Average Handicap Game Durations
By Ian Plummer
This paper reports a disappointing attempt at trying to find a correlation between players' handicaps and game duration for handicap play. The only conclusion which can be inferred is that good players generally play faster. The data shows that 48% of the handicap games were won by the lower handicap player. This is close to 50% expected for a correctly functioning Automatic Handicapping System.
There were two aims to this study; to provide a rule-of-thumb guide to managers as to how long a game might be expected to take between various handicap players (although local conditions would affect this greatly). Secondly to see if there were any anomalies in the timings which would indicate new information.
Data from 379 games from five Easter handicap events held at the Surbiton Croquet Club was collected and kindly supplied by Samir Patel. It details the handicaps of the players and the result with a 'game scheduled time' and 'result recorded time'. These timings are at best inaccurate but are all that were available. Generally they will be greater than the duration of the games since the results were entered into the manager's laptop when he was not in-play. Conversely not all games will start as soon as they are scheduled. Additionally it is impossible to determine if, and how long, a lunch break was taken.
The following corrections were automatically applied to the data:
The data was plotted with the X-axis being the winner's handicap and the Y-axis being the loser's. The value in the cell at their intersection is the average of the times of games satisfying those conditions.
There is a general trend along the diagonal from the origin for games to take longer. This reflects the duration of games between players of the same handicap; low handicap (better) players play faster than high ones.
Games lying in the left hand half of the table generally take less time than those in the right which can be taken as games where the lower handicap player wins are faster than where the high handicap wins.
The data is very sparse. There are 676 cells (26 x 26) lying between [-2 .. 20] on each axis, but with only 379 items of data. Within the data, there is one handicap combination which occurs 5 times; five combinations which separately occur 4 times; 21 combinations which occur 3 times. Not a great deal of averaging is taking place.
The ideal data set would comprise of many games taking place at the same venue during the same period so that the conditions, e.g. hoop width & rigidity and lawn characteristics, were essentially similar. If the handicap range was reduced, such as in class events, then better averaging would be possible.
The conclusion that low handicap players play faster on average is no surprise; they generally know what is going on and have 'seen it before' which eliminates thinking time. They are also more efficient in getting their balls through hoops.
The local conditions would be expected to skew the conclusions. On very difficult courts, e.g. 13 Plummers or more or less than 8 Plummers, lower handicap players would be expected to triumph due to their greater skill and adaptability. Difficult conditions would result in slower play however.
The data shows that in 175 / 363 (48.2%) of these handicap games the lower handicap player won. This shows that the handicap system is working well. In the ideal it would be 50%. (Note 16 games were between people of the same handicap hence 363 = 379 - 16).
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