Here’s some heady stuff from Neil S to offer insights and pose a few questions on the Challenge scores.
I am sure there are some people out there who have looked at these scores and raised the odd eyebrow. I for one think there is a good opportunity here to statistically test the effectiveness of the handicap system. As you probably know, it is possible to assess the probability that a range of numbers would be normally distributed in a random sample of numbers if you know the mean, the standard deviation and “x”. (In this case the Stableford points you would get if you played to 3/4 of your handicap every time).
So I have attempted to do this with some simple statistics (using excel) and this I think poses the question.
What is the probability that these scores constitute a normal distribution for each player based on their individual handicap. I think this then enables us to provide some interesting analysis.
Look at the column at the top of which you will see PROB, meaning probability. You will see that if the workings are correct
- the least likely set of scores belong to Trevor – it is 39% likely that this sample of scores constitutes a normal distribution.
- for Martyn it is 54% likely that these scores constitute a normal distribution
- for Peter Gillies it is 44% likely that these scores constitute a normal distribution.
The inverse is also possibly true. Therefore that it is 61% likely that Trevor’s scores are not normal for his handicap, then and 46% and 56% respectively.
You will notice that in some cases the probability that the range of scores constitutes a normal distribution (which means that 99% fall within 3 standard deviations) is very high. 87% for Tony H and Mike S and 83% for Arthur. This does not suggest that their handicaps are too low. I think it simply suggests that the level of variation and its frequency is normal, whereas with the lower probabilities it is less likely.
Obviously this does not take account of other factors which may interfere with qualifying rounds, such as white tees or indeed nerves or personal choice or indeed that they were just playing well over a protracted period of time – but that after all is what the handicap system is for.
I have guessed the handicaps and this is based on three quarters of handicap being applied. If you or someone knows the correct ones then I can apply these too.
Of course we all know that Martyn is only recently back at the club and he is coming down any way, which just begs the question, what of the other two?
Of course this is intended only to be light hearted and I would welcome any comments what so ever on the methodology or conclusions, but this might at least get a laugh or get Gillies some stick.
|ave||Hcap||3 qtrs||Std dev||Pts||PROB|