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Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments and found the proposed models to be applicable rather universally. In particular, here we compare men's and women's leagues and the separate German leagues during the cold war times and find some remarkable differences.

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A simple electronic instrument is described which displays the signal to be measured in the form of a Lissajous' figure display on an oscilloscope screen. The signal appears on the screen in the form of two identical figures, together with a zero-signal horizontal line. Using two potentiometer controls it is arranged that the top of one figure and the bottom of the other are brought simultaneously to coincide with the zero line, and the peak-to-peak amplitude is then available as a DC analogue output. The technique is rapid, accurate, and has the advantage of a null method that the linearity of the electronic circuits and the signal display does not influence the measurement.