1) The 1st Bundesliga
a. Review of the Matches
Results of Match Day 30
FSV Mainz 05 – Borussia Mönchengladbach 1:0 (0:0)
- FC Cologne – VfB Stuttgart 1:3 (0:0)
TSG Hoffenheim – Eintracht Frankfurt 1:0 (0:0)
VfL Wolfsburg – FC St. Pauli 2:2 (1:0)
Hamburger SV – Hannover 96 0:0 - FC Kaiserslautern – 1. FC Nürnberg 0:2 (0:1)
Werder Bremen – FC Schalke 04 1:1 (0:0)
FC Bayern Munich – Bayer Leverkusen 5:1 (4:0)
Borussia Dortmund – SC Freiburg 3:0 (2:0)
General assessment:
For today, we’ll stick to general observations. Especially since our own observations and work-ups had to be much shorter this week, hardly took place at all.
Gladbach fought back as hard as they could, but Schürrle’s great goal (once again) shortly before the end decided the game in favour of Mainz, who never let up.
Cologne may have actually dropped down a gear a little too early, after the impressive series that already brought their relegation chances close to zero. Stuttgart wanted it badly – and Stuttgart succeeded. Certainly, the often-vaunted potential can be seen every now and then and such a match could always have such an outcome.
Hoffenheim once again showed its better face against Frankfurt. Frankfurt, who had seemingly overcome their (goalless) second-round misery, had another negative experience. Frankfurt are in the bottom, Hoffenheim are finally out of it.
Sensational, in many respects, was the match between Wolfsburg and St. Pauli. It all fitted so well for Wolfsburg: a home game and the opponent with the bankruptcy series as a direct competitor for at least the relegation place “in front of the shotgun”. However, St. Pauli probably didn’t read the script and instead almost spat in the soup of the ex-champion with new coach Magath. If it hadn’t been for the last-minute equaliser… So Wolfsburg still stay in front by a razor-thin margin.
HSV’s mini-crisis continues. A successful season looks different. Hannover, on the other hand, continues to work on a huge season. The path could point in a fairly straight line towards Europe.
Kaiserslautern seemed to be able to work their way out of it after all, but the strong Nuremberg team put a pretty big spoke in their (rescue) wheel.
Werder adopted the squirrel tactic – and used it successfully. One point here, one point there. Seven games unbeaten, five of them draws. At least relegation is moving further away. Schalke, on the other hand, has nothing more to do with anything – except the Champions League. The fact that they are still playing decently is worthy of all honour, even if many would describe it as “a matter of course”. In any case, there have been other examples…
“The big talking point is of course the game between Bayern and Leverkusen. Surely it’s 2nd place against 3rd place, surely it’s two heavyweights over many years, surely every Bayern game has explosive power, divides the nation and is one (of at least two; there are first and second legs) special highlights of the year for the opponent. Nevertheless, this is even more about Jupp Heynckes’ imminent change from Bayer- to -n. How would one go about it oneself? What would you yourself have in mind if you were faced with this task as coach? Of course, there is no question of “losing voluntarily”.
On the other hand, however, please bear in mind (as the numbers later prove quite well) that this game was almost exclusively about Bayern’s future. Because: despite the defeat, Leverkusen are pretty much assured of 2nd place (and Heynckes even still has this fate in his hands). So: if Bayer had won, they would be in the Champions League for sure. Bayern, on the other hand, would probably be out, or at least in the greatest danger of being out. Thanks to the defeat, they are only fairly certain to be in, while Bayern are also at least in the qualifiers. Two birds, one stone.
Not worth mentioning: Bayern can achieve such a result at any time with this, with that or without a coach. The class is evident everywhere and, as a later statistic shows, did not even fall short of expectations.
