No final decision has yet been made on the part of the authors as to whether this type of reporting (let’s call it “statistical”) will be carried out at all this season, and if so, how regularly and extensively. Nevertheless, the foundation has been laid with last week’s preliminary review, which will now almost inevitably be followed by a corresponding review. For: there was certainly enough exciting to observe, which can/should/must be brought into comparison with the preliminary considerations made here.
First of all, however, please understand that the 2nd League has not yet been included. On the one hand, this is due to the fact that the Berlin Hertha – a large part of our circle of acquaintances live in the state and federal capital – has managed the promotion, but on the other hand, it is also due to the hours of work involved, especially since a few more points were included right at the beginning, such as (or: mainly) the comparison of the odds that were specially created (with computer assistance) with those traded on the betting market.
1) The 1st Bundesliga
a. Review of the matches
Results of the 1st match day
Borussia Dortmund – Hamburger SV 3:1 (2:0)
Hannover 96 – TSG Hoffenheim 2:1 (2:1)
Hertha BSC – 1. FC Nürnberg 0:1 (0:0)
VfB Stuttgart – FC Schalke 04 3:0 (1:0)
Werder Bremen – 1. FC Kaiserslautern 2:0 (0:0)
- FC Cologne – VfL Wolfsburg 0:3 (0:1)
FC Augsburg – SC Freiburg 2:2 (0:0)
FSV Mainz 05 – Bayer Leverkusen 2:0 (1:0)
FC Bayern München – Borussia Mönchengladbach 0:1 (0:0)
So what were the “big talking points”? Of course, it has to be said, the outstanding performance of Dortmund at the start of the season, which was crowned with a victory, and the bitter opening defeat at home, in the stadium of the all-round top favourite, from the Bavarian point of view. Bayern were certainly the better team, and they certainly had the greater number of goal-scoring chances and possession. Nevertheless, their game lacked a little bit of a change of rhythm, so that Gladbach were able to adjust to it better and better and actually scored the one, all-important goal.
Well, nevertheless, a few very brief words on the disallowance of the equaliser: whatever the instructions to referees and assistants, the decisions against the goals are always the easy ones. You are not prosecuted for them. The protection: “that was hard to see and who wants to, in fractions of seconds…”. But the fact is that it is not at all necessary to have “seen something”, but that it is a reflex that makes the flag go up. This is purely a protective measure, for one (linesman) himself. “Flag up, all is well.” If, on the other hand, the goal was acknowledged and one was shown afterwards to have made an error of judgement, then God help you. In this case, according to the opinion then held, one would indeed have intervened incorrectly, but decisively.
So: the man on the line sees nothing, not in the action. Above all, he does not see which player goes for the ball. He can’t see it at all because a) he is very far away and b) a lot of players go to the ball. In any case, the goal scorer was clearly not offside. The argumentation that (after the shot was blocked by the goalkeeper, which preceded the decision) all players, including Gomez who was really offside, wanted to get to the ball and that this intention alone should be considered an offence, is at least very short-sighted, if not stupid. The consequence: in more and more actions, justifications are found to prevent the goal actions. And, according to the more than possible loudly and recurrently held view here, goals continue to be the only real seasoning in the soup and, as their frequency decreases, an unwelcome drop in tension is clearly virtually guaranteed. So if the sports magazine “Der Kicker” comes to the conclusion that the referee was right in all important decisions (and here’s the question: who actually gave the Kicker the prerogative to decide on right and wrong?), then one can only assume that the goal-hungry spectator will continue to be upset by a number of disallowed goals in the course of the season or in general in the football future, which is by no means too bright.
If the offside rule were to be made reasonable, the linesman would have to be allowed to indicate an offside position – as was customary in the olden days – but the man at the whistle would still have to be responsible for punishing it. Today it has long been the case that raising the flag is equivalent to a whistle. So the old rule that Otto Rehhagel once laid down that “offside is when the referee blows the whistle” has long been invalid, but would have to be replaced by (or: has long been the common practice): “offside is when the assistant raises the flag”. Because: no referee could afford not to blow the whistle when waving the flag in a decisive situation. But this is only in passing.
It is silly and counter-productive to give the whistle blowers all sorts of reasons to justify a decision against the goals and/or against the goal actions. But this is what happened, and even not only in this scene on this matchday.
