title: Reply to Braun and Schmidt.
abstract: We welcome and appreciate the comment by Braun and Schmidt on our recent correspondence about the gambler's fallacy in goalkeeper behaviour during penalty shoot-outs. Braun and Schmidt assert that the binomial is more appropriate for analysing the data than our resampling approach. Their analyses appear to assume that dive direction is binomially distributed with a probability of 0.5. In fact, there are several biases in goalkeeper behaviour. First, we showed that kickers have a slight bias to kick to the goalkeeper's right, and that goalkeepers also have a slight bias to dive rightwards. This bias did not cross the conventional significance threshold in our data, but it still cannot be ignored when modelling sequences of actions. Repeated independent sampling from any distribution produces a sequential pattern that depends on the bias. The binomial distribution used to test hypotheses about sequential dependence should, therefore, have the same biases as the actual sample.
authors.affiliation: University College London, Institute of Cognitive Neuroscience, 17 Queen Square, London, WC1N 3AR, UK. Electronic address: e.misirlisoy.11@ucl.ac.uk.
authors.forename: Erman
authors.initials: E
authors.lastname: Misirlisoy
authors.affiliation: University College London, Institute of Cognitive Neuroscience, 17 Queen Square, London, WC1N 3AR, UK. Electronic address: p.haggard@ucl.ac.uk.
authors.forename: Patrick
authors.initials: P
authors.lastname: Haggard
mesh_terms: D054874:Athletic Performance; D003071:Cognition; D003163:Competitive Behavior; D011597:Psychomotor Performance; D012916:Soccer