSV 1860 München 42.72 45 2.28 2.28
7 Alemannia Aachen 39.43 41 1.57 1.57
8 Energie Cottbus 43.71 45 1.29 1.29
9 Fortuna Düsseldorf 41.42 42 0.58 0.58
10 FC Ingolstadt 31.25 31 -0.25 0.25
11 FSV Frankfurt 35.61 34 -1.61 1.61
12 Union Berlin 39.72 38 -1.72 1.72
13 MSV Duisburg 48.15 46 -2.15 2.15
14 SC Paderborn 36.02 32 -4.02 4.02
15 VfL Osnabrueck 33.48 27 -6.48 6.48
16 Karlsruher SC 35.70 29 -6.70 6.70
17 Rot Weiss Oberhausen 31.86 24 -7.86 7.86
18 Arminia Bielefeld 27.15 15 -12.15 12.15
4.43 90.31
ø Deviation 5.02Even here, confirmation of the boredom: nowhere near as many and clear outliers as in the 1. Liga. Hertha have climbed to 1st place thanks to the away win in Bochum, albeit only just ahead of surprise team Aue.
d. Evaluation of the 29th Second Division Matchday
Goal expectation
Home Away Total Result DeviationDuisburg Aachen 1.72 1.29 3.01 3 2 1.28 0.71
Osnabrück Bielefeld 2.02 0.94 2.96 0 0 -2.02 -0.94
Augsburg Greuther Fürth 1.39 0.81 2.19 0 0 -1.39 -0.81
Munich 1860 Cottbus 1.56 1.25 2.81 4 0 2.44 -1.25
Oberhausen Düsseldorf 1.05 1.29 2.33 1 2 -0.05 0.71
Bochum Hertha 1.24 1.25 2.49 0 2 -1.24 0.75
Erzgebirge Aue Karlsruhe 1.82 0.93 2.74 1 1 -0.82 0.07
Union FSV Frankfurt 1.60 0.98 2.57 2 0 0.40 -0.98
SC Paderborn Ingolstad 1.31 1.22 2.53 1 1 -0.31 -0.22
13.70 9.95 23.65 12 8 -1.70 -1.95
Expected goal total Expected goal total: Goal total: Goal total
23.65 2.63 20 2.2222 ø expected goal difference: 1.81 ø arrived goal difference: 1.80 1.80
Only 20 goals, but solidly and “expectedly” distributed between home and away teams. Also the average goal deviation even below expectation, so a very “normal” (if not boring) match day.
The determination (expected) Pairing 1 X 2
Duisburg Aachen 47.59% 23.52% 28.88% 36.53%
Osnabrück Bielefeld 62.61% 20.69% 16.69% 46.27%
Augsburg Greuther Fürth 50.64% 27.46% 21.90% 37.98%
Munich 1860 Cottbus 44.79% 24.69% 30.52% 35.47%
Oberhausen Düsseldorf 30.24% 27.67% 42.09% 34.52%
Bochum Hertha 36.18% 26.83% 36.98% 33.97%
Erzgebirge Aue Karlsruhe 58.38% 22.67% 18.95% 42.81%
Union FSV Frankfurt 51.82% 24.92% 23.26% 38.47%
SC Paderborn Ingolstad 38.84% 26.53% 34.63% 34.12%
4.21 2.25 2.54 3.40
Average expected commitment: 37.79%
The determination (arrived) Pairing 1 X 2
Duisburg Aachen 47.59% 23.52% 28.88% 47.59%
Osnabrück Bielefeld 62.61% 20.69% 16.69% 20.69%
Augsburg Greuther Fürth 50.64% 27.46% 21.90% 27.46%
Munich 1860 Cottbus 44.79% 24.69% 30.52% 44.79%
Oberhausen Düsseldorf 30.24% 27.67% 42.09% 42.09%
Bochum Hertha 36.18% 26.83% 36.98% 36.98%
Erzgebirge Aue Karlsruhe 58.38% 22.67% 18.95% 22.67%
Union FSV Frankfurt 51.82% 24.92% 23.26% 51.82%
SC Paderborn Ingolstad 38.84% 26.53% 34.63% 26.53%
4.21 2.25 2.54 3.21
average commitment received: 35.63% Here, if you will, is the refutation of the boredom thesis. With only 35.63% of the determination coming true, the surprises are supposed to have (clearly) outweighed the surprises…! Well, it is probably due to the four draws, which almost always occur as (clear) outsider events. But draws don’t necessarily make for high tension, especially not the 0:0 games…
On the other hand, you can see in the statistics below the table that so far in this league the expected determination has been exceeded (39.97% arrived compared to 39.03% expected), so that a balance is quite welcome here. There have been a bit too many favourite events so far.
e. Preview of the 30th second league matchday
Goal expectation
Home Away TotalIngolstad Bochum 1.00 1.24 2.24
Düsseldorf Union 1.45 0.80 2.24
FSV Frankfurt Munich 1860 1.17 1.28 2.45
Hertha Osnabrück 2.70 0.80 3.50
Cottbus Duisburg 1.53 1.18 2.71
Aachen Erzgebirge Aue 1.90 1.13 3.03
Bielefeld Oberhausen 1.27 1.10 2.37
Greuther Fürth SC Paderborn 1.58 0.57 2.15
Karlsruhe Augsburg 1.01 1.99 3.00
13.60 10.09 23.69
Expected goal total Expected goal average
23.69 2.63 There should be few goals in Ingolstadt and Düsseldorf, even fewer in Fürth. Many, however, at Hertha (see above: with clear favourites there should always be quite a lot of goals), but also in Aachen or Karlsruhe. We shall see.
The determination (expected) Pairing 1 X 2
Ingolstad Bochum 29.60% 28.64% 41.75% 34.40%
Düsseldorf Union 52.51% 26.87% 20.62% 39.04%
FSV Frankfurt Munich 1860 33.62% 27.35% 39.03% 34.02%
Hertha Osnabrück 77.31% 14.08% 8.61% 62.49%
Cottbus Duisburg 45.41% 25.37% 29.22% 35.60%
Aachen Erzgebirge Aue 55.39% 22.31% 22.30% 40.63%
Bielefeld Oberhausen 40.14% 27.83% 32.03% 34.12%
Greuther Fürth SC Paderborn 62.18% 24.72% 13.10% 46.49%
Karlsruhe Augsburg 18.51% 21.32% 60.18% 44.18%
4.15 2.18 2.67 3.71
Average expected fixing: 41.22% Here a rather high value with 41.22%. However, it can also be observed here that the differences in playing strength, which were quite small in the league at the beginning (“the 2nd division is very balanced, anyone can beat anyone” is a much-quoted phrase), increase over the course of the season. Bielefeld, for example, has pulled far away at the back (and this was not predictable), as have Augsburg and Hertha at the top. This means that there are higher favourites, which would not have been the case at the beginning of the season.
The fair odds
Pairing 1 X 2
Ingolstad Bochum 3.38 3.49 2.39
Düsseldorf Union 1.90 3.72 4.85
FSV Frankfurt Munich 1860 2.97 3.66 2.56
Hertha Osnabrück 1.29 7.10 11.61
Cottbus Duisburg 2.20 3.94 3.42
Aachen Erzgebirge Aue 1.81 4.48 4.48
Bielefeld Oberhausen 2.49 3.59 3.12
Greuther Fürth SC Paderborn 1.61 4.04 7.63
Karlsruhe Augsburg 5.40 4.69 1.66
