Charlton's Problems: A Mathematical Solution
Name of Student: Mr A Curbishley
Dissertation Topic: How to maximise Charlton Athletic's points tally
Alan has had a difficult year and has struggled with various new concepts. At the start of the year, he sat down with Professor Murray and agreed his maths-related dissertation for 2005, "How to maximise Charlton Athletic's points tally." Prof. Murray felt that this was an appropriate project given how much progress Alan has made in recent semesters, and is a natural progression from his prior 1995 accountancy project named, "Balance the books" and his 2000/2001 science project, "What goes up musn't go straight down."
In his two former projects, Alan discussed important concepts including, "Solid defence", "Get value for money in the transfer market," and "Conservative tactics and team selection." Thanks to Alan's suggestions, the team since they returned to the Premiership in 2000 have won 71, drawn 53 and lost 82 of their 206 games, yielding 266 points at an average of 1.29 per game. Expressed as probabilities, Charlton enter each game on average with a 0.345 win probability, 0.257 draw probability and 0.398 loss probability. In terms of goals, Charlton have scored 247 goals and conceded 297 goals during these 206 games, at an average rate of 1.199 and 1.442 respectively.
Given that over the course of 206 games, Alan has proved that the team's tactics will deliver on average 49.1 points over the course of a 38 game season, Prof. Murray was surprised that he did not feel this gave the team a suitable buffer from which to launch more attacking tactics. Alan has expressed his interest in continuing his studies, perhaps at a European school of learning, but he will need to adapt in order to progress in this way. It is perhaps not surprising that other students such as Mr Alladyce and Mr Jol have nicknamed Alan, "the worrier."
Indeed, Alan's continual concern about 'reaching 40 points' (which he uses as a basis for his conservative tactics) is not backed by empirical evidence since 'safety' in the prior five seasons was 35, 37, 43, 34 and 34 points respectively (average: 36.6). Infact Alan's alma mater West Ham United are the only club to be relegated with more than 37 points since 2000.
Hence Prof. Murray's main criticism of Alan's work concerns his unwillingness to consider the possibility that more attacking tactics which increase the number of matches the team wins, even if at the expense of some draws, might actually maximise Charlton's points total. For example, if Alan was willing to contemplate 2 strikers, backed up by 2 true 'wingers' then he may find that we win more games, lose more games but draw less. It is feasible that these tactics may result in new probabilities of 0.45 for a win, 0.1 for a draw and 0.45 for a loss.
However Prof. Murray then used complex equations to produce an interesting result which surprised Alan. The new probabilities actually increased the total expected points from 49.1 to 55.1. This points total would have seen Charlton finish 8th, 7th, 8th, 7th and 7th respectively over the past five seasons, enough to see Alan fulfil his European dream in 2004/05 at least.
Alan admitted to feeling a little faint upon hearing Prof. Murray's outstanding analysis, and began to provide aggressive counter-arguments. "My cautious approach provides plenty of hard-fought wins and draws. What if a more cavalier approach sees these matches lost, even if some other current draws or defeats turn into victories?" Again Prof. Murray had an answer ready. "Alan," he explained, puffing hard on his cigar, "...given that all matches begin tied, then any attacking tactic is rational provided the increase in the probability of a win is at least half of the increased probability of a loss." This 'leverage' is thanks to 3 points for a win, introduced in 1982, which favours an attacking side. Prof. Murray was not sure if Alan was aware of the change.
Alan continued to be confused. "How am I supposed to keep the team motivated if they are coming off the pitch 17 times a season on the losing side? I often tell them before games that we should be 'happy with a point'." Prof. Murray had the final word, "Alan, just show them the League table."