The opinion expressed here: this goal was as regular as a goal can be. Before the digression here degenerates again, the author slaps himself on the simply unstoppable fingers… and takes a self-imposed break…
Hannover won rather happily against Hoffenheim, as one could see from all the reports. Especially the 1:0 caused a stir, of course, when once again a direct free kick was taken before the wall (and the goalkeeper) were in position. As nice as it sounds that a controversial goal is recognised for once (contrary to the permanent disallowance, for diffuse reasons), here it was rather the audacity of Jan Schlaudraff and a slightly inconsistent behaviour of the referee that was responsible. It should be clear when the game should be continued without the whistle and when with it. Everything here indicates that a whistle was to be expected, on all sides.
Wolfsburg’s clear victory was a little deceptive, because Cologne pressed for the equaliser, had to continue the game with 10 men due to the rather harmless yellow card against Novakovic – and his opponent, after a small scuffle – due to the preliminary warning, and therefore the consequence yellow-red, whereupon two more goals were scored against Cologne in the final phase. One good commentary was captured after all, revealing quite a lot: After the referee realised that Novakovic had already been given a yellow warning and therefore yellow-red would be the consequence, the announcer realised: “Whether he would have given this yellow card if he had known that Novakovic had already been cautioned…. I have considerable doubts about that.”
What it reveals? Yes, the spokesman is right. The ref would not have cautioned if he had remembered yellow. So one concludes: decisions are not made in good faith and solely on the basis of what is seen in an action, but they are made according to psychological considerations. However, none of the rules officials would ever dare to acknowledge this truth or even consider it. Because it would shake up the entire set of rules. “You can’t give a penalty here.” “Why not?” “Well, because there were one or two critical situations earlier on the other side as well, where there was already no penalty.” So it’s not about foul or non-foul, it’s about the previous history. That is the truth.
As soon as one is prepared to engage in the argumentation, many things become easier to judge. For example, the raised flag at the Bayern equaliser…
Sp S U N Pkt T GT Diff
1 VfL Wolfsburg 1 1 0 0 3 3 – 0 +3
2 VfB Stuttgart 1 1 0 0 3 3 – 0 +3
3 Borussia Dortmund 1 1 0 0 3 3 – 1 +2
4 FSV Mainz 05 1 1 0 0 3 2 – 0 +2
5 Werder Bremen 1 1 0 0 3 2 – 0 +2
6 Hannover 96 1 1 0 0 3 2 – 1 +1
7 Borussia Mönchengladbach 1 1 0 0 3 1 – 0 +1
8 1.FC Nürnberg 1 1 0 0 3 1 – 0 +1
9 SC Freiburg 1 0 1 0 1 2 – 2 +0
10 FC Augsburg 1 0 1 0 1 2 – 2 +0
11 TSG Hoffenheim 1 0 0 1 0 1 – 2 -1
12 FC Bayern München 1 0 0 1 0 – 1 -1
13 Hertha BSC 1 0 0 1 0 – 1 -1
14 Hamburger SV 1 0 0 1 0 1 – 3 -2
15 Bayer Leverkusen 1 0 0 1 0 – 2 -2
16 1.FC Kaiserslautern 1 0 0 1 0 – 2 -2
17 FC Schalke 04 1 0 0 1 0 – 3 -3
18 1.FC Köln 1 0 0 1 0 – 3 -3
23 23 0
Total number of games 9
Goals ø 2.56
Well, lucky for reader, lucky for author: the table gives nothing worth commenting on.