Dortmund made the most of the advantage. As noted in the same place a week ago, the sequence of games was somewhat unfortunate and not entirely fair, especially at this stage of the season. After the defeat of Leverkusen, Dortmund really did have a much easier time professionally dismantling “sparring partner” Freiburg? What if they had not yet known the (rival) result?
b. The standings
Sp S U N Pkt T GT Diff
1 Borussia Dortmund 30 21 6 3 69 62 – 18 +44
2 Bayer Leverkusen 30 18 7 5 61 60 – 40 +20
3 FC Bayern Munich 30 16 7 7 55 66 – 36 +30
4 Hannover 96 30 17 3 10 54 43 – 42 +1
5 FSV Mainz 05 30 15 3 12 48 46 – 38 +8
6 1.FC Nürnberg 30 13 7 10 46 45 – 38 +7
7 Hamburger SV 30 12 7 11 43 44 – 45 -1
8 SC Freiburg 30 12 5 13 41 38 – 44 -6
9 TSG Hoffenheim 30 10 10 40 45 – 42 +3
10 FC Schalke 04 30 11 7 12 40 35 – 34 +1
11 Werder Bremen 30 8 11 35 40 – 56 -16
12 1.FC Köln 30 10 5 15 35 40 – 57 -17
13 1.FC Kaiserslautern 30 9 7 14 34 40 – 48 -8
14 VfB Stuttgart 30 9 6 15 33 52 – 55 -3
15 Eintracht Frankfurt 30 9 6 15 33 29 – 40 -11
16 VfL Wolfsburg 30 6 11 13 29 34 – 44 -10
17 FC St. Pauli 30 8 5 17 29 32 – 53 -21
18 Borussia Mönchengladbach 30 7 5 18 26 43 – 64 -21
794 794 0
Total number of games 270
Goals ø 2.94
You get used to everything. Hannover, Mainz, Nuremberg, Freiburg 4, 5, 6, 8. Schalke, Werder, Stuttgart Wolfsburg on the other hand 10, 11, 14, 16? Who can do more than shrug their shoulders?
At the bottom, however, it has suddenly become rather lonely for the three. No team is within striking distance, so that for the time being, at least temporarily, “only” the relegation place is at stake. Will a fourth team “intervene”? We shall see. In any case, Frankfurt is the most likely, thanks to the poor goal difference.
c. The title question
Team Number of German champions in 5000 simulations Championships in percent Fair odds as reciprocal of probabilities1 Borussia Dortmund 4989 99.78% 1.00
2 Bayer Leverkusen 11 0.22% 455
5000 100.00%
A chance of 1/455? We hardly know such a thing from everyday life, at least not consciously: You hit a plein (one number) in roulette, for example the 28, divide the one remaining on the table (the practice: you don’t deduct it, the croupiers don’t either), but slip it to a cheval (two numbers), between the 28 and the 29, and you get… the 29. The chance for that: 1 in 37 times 1 in 18.5 = 1/37 * 2/37 = 2/729, that’s about 1 in 365 (instead of 1 in 455, like Leverkusen’s chance. But: you have to manage that first.
Chance changes compared to the previous week due to the results of matchday 30
Team Number of German champions in 5000 simulations Championships in percent
Bayer Leverkusen -191 -3.82%
Borussia Dortmund 191 3.82%
0 0.00%
Without words…
d. The title chances in the development
The graph at least no longer shows a gap of 100%.
e. Direct Champions League qualification via 2nd place
The probability distribution for 2nd place after matchday 30
Team Number 2nd place 2nd place in percent Fair odds as inverse of probabilities
1 Bayer Leverkusen 4402 88.04% 1.14
2 FC Bayern Munich 561 11.22% 8.91
3 Hannover 96 26 0.52% 192.31
4 Borussia Dortmund 11 0.22% 454.55
5000 100.00%
Confirmation of the above: Bayer nevertheless with more than one leg in the Champions League. And Heynckes and his men still have the remaining percentage in hand (they, for example, can also acknowledge the 88% with a shrug of the shoulders and say: “We’ll make it clear!”.
The statistics for 3rd place have not yet been recorded. However, it can at least be mentioned here that in the simulation, Bavaria only did worse than 3rd place in 551 out of 5000 cases, so their chances now, after the victory, are almost 90%. However, the comparison to the previous week is missing. How much did they gain? More interestingly perhaps, how much would they have lost if they had lost?
