Improved training of football referees and the decline in home advantage post-WW2

ObjectivesResearch has identified a decline in home advantage (HA) in a number of professional leagues since World War 2 (WW2). The purpose of the current study was to identify whether the decline in HA in English and Scottish Professional Football Leagues is mirrored by the radical transformation in the training of referees post-WW2, thus providing a new insight into the cause of HA.DesignA longitudinal quasi-experimental design.MethodsHA was calculated for each team at the end of every season for the four English and the Scottish Premier League post-WW2. We also compiled a list of events, statements and quotations to illustrate the dramatic change in the way referees have been trained (physically and psychologically), and assessed over the same period.ResultsWe observed a systematic decline in HA in professional English and Scottish leagues post-WW2, but with the steepest decline observed in lower divisions with smaller crowds. Of the factors thought to influence HA, crowd support appears the most consistent with these observations. Crowds are known to influence referees' decisions to favour the home side. However we argue that improved training of referees since WW2 has contributed to an improved ability to make objective decisions and a greater resilience to crowd influence, which explains the decline in HA but also accounts for the steeper decline observed with smaller crowds.ConclusionsThe continued existence of HA, and the less steep decline observed in top leagues suggests that referees' judgements are still not immune to the influence of larger crowds.     

Patterns in the Philosophy of Mathematics

Books reviewed in this article:
Michael D. Resnik, Mathematics as a Science of Patterns
Penelope Maddy, Naturalism in Mathematics
Jerrold J. Katz, Realistic Rationalism
Jaakko Hintikka, The Principles of Mathematics Revisited     

The mean-integral representation of rectangles

To assess perceptual interaction between the height and width of rectangles, we used an accuracy variant of the Garner paradigm. We measured the discriminability of height and width (baseline tasks) and size and shape (correlated tasks). From thed′ values in these conditions, we estimated perceptual distances and inferred amean-integral representation in which height and width corresponded to nonindependent dimensions in a perceptual space. This model accounted well for performance in these two-stimulus conditions, and it also explained 70% –80% of the decline in performance in selective and divided attention. In a second experiment, conducted for purposes of comparison with the rectangle discrimination Experiment, we studied the discrimination of horizontal and vertical line segments connected in an L-shape. In size discrimination, observers were equally good with line pairs and rectangles, suggesting holistic perception; but in shape discrimination, they appeared to combine information from the two line-pair components of the rectangle independently. The mean-integral model was again successful in relating performance in the Garner tasks quantitatively.     

The effects of objectives and constraints on motor control strategy in reciprocal aiming movements

The goal of this study was to examine how the kinematics of reciprocal aiming movements were affected by both the objective of the movement and the constraints operating on that movement. In Experiment 1, the objective of the movement was indirectly manipulated by capitalizing on the fact that subjects determine their own accuracy and speed limits, despite uniform task instructions to move as quickly and accurately as possible. A Fitts' type reciprocal aiming paradigm was employed, in which 69 subjects were asked to move a stylus repetitively between two spatially separated targets. Four target widths were orthogonally combined with four movement amplitudes, resulting in 16 conditions. Movements were made on an X-Y digitizing tablet. Based on the mean variable error produced on both targets, subjects were differentiated post hoc into three movement objective groups: speed, accuracy, and speed-plus-accuracy. Kinematic analyses revealed that the programming and execution of movements were systematically influenced by both the movement objective and the movement constraints. That is, movement time, peak velocity, dwell time, acceleration and deceleration time, normalized acceleration and normalized deceleration varied systematically as a function of both the speed-accuracy movement objective and the movement constraints of target size and movement distance. Moreover, the consequences of changing the constraints of the movement were affected by an interaction with the objective of the movement. In Experiment 2, the objective of the movement was directly manipulated by varying speed and/or accuracy instructions to subjects. The basic results of Experiment 1 were substantiated. Overall, the results were consistent with the view that motor control is dependent upon sensory consequences.