b. The title question
Explanation: these figures are the result of a computer simulation 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
Borussia Dortmund 2023 40.46% 2.47
FC Bayern Munich 1627 32.54% 3.07
Bayer Leverkusen 301 6.02% 16.61
VfL Wolfsburg 289 5.78% 17.30
Hannover 96 165 3.30% 30.30
Werder Bremen 155 3.10% 32.26
FSV Mainz 05 130 2.60% 38.46
VfB Stuttgart 100 2.00% 50.00
Borussia Mönchengladbach 73 1.46% 68.49
FC Schalke 04 44 0.88% 113.64
Hamburger SV 33 0.66% 151.52
1.FC Nuremberg 19 0.38% 263.16
TSG Hoffenheim 18 0.36% 277.78
1.FC Kaiserslautern 9 0.18% 555.56
SC Freiburg 7 0.14% 714.29
1.FC Köln 3 0.06% 1666.67
Hertha BSC 3 0.06% 1666.67
FC Augsburg 1 0.02% 5000.00
Dortmund moved up to 1 right away. On the one hand, of course, the 3 points gained compared to Bayern’s 0, on the other hand Dortmund’s gain in playing strength compared to Bayern’s loss, which the (well-fed and docile) computer assigns to the two teams based on their results. Furthermore, 73% remain with the two top teams. This is slightly less than the previous week, logically due to Bayern’s defeat, which promises everyone a small glimmer of hope. It only gets really interesting when looking at the…
Change in chances compared to the previous week due to the results of Matchday 1
Team Gain/Loss German Champion in 5000 Simulations Championships in per cent
Borussia Dortmund 628 12.56%
VfL Wolfsburg 128 2.56%
FSV Mainz 05 74 1.48%
Borussia Mönchengladbach 49 0.98%
Werder Bremen 44 0.88%
VfB Stuttgart 43 0.86%
Hannover 96 27 0.54%
1.FC Nuremberg 8 0.16%
1.FC Kaiserslautern 5 0.10%
FC Augsburg 1 0.02%
SC Freiburg 1 0.02%
Hertha BSC -2 -0.04%
TSG Hoffenheim -4 -0.08%
1.FC Cologne -7 -0.14%
Hamburger SV -26 -0.52%
FC Schalke 04 -55 -1.10%
Bayer Leverkusen -142 -2.84%
FC Bayern Munich -772 -15.44%
An extreme shift by actually two results, which certainly intuitively seems like a lot (maybe too much). Nevertheless, computer logic is at least incorruptible and at most calls for a human explanation. A gain of 12.56% (Dortmund) is already gigantic, one would think, but a loss of 15.44% (Bayern) is downright outrageous. So how should a result be…?
Well, it should be repeated as a matter of priority that Bayern have not only lost points but also their playing strength, and this effect continues to have an impact on all games, at the same time as their rivals have gained. And, if one wants to be so pedantic, then this effect would obviously be greatest on Matchday 1, since the greatest possible number of matches are outstanding on which it has an effect. Otherwise, one should let one’s intuition (which, for example, was initially called into question by computer logic, even among chess lovers, before computer moves gradually became second nature: the computer moves bishop to c7, then that’s also good!
Losses, of course, were also suffered by Leverkusen, who were considered favourites in the market in Mainz, as well as Schalke or HSV, the teams that went home with defeats, of course. Otherwise, of course, the winning teams have cut themselves a slice of the (still a long way to go in terms of chances) cake.
c. The title chances in development
Well, graphically it doesn’t get any more pleasing for Bavaria. The others divide up the remaining 27%, partly with gains, partly with losses. Surely it will only get a little more interesting as the season progresses.
d. Comparison of title chances with the betting exchange betfair
Back Lay Probability (Back)
FC Bayern Munich 1.94 1.96 51.55%
Borussia Dortmund 3.25 3.3 30.77%
Bayer Leverkusen 23 24 4.35%
VfL Wolfsburg 25 27 4.00%
Hannover 96 130 200 0.77%
Werder Bremen 50 65 2.00%
FC Schalke 04 40 50 2.50%
Hamburger SV 100 150 1.00%
VfB Stuttgart 50 55 2.00%
FSV Mainz 05 160 240 0.63%
Borussia Mönchengladbach 75 90 1.33%
TSG Hoffenheim 110 160 0.91%
1.FC Nuremberg 310 400 0.32%
1.FC Cologne 550 770 0.18%
SC Freiburg 1000 1500 0.10%
Hertha BSC 310 1000 0.32%
1.FC Kaiserslautern 410 800 0.24%
FC Augsburg 1000 1500 0.10%
The market does not share the extreme views of the computer, which somewhat confirms the intuition theory. You just inevitably think: the season is still soooo long. A lot can still happen. Well, the question will certainly remain unanswered for a while: who is right? Because: the mathematical proof of the correctness of the computer view is a) very difficult to carry out and b) would not be scientifically accepted (even if there is a method that would be gladly presented one day and specially developed).
On the other hand, it is of course readily conceded here that proof of the correctness of probability estimates is exactly —- impossible. One can only bet on it – and then regularly count one’s money, and if it has become more of it pat oneself on the back or buy something fine with it, be it even to make it one’s profession — or get clues with statistical figures as to how good the numbers are in comparison (which, however, can be a decreasingly relevant question of luck or bad luck, depending on the length of time).