The changes from the previous week:
Team Win/loss absolute Win/loss in per cent
1 FC Bayern Munich 293 5.86%
16 Hannover 96 -2 -0.04%
17 Bayer Leverkusen -100 -2.00%
18 Borussia Dortmund -191 -3.82%
0 0.00%
The statistics for the gain for 2nd place show them 5.86%, but at the same time Leverkusen has only lost 2%. The reason: Dortmund is no longer a competitor.
f. The relegation question
The distribution of the percentages for relegation
Note: There would also be a detailed breakdown of 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 through 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 Total1 Borussia Mönchengladbach 92.20% 2.02% 94.22%
2 FC St. Pauli 72.30% 5.67% 77.97%
3 VfL Wolfsburg 25.20% 10.68% 35.88%
4 Eintracht Frankfurt 5.56% 7.79% 13.35%
5 VfB Stuttgart 1.94% 2.87% 4.81%
6 1.FC Cologne 0.96% 1.95% 2.91%
7 1.FC Kaiserslautern 1.24% 1.60% 2.84%
8 Werder Bremen 0.60% 0.75% 1.35%
200.00% 33.33% 233.33%
Even if one cannot speak of boredom here, if only because of the two-thirds affected, there is still a huge leap from Wolfsburg to Frankfurt, another one behind Frankfurt. I wonder if it will get (more) exciting again?
The change in chances from the 29th to the 30th matchday with regard to relegation
Team Change in chances1 VfB Stuttgart -16.11%
2 Werder Bremen -0.65%
3 TSG Hoffenheim -0.05%
13 1.FC Cologne 0.63%
14 1.FC Kaiserslautern 0.96%
15 FC St. Pauli 1.85%
16 VfL Wolfsburg 2.12%
17 Eintracht Frankfurt 3.73%
18 Borussia Mönchengladbach 7.53%
0.00%
The winners, of course, are Stuttgart, who won away from home, and the big losers are Borussia Mönchengladbach. Otherwise, only a few percentages shuffle back and forth. It is clear that Frankfurt did itself no great favours with the defeat. Wolfsburg and St. Pauli have both worsened, which once again bears testimony to the unfairness of the three-point rule (which will be examined in more detail in a separate text; gladly made available to anyone interested).
g. The relegation issue in development
Consider here that a total of two curves will settle at 100%, but one at 33.33%. Top candidates for realising these three chances are now Gladbach, St. Pauli and “the rest”, which is essentially embodied by Wolfsburg. The remaining curves are currently moving quite rapidly towards zero.
h. The points expectations and the deviations
Explanation: for each game 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 absolute1 Hannover 96 35.53 54 18.47 18.47
2 Borussia Dortmund 55.62 69 13.38 13.38
3 1.FC Nürnberg 35.40 46 10.60 10.60
4 Bayer Leverkusen 51.48 61 9.52 9.52
5 FSV Mainz 05 39.89 48 8.11 8.11
6 SC Freiburg 37.06 41 3.94 3.94
7 1.FC Köln 33.35 35 1.65 1.65
8 1.FC Kaiserslautern 33.54 34 0.46 0.46
9 FC St. Pauli 30.85 29 -1.85 1.85
10 Hamburger SV 45.55 43 -2.55 2.55
11 FC Bayern Munich 58.30 55 -3.30 3.30
12 Eintracht Frankfurt 36.69 33 -3.69 3.69
13 TSG Hoffenheim 43.84 40 -3.84 3.84
14 Borussia Mönchengladbach 32.07 26 -6.07 6.07
15 FC Schalke 04 46.49 40 -6.49 6.49
16 Werder Bremen 44.10 35 -9.10 9.10
17 VfB Stuttgart 43.52 33 -10.52 10.52
18 VfL Wolfsburg 43.03 29 -14.03 14.03
4.68 127.56
ø Deviation 7.09Everything pretty much the same. Hannover remains the sensational team (or did the computer really just underestimate them?). Dortmund is outstanding – but not in first place. Bayern is “only” three points below expectations, which in the meantime almost amounts to a game turned around (victory instead of defeat). Otherwise, the four big problem children (which they have been since the beginning of the records) are still in the last four places – quite amazing that there has not been a single real “correction” (as usual in previous seasons).
The average deviation only provides information about the size of the surprises this season afterwards.
The international comparison for the average point deviation
Note: the theory is that the German Bundesliga is the most exciting of 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.
