ABSTRACT
Imagine the competitors at an athletic meet as they ready themselves to participate i n the high jump event for a state, national, or even international title. The winner, of course, w i l l be the person who clears the highest setting of the cross bar. However, the competition requires the athletes to face a series of progressively higher settings of the cross bar unt i l just the winner is left. This competit ion considers the difficulty of the jumps in terms of just one quantifiable empirical variable: the height of the bar above the ground. But that is a gross simplification; other variables (factors, facets, dimensions) invariably play a role: the competition surface; the air temperature; the prevailing w ind (direction and strength); the relative humidity, or rain; the lighting (brightness, natural or artificial); even, the support (or lack of it) from the audience. What about the ability of the athletes? We take more notice of their latest competition results, than of any other relevant but usually dismissed indicator: each athlete's health status, recent injuries, suppleness relative to that state i n other competitions, motivation, confidence, family or other personal circumstances, and so forth. Ignoring most of these influences on difficulty or ability while we try to predict which of the contestants is likely to succeed at each of the jumps in turn, we consider just two key influences for each jump attempt. For the indicator of the relative difficulty of each jump we use just the height of the bar; and for the ability of the athlete we refer only to the most recent results in competition. Interestingly, both the difficulty and the ability are expressed on the same scale: the meter scale of linear measure-ignoring all other likely influences.
