Now, on 2 November 2010, the 1st Football Bundesliga is well underway again, after the 10th round played in the meantime, and continues to captivate the fan week after week. There are, as always, a number of much and hotly debated issues. There are a few false starts and a few positive surprises to observe. For example, there is the question of whether the World Cup has had a positive effect, whether the German league has made up ground in international comparison, whether it is more exciting compared to other leagues and whether this allows conclusions to be drawn about its quality.
But one thing remains undoubted: the excitement is considerably increased by the multitude of perceived surprises. One simply wants to know whether Bayern can move all the way to the top after all, whether Schalke will come out on top or whether Mainz’s flight of fancy will continue. Whether this is envied abroad or not, such a circumstance increases the motivation to watch the next matchday, perhaps the next match live in the stadium, wherever one prefers to go and whichever is accessible. Sky subscribers can look forward to the appearance of their favourite club in a single match or, alternatively, can watch the conference call. The “ordinary” football fan can continue to look forward to the Sportschau, Saturday and Sunday, with pictures from the matches, interviews or analyses of critical referee decisions, with the newly opened or ended coach discussions or the new standings situation. In addition, everyone can wait for the daily newspapers or trade magazines to come out so that they can keep up with the action and not miss any information. The Bundesliga is the favourite child of the Germans and such a great World Cup performance as the one in South Africa in 2010 combined with such an incredible start to the season has poured plenty of water on these enthusiasm mills. For every journalist, such a course of events should be a feast for the eyes, the media should be grateful.
But a question that is perhaps the most exciting of all, that is even discussed in polls, that is hotly debated (and coldly doused) at thousands of counters every day, that naturally changes week by week as results occur, has a crucial but fixable flaw in its discussion. The question first is:
Who will be German champion?
The flaw is that there should always be only one answer to this. Every expert or wannabe can give his or her tip on the matter, can give his or her more or less detailed and well-founded opinion on the matter, but it is always limited to the one answer that one has to settle on. Of course, experience teaches that, with the exception of the open championship decision of 1922, there has in fact always been exactly one champion, but there would still be doubts about the ultimate single winner at any point in time.
These doubts find a mathematical consideration, so to speak, as soon as one begins to seriously consider the chances of the individual teams. The question “Who will be German champion?” would in itself have to be replaced by the much less prophetic, but nonetheless precisely for that reason realistic, “Who has how great a chance of winning the title of German champion this season?”
Rephrased, albeit less strikingly: What are the probabilities for the chances participating in the competition? How big today, how big after the next matchday? A question that cries out for an answer.
An answer can be provided by a specially developed simulation programme. This would have a guaranteed fascination for readers/listeners/viewers, in all directions. The question to be considered would perhaps be that of the credibility, the reliability of the simulation. However, these doubts could also be gradually reduced if the calculated figures, which are changed by the results of the match day, are looked at each week anew.
To check the figures or as a further gimmick, it could be offered to compare the respective probabilities determined by the computer via simulation with the odds with which the teams are traded on the betting market.
As an example, here are the odds produced by the computer after 10 match days of the 2010/2011 season in a simulation with 1000 runs (which take less than 5 seconds):
Dortmund 571 57.10% 1.75
Bayern 154 15.40% 6.49
FSV Mainz 05 83 8.30% 12.05
Leverkusen 74 7.40% 13.51
TSG Hoffenheim 45 4.50% 22.22
Werder Bremen 30 3.00% 33.33
VfL Wolfsburg 21 2.10% 47.62
Hamburger SV 20 2.00% 50.00
Frankfurt 1 0.10% 1000.00
- FC Nuremberg 1 0.10% 1000.00
1000 100.00%
In the first column the number of championships in the 1000 attempts, in the next this is expressed as a percentage, in the last the market odds, which are the reciprocal of the probability. Logically, a very rare occurrence like the championship titles of Nuremberg and Frankfurt, which managed it once each, is only “slips”. You cannot get a realistic estimate of the chances by giving 1/1000. You would need a lot more simulations for that. At the same time, other teams not listed here could also have a chance, perhaps even a higher one.
So for the computer, Dortmund are quite clear favourites. After all, they are 57.1% likely to become champions. For the Bavarians, however, the gap is so large, despite their higher quality (also recognised by the computer), that they still have the second-biggest chance, but with only 15.4%, they are quite clearly behind Dortmund.
Note: The simulation is based on very realistic parameters and a flawless algorithm, which could be explained for verification or confirmation.
The comparison with the betting market showed the following prices traded on the betting exchange betfair (www.betfair.com) today:
Dortmund 407 40.65% 2.46
Bayern 317 31.75% 3.15
FSV Mainz 05 63 6.25% 16
Leverkusen 100 10.00% 10
TSG Hoffenheim 38 3.85% 26
Werder Bremen 15 1.54% 65
VfL Wolfsburg 20 2.00% 50
Hamburger SV 51 5.13% 19.5
Frankfurt 6 0.59% 170
- FC Nuremberg 2 0.17% 600
1019 101.91%
Note: The numbers traded on the betting market are in the last column. These were entered first and the probabilities and the theoretically underlying number of title wins with 1000 times were calculated from them in order to make the values comparable with the computer figures.
Obviously, the market estimates Bayern Munich’s chances higher than the computer. Of course, often a single result is responsible for such an assessment, it does not have to be “mass intelligence”. Bayern scored 4 goals against Freiburg on Friday, having previously scored only 8 goals in 8 games, so, perhaps an intuitive assessment, they are now “getting rolling”. In addition, one speculates perhaps on a long second half of the season (also intuitive) and takes the return of Robben and Ribery into one’s emotional calculations. Well, respect must be shown to them in any case, just as intuitively, but a computer simply doesn’t care.
This is probably the main discrepancy between the computer and the betting market. Bayern’s higher ranking is completely to Dortmund’s detriment, while there are only minor deviations for the other teams.
A bet recommended by the computer would now be to bet Borussia Dortmund to win the title.
How are these numbers likely to develop after the next matchday? How does the computer react, how does the betting market react?
Such assessments could be presented in weekly form, so that the development of the numbers is added as an additional element of suspense compared to a one-time view.