Liga 1 ø Deviation Change from previous week
Germany, 1st BL 7.09 -0.04
Italy 5.18 -0.31
Spain 4.18 0.24
France 3.69 0.08
England 2.25 0.01
Germany, 2.BL 5.42 0.40
As you can still see: the German 1st division dominates Europe in terms of size, variety of surprises. Reliable (but boring) teams play mainly in England. The 2nd league (as of this week “included in the programme”) is in 2nd place.
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 53.86 62 31.58 18 21.71
2 1.FC Nürnberg 38.04 45 47.57 38 16.53
3 FSV Mainz 05 41.65 46 44.15 38 10.51
4 Hannover 96 38.50 43 47.76 42 10.26
5 1.FC Kaiserslautern 37.35 40 50.02 48 4.67
6 Bayer Leverkusen 53.76 60 37.74 40 3.98
7 FC Bayern Munich 57.48 66 30.33 36 2.84
8 SC Freiburg 39.11 38 45.96 44 0.85
9 TSG Hoffenheim 46.19 45 42.22 42 -0.97
10 1.FC Köln 37.68 40 50.94 57 -3.75
11 Eintracht Frankfurt 37.67 29 44.44 40 -4.23
12 FC St. Pauli 33.79 32 50.49 53 -4.30
13 Borussia Mönchengladbach 40.61 43 57.23 64 -4.38
14 VfB Stuttgart 48.05 52 45.03 55 -6.02
15 FC Schalke 04 45.45 35 37.40 34 -7.06
16 Hamburger SV 47.00 44 40.58 45 -7.41
17 VfL Wolfsburg 43.87 34 41.02 44 -12.85
18 Werder Bremen 47.75 40 43.36 56 -20.39
787.81 794 0.00
Goals ø expected: Goals ø scored: ø Deviation 7.93
2.92 2.94 In terms of magnitude, the average deviation in terms of goals is almost as large as that in terms of points. This is astonishing (as can be seen in the note), as the goals obviously have a higher deviation potential, as there is, as recently, a 5:1, but also sometimes a 7:0. The (goal) deviation is open upwards, that for the points is limited.
Also for this statistic the foreign comparison:
Place Country League 1 ø Goal difference Change from previous week
1 Germany, 1.BL 7.93 0.07
2 Italy 5.12 -1.10
3 Spain 5.11 -0.04
4 England 4.33 -0.22
5 France 4.44 -0.11
6 Germany, 2.BL 8.29 0
Here even the 2nd league is ahead of the 1st, which makes one wonder. Why these discrepancies in Germany of all places? Surely the computer should achieve the greatest reliability here, due to the large amount of information available (which is of course incorporated here or there). And why is the deviation in the 2nd league even higher than in the 1st? Presumably there were a bit more outlier results there, which are only reflected in the goal statistics (remember the 5:5 between Cottbus and Karlsruhe).
Otherwise, there were mostly corrections in the right direction: decreasing deviation.
j. The playing strength ranking
Note: The 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 Shift1 Borussia Dortmund 1.83 0.83 2.20 +0
2 FC Bayern Munich 2.21 1.11 2.00 +0
3 Bayer Leverkusen 1.88 1.28 1.47 +0
4 FC Schalke 04 1.29 1.09 1.19 +0
5 Hamburger SV 1.53 1.36 1.13 +0
6 1.FC Nürnberg 1.44 1.32 1.10 +0
7 FSV Mainz 05 1.41 1.39 1.02 +0
8 Hannover 96 1.40 1.42 0.99 +1
9 Werder Bremen 1.48 1.53 0.97 -1
10 TSG Hoffenheim 1.37 1.44 0.96 +0
11 VfB Stuttgart 1.56 1.71 0.92 +1
12 SC Freiburg 1.27 1.49 0.86 -1
13 VfL Wolfsburg 1.18 1.46 0.81 +0
14 1.FC Kaiserslautern 1.22 1.61 0.76 +0
15 Borussia Mönchengladbach 1.34 1.80 0.75 +1
16 1.FC Köln 1.32 1.81 0.73 -1
17 Eintracht Frankfurt 0.97 1.46 0.66 +0
18 FC St. Pauli 1.09 1.78 0.62 +0
25.84 25.84 +0
Goals ø expected
2.871 Not so much exciting. Gladbach slips past Klön. And that despite a defeat. The reason: a 1:3 at home scores more than a 0:1 away. Is Frankfurt really worse than them? After all, their goal difference in the second half of the season is a depressing 5:19. The points tally is a meagre 6 in 13 games. Gladbach – just for comparison – has 17:17 goals and already 15 points in the same period. If you ONLY saw these statistics, you wouldn’t doubt who the better team is….