The shifts in odds estimates at betfair
The shifts in probabilities
FC Bayern Munich -9.80%
Borussia Dortmund 12.25%
Bayer Leverkusen -3.06%
VfL Wolfsburg 1.83%
Hannover 96 0.21%
Werder Bremen 0.18%
FC Schalke 04 -1.20%
Hamburger SV -1.08%
VfB Stuttgart 0.33%
FSV Mainz 05 0.31%
Borussia Mönchengladbach 0.83%
TSG Hoffenheim -0.76%
1.FC Nuremberg 0.08%
1.FC Cologne -0.34%
SC Freiburg -0.08%
Hertha BSC -0.30%
1.FC Kaiserslautern -0.16%
FC Augsburg -0.11%
(This time the order according to the original estimates of the ranking)
Bayern on the market with a loss of “only” just under 10%, Dortmund on the other hand with a comparable gain to the computer. Why is this? Well, one can assume that of all things, the opening match was followed with joy and excitement not only in Germany and indeed everywhere (it was also on public television). So it wasn’t the naked result that was responsible for the many Dortmund fans (i.e. those who also supported the supporters monetarily), but rather the performance shown. The more or less moderate shifts for the other teams should remain uncommented here.
e. Direct Champions League qualification via second place
Whether this point will be included in the upcoming season is still undecided.
The probability distribution for 2nd place after the 2nd matchday
The changes compared to the previous week:
f. The relegation question
The usual point,
The distribution of percentages for relegation
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 relegated is added by the relegation, whereby the first division team is generally rated as 2/3 to 1/3 favourites 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 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 Hertha BSC 35.52% 4.41% 39.93%
2 FC Augsburg 34.80% 4.16% 38.96%
3 1.FC Kaiserslautern 29.40% 3.96% 33.36%
4 1.FC Köln 24.92% 3.78% 28.70%
5 SC Freiburg 20.92% 3.33% 24.25%
6 TSG Hoffenheim 13.00% 2.71% 15.71%
7 1.FC Nuremberg 9.76% 2.26% 12.02%
8 FC Schalke 04 7.14% 1.78% 8.92%
9 Hamburger SV 7.20% 1.69% 8.89%
10 Borussia Mönchengladbach 4.80% 1.28% 6.08%
11 VfB Stuttgart 3.50% 0.99% 4.49%
12 FSV Mainz 05 2.70% 0.82% 3.52%
13 Hannover 96 2.04% 0.69% 2.73%
14 Werder Bremen 2.00% 0.57% 2.57%
15 VfL Wolfsburg 1.20% 0.46% 1.66%
16 Bayer Leverkusen 1.06% 0.42% 1.48%
17 FC Bayern Munich 0.04% 0.01% 0.05%
18 Borussia Dortmund 0.00% 0.01% 0.01%
200.00% 33.33% 233.33%
Hertha’s defeat, which weighs double at home against a rival, has put them right at the top (not aspired to). Surely this would be in slight competition with the betting market (which is not surveyed and contrasted here), where Hertha are slightly higher than the computer influenced by the so nasty people — and capital as well as hometown despising — hand. But didn’t Mario Basler, who once laced up the boots for them and now runs the Bild column, even more brazenly put the old lady at 18 right from the start in that very column?
The change in chances from matchday 1 to matchday 2 with regard to relegation
This is omitted as no estimates were given in advance.
g. The relegation question in the development
This is omitted as no estimates were given in advance.
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 absolute
1 Borussia Mönchengladbach 0.36 3 2.64 2.64
2 1.FC Nürnberg 1.28 3 1.72 1.72
3 FSV Mainz 05 1.37 3 1.63 1.63
4 VfL Wolfsburg 1.46 3 1.54 1.54
5 VfB Stuttgart 1.51 3 1.49 1.49
6 Hannover 96 1.80 3 1.20 1.20
7 Werder Bremen 1.87 3 1.13 1.13
8 Borussia Dortmund 2.15 3 0.85 0.85
9 SC Freiburg 1.26 1 -0.26 0.26
10 FC Augsburg 1.46 1 -0.46 0.46
11 Hamburger SV 0.64 0 -0.64 0.64
12 1.FC Kaiserslautern 0.91 0 -0.91 0.91
13 TSG Hoffenheim 0.96 0 -0.96 0.96
14 FC Schalke 04 1.24 0 -1.24 1.24
15 1.FC Köln 1.29 0 -1.29 1.29
16 Bayer Leverkusen 1.39 0 -1.39 1.39
17 Hertha BSC 1.46 0 -1.46 1.46
18 FC Bayern Munich 2.52 0 -2.52 2.52
ø Deviation 1.30
At least it’s interesting to see (and initially responsible for a brief gulp from the first-time viewer) that Mönchengladbach overachieved more points than Bayern underachieved Shouldn’t that be about…? No, it shouldn’t. Every missed draw results in an over-fulfilment of the points expectation in total (as already briefly touched on in italics above). Especially in Bayern – Gladbach the draw was the least likely, so that the overfulfilment is minimal. On the other hand, in the most probable (and even the only one that happened!) draw, Augsburg – Freiburg, the point expectation was 2,428 points, which would be distributed, of which only 2 were awarded, one to each team.
