Another way to approach the linear combination is to look at it geometrically. This is where the idea of barycentric coordinates can help. A barycentric coordinate system describes the location of a point as the weighted sum of the regular coordinates of the vertices forming a simplex. In other words, it describes a linear combination with respect to a set of points, where in -dimensional space.
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Let’s start with the small print. We asked 51 judges to select their top 50 men’s Ashes cricketers, from which we calculated a top 100: 50 points for No 1, 49 for No 2 and so on. The voting rules were simple. Players were assessed solely on their performances in Ashes cricket, though judges could interpret that any way they liked. (Yep, someone did vote for Gary Pratt.) The judges had to pick at least 15 players from each country and a minimum of five from each of five different eras: players who made their debut before the first world war; in the interwar years; from the second world war to 1974; from 1975 till 1999; and from 2000 onwards.
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