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.
In the 1. league there were only four changes of tendency on this matchday: 3 were in Wolfsburg: Pauli’s equaliser, the opening goal, the renewed Wolfsburg equaliser. Plus the 1:1 in Bremen with one change. So: no more suspense. The average drops again (compared to the 0.9 achieved in the previous week).
Here, too, the international comparison:
Country Matches Compensation HF AF Total per match
Germany 1 270 143 54 43 240 0.889
England 324 166 52 42 260 0.802
Germany 2 269 126 48 38 212 0.788
Italy 330 139 48 36 223 0.676
France 310 137 36 34 207 0.668
Spain 320 123 37 40 200 0.625
The 2nd division is included in this comparison and, as you can see, it is right up front. The champions in defending a lead the Spaniards.
l. The mathematical review of the results of matchday 30
Goal expectation
Home Away Total DeviationMainz Gladbach 1.77 1.25 3.02 1 0 -0.77 -1.25
FC Köln Stuttgart 1.90 1.51 3.41 1 3 -0.90 1.49
Hoffenheim Frankfurt 1.54 0.94 2.48 1 0 -0.54 -0.94
Wolfsburg St. Pauli 1.67 0.93 2.60 2 2 0.33 1.07
HSV Hannover 1.91 1.21 3.12 0 0 -1.91 -1.21
Kaiserslautern Nuremberg 1.34 1.24 2.58 0 2 -1.34 0.76
Bremen Schalke 04 1.32 1.12 2.44 1 1 -0.32 -0.12
FC Bayern Leverkusen 1.84 1.21 3.05 5 1 3.16 -0.21
Dortmund Freiburg 1.93 0.65 2.58 3 0 1.07 -0.65
15.22 10.05 25.27 14 9 -1.22 -1.05
Expected goal total Expected goal average Scored goal average
25.27 2.81 2.56 ø expected goal difference 1.86 ø goal difference 2.00
The number of goals was again undercut, so that in retrospect one should perhaps speak of the flood of goals last weekend as another flash in the pan? The average goal deviation, on the other hand, was greater than expected (which is otherwise rather unlikely or rare with few goals). This can be attributed to individual games, such as the Bayern game. But even a 0:0, like the one in Hamburg, can have a negative effect if many goals were expected.
m. The fixing
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
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 commitment: 38.92%
The determination arrived Pairing 1 X 2
Mainz Gladbach 49.50% 23.50% 26.99% 49.50%
FC Köln Stuttgart 46.85% 22.33% 30.82% 30.82%
Hoffenheim Frankfurt 51.31% 25.75% 22.94% 51.31%
Wolfsburg St. Pauli 54.77% 24.42% 20.82% 24.42%
HSV Hannover 53.73% 22.37% 23.90% 22.37%
Kaiserslautern Nuremberg 38.92% 26.69% 34.39% 34.39%
Bremen Schalke 04 41.05% 27.45% 31.50% 27.45%
FC Bayern Leverkusen 52.08% 22.95% 24.96% 52.08%
Dortmund Freiburg 67.69% 20.58% 11.73% 67.69%
4.56 2.16 2.28 3.60
average determination received: 40.00%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.
However, the expected average determination was exceeded, which indicates favourite events and fewer outsider trumps. Encouraging in that in this way the long-term deficit of favourites might even out (and this would be even more in favour of the computer).
n. Overall league statistics
Note: such statistics are 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
270 123 59 88 450 344 1.134
Statistics of expected results Matches Home wins Draws Away wins Goals Conceded Home advantage
270 123.49 63.68 82.82 442.8 344.9 1.124
Statistics of absolute deviations Matches Home wins Draws Away wins Goals Conceded Home advantage
0 -0.49 -4.68 5.18 7.2 -0.9 0.00922
Percentage difference statisticsMatches Home wins Draws Away wins Goals conceded Home advantage
0 -0.40% -7.93% 5.89% 1.60% -0.26% 0.81%
Determination expected Determination arrived
39.37% 38.13%
ø Goal difference ø Goal difference expected
1.96 1.91 Here it remains that the deviations are very moderate, with only the shift between draws and away wins. The goals have converged even further and so has the fixing (a little). The average goal deviation is constant.