This effect (mentioned in italics above) is also best seen after the 1st matchday: both teams are in the table with a deficit. Even the away club, which is considered a little more successful, has underachieved its expectation with -0.26 points, which in this sense provides evidence for the thesis of the unfairness of the three-point rule set up above. What did the teams do so wickedly wrong that they both had to concede a penalty? A great football match with a fair result, incidentally also the one with the most changes of tendency (lead – equalisation – lead – equalisation). Apart from that, Hertha disappointed expectations the most, and not only in terms of results, but even in terms of play.
The international comparison for the average point difference
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.
Liga 1 ø Deviation Change from previous week
Germany, 1st BL 1.30
So far, only the 2nd league could be included, so the completion of the statistics is still delayed. The 1st Bundesliga can also be followed in this way. Is 1.3 a lot? You will get an answer to that a little later…
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 deviation
1 Borussia Mönchengladbach 0.90 1 3.04 0 3.15
2 VfL Wolfsburg 1.46 3 1.33 0 2.87
3 VfB Stuttgart 1.48 3 1.28 0 2.80
4 FSV Mainz 05 1.41 2 1.43 0 2.01
5 Werder Bremen 1.90 2 1.15 0 1.26
6 1.FC Nürnberg 1.25 1 1.38 0 1.12
7 Borussia Dortmund 1.88 3 0.74 1 0.87
8 Hannover 96 1.75 2 1.12 1 0.37
9 SC Freiburg 1.03 2 1.17 2 0.13
10 FC Augsburg 1.17 2 1.03 2 -0.13
11 TSG Hoffenheim 1.12 1 1.75 2 -0.37
12 Hamburger SV 0.74 1 1.88 3 -0.87
13 Hertha BSC 1.38 0 1.25 1 -1.12
14 1.FC Kaiserslautern 1.15 0 1.90 2 -1.26
15 Bayer Leverkusen 1.43 0 1.41 2 -2.01
16 FC Schalke 04 1.28 0 1.48 3 -2.80
17 1.FC Köln 1.33 0 1.46 3 -2.87
18 FC Bayern Munich 3.04 0 0.90 1 -3.15
25.70 23 0.00
Goals ø expected: Goals ø scored: ø Deviation 1.62 2.86 2.56
Gladbach took the cake here too. Sure, staying in Munich without conceding a goal is already more than just surprising (and brings most of the good statistics with it). Cologne, however, with a missed 2.87 goals, only just ahead of Bayern. Here, the goals conceded, three of which were conceded, have a huge impact. Hertha, of course, moved into the rear of the midfield, as they only lost 0:1.
Also for this statistic the international comparison:
Place Country League 1 ø Goal difference Change from previous week.
1 Germany, 1.BL 1.62
6 Germany, 2.BL
Comment: see above.
j. The playing strength ranking
Note: Playing strength is measured in goals expected to be scored 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.
Team For Against Quotient For/Again Shift
1 Borussia Dortmund 1.74 0.89 1.96 +1
2 FC Bayern Munich 2.00 1.04 1.92 -1
3 Bayer Leverkusen 1.68 1.27 1.32 +0
4 VfL Wolfsburg 1.50 1.22 1.23 +0
5 Hannover 96 1.48 1.35 1.10 +0
6 Werder Bremen 1.57 1.44 1.09 +1
7 FSV Mainz 05 1.41 1.35 1.05 +1
8 VfB Stuttgart 1.62 1.62 1.00 +2
9 FC Schalke 04 1.24 1.25 0.99 -3
10 Hamburger SV 1.39 1.44 0.97 -1
11 Borussia Mönchengladbach 1.39 1.46 0.95 +0
12 TSG Hoffenheim 1.34 1.54 0.87 +0
13 1.FC Nürnberg 1.22 1.44 0.85 +0
14 SC Freiburg 1.20 1.56 0.77 +1
15 1.FC Köln 1.29 1.72 0.75 -1
16 1.FC Kaiserslautern 1.18 1.64 0.72 +0
17 Hertha BSC 1.14 1.67 0.68 +0
18 FC Augsburg 0.99 1.50 0.66 +0
25.39 25.39 +0
Goals ø expected 2.821
As you can see a bit of movement right away. Dortmund ousted Bayern from 1st place, but if you listen to the comments (including those on Sky 90, the Sunday evening programme on Sky Deutschland), even experts here agree. Dortmund simply impressed everyone, Bayern disappointed. Stuttgart and Schalke were close before, so the change of places is not surprising – at the same time not irritating.
