EC, the point of my post is that Kauto has a dramatically higher rate of mistakes at Cheltenham than anywhere else.
By making it into left vs right, there isn't enough data to support with confidence the suggestion that he's better going right-handed. He may have a higher rate of mistakes going right-handed at the moment but he hasn't yet jumped enough fences both ways for us to be sure that that isn't a product of random chance.
Here's Kauto's stats broken down by course, along with:
- the number of fences he's actually attempted to jump
- the number of mistakes he's made (defined as anything marked as a fall, unseated rider, 'hit', 'blunder', 'mistake' or 'not fluent' within the race comments)
- the average number of mistakes per fence attempted, expressed as a decimal
- a margin of error for each average, given a 95% confidence level
- the range of values that his 'true' rate of mistakes is between, given the margin of error
[code]
[b]Course Fences Mistakes Average MoE Range[/b]
Kempton 54 3 0.0556 0.0611 [0,0.1167]
Aintree 51 2 0.0392 0.0533 [0,0.0925]
Haydock 48 5 0.1042 0.0864 [0.0177,0.1906]
Cheltenham 47 9 0.1915 0.1125 [0.0790,0.3040]
Newbury 33 1 0.0303 0.0585 [0,0.0888]
Sandown 26 1 0.0385 0.0739 [0,0.1124]
Exeter 24 2 0.0833 0.1106 [0,0.1939]
Ascot 17 0 0 0 [0,0]
Down Royal 15 0 0 0 [0,0]
[/code]
As you can see, although Cheltenham jumps off the list (19% rate of mistakes), when you factor in the margin of error you can only say the following (given the 95% level of confidence we chose):
He's better at Ascot than at Haydock or Cheltenham
He's better at Down Royal than at Haydock or Cheltenham
Groundbreaking, eh?
In order to reduce the margin of error, we need to increase the sample size. One way is to group data together under a common heading. For example, left-handed vs right-handed:
[code]
[b]Direction Fences Mistakes Average MoE Range[/b]
Left 179 17 0.0950 0.0429 [0.0520,0.1379]
Right 136 6 0.0441 0.0345 [0.0096,0.0786]
[/code]
As you can see, the ranges still overlap. So we can not say with confidence that his higher mistake rate going left-handed is statistically significant - it may be a product of random chance.
However, if we compare Cheltenham to all of the other courses:
[code]
[b]Course Fences Mistakes Average MoE Range[/b]
Cheltenham 47 9 0.1915 0.1125 [0.0790,0.3040]
Elsewhere 268 14 0.0522 0.0266 [0.0256,0.0789]
[/code]
And there it is - the ranges don't overlap (just barely!) and so we can say with 95% confidence that Kauto's higher rate of mistakes at Cheltenham than everywhere else is not simply down to chance.
(Edited massively for introduction of margin of error, better analysis, and less extraneous crap...).