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, since the rest no longer has any significant 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 31st 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 TotalFreiburg Hannover 1.33 1.28 2.61
Frankfurt FC Bayern 0.86 1.92 2.78
Schalke 04 Kaiserslautern 1.67 0.88 2.55
St. Pauli Bremen 1.35 1.61 2.96
Stuttgart HSV 1.65 1.53 3.18
Leverkusen Hoffenheim 2.13 1.12 3.25
Gladbach Dortmund 0.94 2.07 3.01
Wolfsburg FC Cologne 1.83 1.17 3.00
Nuremberg Mainz 1.64 1.29 2.93
13.39 12.88 26.27
Expected goal total Expected goal average
26.27 2.92 This time, a somewhat more goal-filled matchday is expected, which is due to specific pairings (and should not be teased apart here). Many goals in any case in Leverkusen, Stuttgart, very few in hardly any match (so this as a reason). The home teams are only just ahead overall, which is related to the upward performances of Dortmund AND Bayern.
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
Freiburg Hannover 37.84% 26.70% 35.46% 34.02%
Frankfurt FC Bayern 16.10% 21.66% 62.24% 46.02%
Schalke 04 Kaiserslautern 56.04% 24.39% 19.57% 41.18%
St. Pauli Bremen 31.81% 24.54% 43.65% 35.19%
Stuttgart HSV 40.63% 23.77% 35.60% 34.83%
Leverkusen Hoffenheim 60.16% 20.54% 19.30% 44.13%
Gladbach Dortmund 16.20% 20.47% 63.33% 46.92%
Wolfsburg FC Cologne 52.76% 23.10% 24.14% 39.00%
Nuremberg Mainz 45.45% 24.52% 30.03% 35.69%
3.57 2.10 3.33 3.57
Average Expected Settlement: 39.6739.67% is a somewhat above average figure. This might be perplexing in that the top teams are away from home, which normally argues for a slightly shallower favourite. Nevertheless, they are both at over 60% chance of winning (and thus at well over 45% expected determination) and in other pairings rather good meets weak or the better teams are at home (Schalke, Leverkusen!).
The fair odds
Note: the fair odds are only 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
Freiburg Hannover 2.64 3.75 2.82
Frankfurt FC Bayern 6.21 4.62 1.61
Schalke 04 Kaiserslautern 1.78 4.10 5.11
St. Pauli Bremen 3.14 4.07 2.29
Stuttgart HSV 2.46 4.21 2.81
Leverkusen Hoffenheim 1.66 4.87 5.18
Gladbach Dortmund 6.17 4.89 1.58
Wolfsburg FC Cologne 1.90 4.33 4.14
Nuremberg Mainz 2.20 4.08 3.33
2) The 2nd Bundesliga
a. The standings
Sp S U N Pkt T GT Diff1 Hertha BSC 30 20 5 65 63 – 25 +38
2 FC Augsburg 30 18 7 5 61 53 – 21 +32
3 VfL Bochum 30 17 4 9 55 40 – 33 +7
4 SpVgg Greuther Fürth 30 15 9 6 54 41 – 22 +19
5 Erzgebirge Aue 29 14 7 8 49 34 – 32 +2
6 Energie Cottbus 30 14 6 10 48 57 – 45 +12
7 MSV Duisburg 30 13 7 10 46 45 – 33 +12
8 TSV 1860 Munich 30 12 9 45 42 – 31 +11
9 Fortuna Düsseldorf 30 14 3 13 45 41 – 35 +6
10 Alemannia Aachen 30 11 8 11 41 50 – 55 -5
11 Union Berlin 30 10 8 12 38 32 – 36 -4
12 FSV Frankfurt 29 11 4 14 37 39 – 42 -3
13 FC Ingolstadt 30 9 7 14 34 38 – 43 -5
14 SC Paderborn 30 8 8 14 32 27 – 42 -15
15 Karlsruher SC 30 7 8 15 29 39 – 64 -25
16 VfL Osnabrueck 30 7 6 17 27 37 – 57 -20
17 Rot Weiss Oberhausen 30 6 7 17 25 26 – 53 -27
18 Arminia Bielefeld 30 3 7 20 16 25 – 60 -35
729 729 0
Total number of games 269
Goals ø 2.71
Statistics received/expected
Games HS U HN T GT
arrived: 269 132 60 77 419 310
269 126 65.6 77.4 414 303
Deviation 0 6.1 -5.6 -0.4 5.1 7
ø expected determination
39.08%
ø determination received
40.16% Here the tendency remains: there are too many favourite victories. The deviations remain within limits, even if the home victories have appeared too numerous by about 6 (which then again confirms the trend of too many favourite events).