k. The frequency of tendency changes
Note: a “change of tendency” is considered to be a goal which equalises a lead or gives 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.
In total, there were 5 changes of tendency on the first matchday. Hannover conceded the equaliser, took the lead again, and Augsburg, as already mentioned, were behind (the 0:1 doesn’t count), equalised, were behind again and equalised again. Apart from HSV in Dortmund, none of the losers managed to score a goal at all, so there was no change in the trend anyway (the HSV goal was the 1:3). Furthermore, it would hardly have been possible to speak of an exciting match day if it had not been for the joy that it had started again at all.
Here, too, the international comparison:
Country Matches Compensation HF AF Total per match
Germany 1 9 3 1 5 0.556
Germany 2 27 11 5 2 18 0.667
In the 2nd division, there were a lot of trend changes, so to speak, in normal international terms. However, Germany were pretty clearly ahead last season in terms of that element of excitement. Will they take the lead again? One will see.
l. The mathematical review of the matchday 1 results
Goal expectation Home Away Total Deviation
Dortmund HSV 1.88 0.74 2.62 3 1 1.12 0.26
Hannover Hoffenheim 1.75 1.12 2.87 2 1 0.25 -0.12
Hertha Nürnberg 1.38 1.25 2.63 0 1 -1.38 -0.25
Stuttgart Schalke 04 1.48 1.28 2.76 3 0 1.52 -1.28
Bremen Kaiserslautern 1.90 1.15 3.05 2 0 0.10 -1.15
FC Cologne Wolfsburg 1.33 1.46 2.78 0 3 -1.33 1.54
Augsburg Freiburg 1.17 1.03 2.20 2 0.83 0.97
Mainz Leverkusen 1.41 1.43 2.84 2 0 0.59 -1.43
FC Bayern Gladbach 3.04 0.90 3.94 0 1 -3.04 0.10
15.34 10.37 25.70 14 9 -1.34 -1.37
Expected goal total Expected goal average Goal average achieved 25.70 2.86 2.56
ø expected goal difference 1.88 ø goal difference 2.16
The first observation: there were too few goals. Last season it was argued a little that the World Cup with the positive (as among other things offensive) appearance of the Germans ensured a continuation of the effect in the league: everyone played forward optimistically. Otherwise, the first match days are predestined for many goals, on the one hand because of the summer weather (well, 2011 and summer, an extra chapter…) and the streaming spectators, and on the other hand because of the expectations that cannot yet be disappointed. If things don’t click yet, how can they succeed in the “dark days of winter”, when the battles for position and points are on the agenda? In case you want to hear the dreaded suspicion already today: the whistle will be blown even tighter and even more against goal situations, as already explained above. So: apart from coincidence, it could also be a systematic effect: there are fewer goals. Again: let’s see. In any case, the computer is not immediately steered in this direction (even if human hands could).
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
Dortmund HSV 64.41% 21.40% 14.19% 48.08%
Hannover Hoffenheim 52.38% 23.25% 24.36% 38.78%
Hertha Nuremberg 40.08% 25.68% 34.24% 34.38%
Stuttgart Schalke 04 42.11% 24.88% 33.01% 34.82%
Bremen Kaiserslautern 54.90% 22.07% 23.02% 40.32%
FC Cologne Wolfsburg 34.63% 24.85% 40.52% 34.59%
Augsburg Freiburg 39.06% 28.62% 32.32% 33.89%
Mainz Leverkusen 37.39% 24.59% 38.02% 34.48%
FC Bayern Gladbach 80.01% 12.14% 7.84% 66.11%
4.45 2.07 2.48 3.65
average expected fixing: 40.61%
For recap purposes only, here are the expected figures given in last week’s text.