Also this table with no excessive tension at present. 1st and 2nd place seem to be taken and there is only a duel for 3rd place (as things stand). At the bottom of the table, Osnabrück and KSC may still be in contention for relegation, Oberhausen may still be able to intervene, but is consistently (presumably) playing too badly.
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 4075 917 8 2.67 99.89%
FC Augsburg 925 3884 178 59.33 97.37%
SpVgg Greuther Fürth 0 84 2554 851.33 18.71%
VfL Bochum 0 115 2170 723.33 16.77%
Erzgebirge Aue 0 0 68 22.67 0.45%
Energie Cottbus 0 0 17 5.67 0.11%
MSV Duisburg 0 0 3 1.00 0.02%
Fortuna Düsseldorf 0 0 2 0.67 0.01%
5000 5000 5000 1666.67 2.33
Here is the first confirmation of this: Hertha and Augsburg at well over 90%, duel between Bochum and Fürth around 33.3%.
c. Expected points and deviations
Team Name Points expected Points scored Deviation Deviation absolute1 Erzgebirge Aue 36.86 49 12.14 12.14
2 Hertha BSC 54.19 65 10.81 10.81
3 SpVgg Greuther Fürth 46.01 54 7.99 7.99
4 FC Augsburg 53.94 61 7.06 7.06
5 VfL Bochum 48.37 55 6.63 6.63
6 Energie Cottbus 45.33 48 2.67 2.67
7 Fortuna Düsseldorf 43.27 45 1.73 1.73
8 FC Ingolstadt 32.43 34 1.57 1.57
9 TSV 1860 Munich 44.16 45 0.84 0.84
10 FSV Frankfurt 36.89 37 0.11 0.11
11 Alemannia Aachen 41.32 41 -0.32 0.32
12 Union Berlin 40.60 38 -2.60 2.60
13 MSV Duisburg 49.28 46 -3.28 3.28
14 SC Paderborn 36.66 32 -4.66 4.66
15 VfL Osnabrueck 33.88 27 -6.88 6.88
16 Karlsruher SC 36.47 29 -7.47 7.47
17 Rot Weiss Oberhausen 33.10 25 -8.10 8.10
18 Arminia Bielefeld 28.63 16 -12.63 12.63
5.62 97.49
ø Deviation 5.42Aue remain in front. Of course, they impressed again with a win 5:1 away!). Otherwise, no very big standouts other than those you already know. Ingolstadt has worked its way into the plus with brilliant results, also Düsseldorf (started with 6 defeats!) already in the plus.
d. Evaluation of the 30th matchday of the second division
Goal expectation
Home Away Total DeviationIngolstad Bochum 1.00 1.24 2.24 3 0 2.00 -1.24
Düsseldorf Union 1.45 0.80 2.24 3 0 1.55 -0.80
FSV Frankfurt Munich 1860 1.17 1.28 2.45 2 1 0.83 -0.28
Hertha Osnabrück 2.70 0.80 3.50 4 0 1.30 -0.80
Cottbus Duisburg 1.53 1.18 2.71 3 1.47 -0.18
Aachen Erzgebirge Aue 1.90 1.13 3.03 1 5 -0.90 3.87
Bielefeld Oberhausen 1.27 1.10 2.37 3 3 1.73 1.90
Greuther Fürth SC Paderborn 1.58 0.57 2.15 2 0 0.42 -0.57
Karlsruhe Augsburg 1.01 1.99 3.00 0 1 -1.01 -0.99
13.60 10.09 23.69 21 11 7.40 0.91
Expected Goal Total Expected Goal Average Scored Goal Average
23.69 2.63 3.56 ø expected goal difference 1.79 ø goal difference 2.43
The goal glut has taken hold in League 2. Suddenly 32 instead of the expected (barely) 24. The home teams clearly in front, despite a 1:5 result. Away goals barely outscored despite this.
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 commitment: 41.22%
The determination (arrived) Pairing 1 X 2
Ingolstad Bochum 29.60% 28.64% 41.75% 29.60%
Düsseldorf Union 52.51% 26.87% 20.62% 52.51%
FSV Frankfurt Munich 1860 33.62% 27.35% 39.03% 33.62%
Hertha Osnabrück 77.31% 14.08% 8.61% 77.31%
Cottbus Duisburg 45.41% 25.37% 29.22% 45.41%
Aachen Erzgebirge Aue 55.39% 22.31% 22.30% 22.30%
Bielefeld Oberhausen 40.14% 27.83% 32.03% 27.83%
Greuther Fürth SC Paderborn 62.18% 24.72% 13.10% 62.18%
Karlsruhe Augsburg 18.51% 21.32% 60.18% 60.18%
4.15 2.18 2.67 4.11
Average number of incoming commitments: 45.66% Same trend here: too many favourite wins. 45.66% is pretty clear. And, as could be seen before, the favourites have thus confirmed themselves (even more). A continuing trend, then, in the otherwise so well-balanced second division? We shall see…
e. Preview of the 31st Second Division Matchday
Goal expectation
Home Away TotalErzgebirge Aue Cottbus 1.45 1.10 2.56
Osnabrück FSV Frankfurt 1.48 1.29 2.77
SC Paderborn Bochum 0.92 1.27 2.19
Munich 1860 Greuther Fürth 1.04 1.02 2.06
Oberhausen Karlsruhe 1.49 1.45 2.94
Union Ingolstad 1.37 1.08 2.45
Augsburg Aachen 2.21 0.95 3.16
Düsseldorf Bielefeld 2.46 0.56 3.02
Duisburg Hertha 1.14 1.53 2.67
13.57 10.26 23.83
Expected goal total Expected goal average
23.83 2.65 Everything in the normal range here. There should be many goals in Augsburg and Düsseldorf, very few in Munich, in the (small) derby.
The determination (expected) Pairing 1 X 2
Erzgebirge Aue Cottbus 45.18% 26.05% 28.77% 35.47%
Osnabrück FSV Frankfurt 41.89% 25.15% 32.96% 34.74%
SC Paderborn Bochum 26.92% 28.55% 44.54% 35.23%
Munich 1860 Greuther Fürth 35.41% 30.16% 34.43% 33.49%
Oberhausen Karlsruhe 38.58% 24.44% 36.98% 34.53%
Union Ingolstad 43.57% 26.82% 29.61% 34.95%
Augsburg Aachen 66.10% 18.99% 14.90% 49.53%
Düsseldorf Bielefeld 79.08% 14.34% 6.59% 65.02%
Duisburg Hertha 28.34% 25.30% 46.36% 35.92%
4.05 2.20 2.75 3.59
average expected determination: 39.88% At 39.88% expected a rather high, but not exaggerated value. Especially the Bielefeld (away) games stand out with very high values.
The fair odds
Pairing 1 X 2
Erzgebirge Aue Cottbus 2.21 3.84 3.48
Osnabrück FSV Frankfurt 2.39 3.98 3.03
SC Paderborn Bochum 3.72 3.50 2.25
Munich 1860 Greuther Fürth 2.82 3.32 2.90
Oberhausen Karlsruhe 2.59 4.09 2.70
Union Ingolstad 2.29 3.73 3.38
Augsburg Aachen 1.51 5.26 6.71
Düsseldorf Bielefeld 1.26 6.98 15.18
Duisburg Hertha 3.53 3.95 2.16
Well, the most exciting question at the moment might be: Will there be any suspense at all in the decisive questions? The title in League 1 seems to have been awarded. Unless there is a plein and a cheval in a row….