The determination arrived
Pairing 1 X 2
Dortmund HSV 64.41% 21.40% 14.19% 64.41%
Hannover Hoffenheim 52.38% 23.25% 24.36% 52.38%
Hertha Nuremberg 40.08% 25.68% 34.24% 34.24%
Stuttgart Schalke 04 42.11% 24.88% 33.01% 42.11%
Bremen Kaiserslautern 54.90% 22.07% 23.02% 54.90%
FC Cologne Wolfsburg 34.63% 24.85% 40.52% 40.52%
Augsburg Freiburg 39.06% 28.62% 32.32% 28.62%
Mainz Leverkusen 37.39% 24.59% 38.02% 37.39%
FC Bayern Gladbach 80.01% 12.14% 7.84% 7.84%
4.45 2.07 2.48 3.62
average determination received: 40.27%
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.
As can be seen, the expected value was only slightly undercut. This would not be surprising only if there had not been the Bayern defeat. After all, the occurrence of a 7.84% chance is not an everyday occurrence by Bundesliga standards (so while one might like to say that it would be expected in one game out of 13, there first has to be a game with such a chance distribution for this surprise to occur).
So what does this result of only a slight deviation tell us? Well, quite clearly: in almost all other games the event with the greatest chance occurred. Not in the case of Mainz – Leverkusen, but there the deviation between home win and away win is negligible, in the case of Hertha against Nuremberg likewise not great, so that only the Augsburg X remains, which could be called a small surprise (and which would be contradictory especially here, since it is stated above that of all things the draw came, which had the highest value, but on the other hand too few draws came). The clearer favourites all prevailed.
n. Overall league statistics
Note: statistics of this kind are regularly compiled 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
306 141 63 102 505 392 1.126
Statistics of expected results
Matches Home wins Draws Away wins Goals Conceded Home advantage
306 140.06 72.05 93.87 500.8 390.3 1.124
Statistics of absolute deviations
Matches Home wins Draws Away wins Goals Conceded Home advantage
0 0.94 -9.05 8.13 4.2 1.7 0.00197
Statistics of percentage deviations
Matches Home wins Draws Away wins Goals conceded Home advantage
0 0.67% -14.37% 7.97% 0.83% 0.43% 0.18%
Determination expected Determination arrived 39.48% 38.34% ø Goal difference ø Goal difference expected 1.94 1.90
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 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.
Since the season is too young to list it here already with overall statistics as an extra service, here are the values for the whole of last season. As you can see, all the deviations are quite moderate. The only noticeable thing is that there were too few draws, which almost entirely translated into away victories. Well, the computer automatically adjusts its parameters so that it initially expects fewer draws (this adjustment is made weekly). On Matchday 1, the trend continued.
The determination arrived/expected has converged to some extent towards the end. If memory serves, it was this divergence that was almost responsible for starting these records: there were so many surprises at the beginning, the whole league was upside down. This has levelled out a bit, even if a deviation of over 1% (towards “surprises” as arrived smaller than expected) is still comparatively large.
o. Review of the betting recommendations
Pairing 1 X 2
Dortmund HSV 1.56 4.40 7.20
Hannover Hoffenheim 2.22 3.55 3.6
Hertha Nuremberg 2.16 3.55 3.85
Stuttgart Schalke 04 2.36 3.60 3.35
Bremen Kaiserslautern 1.87 3.85 4.70
FC Cologne Wolfsburg 2.70 3.55 2.82
Augsburg Freiburg 2.34 3.60 3.30
Mainz Leverkusen 4.20 3.80 1.97
FC Bayern Gladbach 1.23 7.60 15.50
Here is the illustration from last week’s text with the bets marked in yellow, i.e. recommended. As you can see, Hannover would have won (who dared?), as would Nürnberg, Werder, Wolfsburg and Mainz. Lost would be the bets on Schalke and Freiburg, so of course the result remains positive.
If you calculate it in units (and, possible that it will be permanently quoted here as a statistic), then the following picture emerges:
Hannover +1.22 units (the unit for the stake is lost in the European odds, you win stake * odds, so for 100 euros you would get 220 back, which is a profit of 122 euros).
Nuremberg +2.85 units
Schalke -1 unit
Bremen + 0.87 units
Wolfsburg +1.82 units
Freiburg -1 unit
Leverkusen + 3.2 units.
That makes a total profit of +7.96 units.
In addition to the good Dortmund Meister recommendation, all we can say is: it’s starting to feel pretty good.
p. The preview of the 2nd matchday
Note: The computer uses a specially developed – of course explainable and highly logical – algorithm 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 Total
Kaiserslautern Augsburg 1.43 0.98 2.42
Nuremberg Hanover 1.33 1.32 2.65
HSV Hertha 1.83 1.04 2.86
Hoffenheim Dortmund 0.95 1.63 2.59
Freiburg Mainz 1.32 1.33 2.66
Schalke 04 FC Cologne 1.71 0.98 2.70
Wolfsburg FC Bayern 1.22 1.54 2.76
Gladbach Stuttgart 1.76 1.51 3.27
Leverkusen Bremen 1.95 1.23 3.18
13.51 11.58 25.09
Expected goal total Expected goal average 25.09 2.79
Already somewhat more moderate the goal expectation in the total. Whether a consequence of the results or the pairings themselves are responsible for this? We don’t know, of course it’s a mixture of effects. But there are no clear favourites as on the first matchday, especially since Bayern and Dortmund have to play away from home. The highest-scoring game was in Gladbach (well, adjustments can still be made here, because Gladbach seemed quite stable), closely followed by Leverkusen. Low-scoring, however, was Lautern against Augsburg.
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 the 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
Kaiserslautern Augsburg 47.70% 26.22% 26.08% 36.43%
Nürnberg Hannover 37.49% 25.37% 37.14% 34.29%
HSV Hertha 56.22% 22.45% 21.33% 41.19%
Hoffenheim Dortmund 22.11% 24.28% 53.61% 39.52%
Freiburg Mainz 37.09% 25.34% 37.58% 34.29%
Schalke 04 FC Cologne 54.69% 23.52% 21.79% 40.19%
Wolfsburg FC Bayern 30.43% 24.53% 45.04% 35.56%
Gladbach Stuttgart 44.08% 22.49% 33.43% 35.66%
Leverkusen Bremen 54.19% 21.66% 24.15% 39.89%
3.84 2.16 3.00 3.37
average expected determination: 37.45
As expected, the computer then expects a lower fixing when the top favourites play away.
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
Kaiserslautern Augsburg 2.10 3.81 3.83
Nuremberg Hanover 2.67 3.94 2.69
HSV Hertha 1.78 4.45 4.69
Hoffenheim Dortmund 4.52 4.12 1.87
Freiburg Mainz 2.70 3.95 2.66
Schalke 04 FC Cologne 1.83 4.25 4.59
Wolfsburg FC Bayern 3.29 4.08 2.22
Gladbach Stuttgart 2.27 4.45 2.99
Leverkusen Bremen 1.85 4.62 4.14
Comparison with the betting exchange betfair
(The betting recommendations)
Pairing 1 X 2
Kaiserslautern Augsburg 1.94 3.65 4.60
Nürnberg Hannover 2.48 3.45 3.25
HSV Hertha 2.00 3.80 4.10
Hoffenheim Dortmund 5.20 4.00 1.76
Freiburg Mainz 2.40 3.25 3.55
Schalke 04 FC Cologne 1.66 4.00 6.40
Wolfsburg FC Bayern 4.40 4.00 1.88
Gladbach Stuttgart 2.82 3.65 2.68
Leverkusen Bremen 1.95 3.70 4.40
The gamble is taken again: the betting recommendations. Now it’s out once, let’s just keep it that way. Of course, anyone who dabbles in this would be encouraged to get their own profile. Instead of betting Augsburg to win, one could just as well pay the winning price on Lautern (i.e. play “lay” Kaiserslautern, instead of “back” Augsburg). This recommendation would apply even more to Schalke: rather a “lay” there than playing Cologne to win. On the other hand, the local providers tend to offer only very poor rates on the “lay” side (although you can still play it; it is usually marked as a “handicap bet”). Only then it would be advisable again to play the Cologne win. because of these mostly too bad odds.
It must be mentioned here that these rates are taken from the “early market”. In the course of the week, there may be considerable shifts in these values. Nevertheless, it is an appropriate tip here: the best bets often arise precisely on the “early market”. As soon as the team news players intervene, it becomes more difficult and the prices are not only more stable but often also more reliable (much mass, much intelligence?!).
2) The 2nd Bundesliga
a. The table situation
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 might still depend on the pairing. Since the top favourites are ahead here, it could well be 50% that the second league third place team has against the first league third last.
c. Point expectations and discrepancies
d. Evaluation of the 3rd second division matchday
average determination arrived at: 45.66%
e. Preview of the 4th second league matchday
Maybe starting next week!