Preliminary statistical analysis of. the international eventing. results 2013

Transcription

1 Lausanne 28/1/14 Preliminary statistical analysis of the international eventing results 2013

2 Overview of the talk Statistical analysis The data The statistical technique Analysis of the falls data (related to a fence) Analysis of results data Fall statistics: Belgian situation

3 The major steps in a statistical analysis Define the interesting questions and factors, that might affect risk Query the FEI database and compose file with data Encode data for statistical analysis Perform the analysis Interpretation of the results

4 1. The questions addressed in this analysis What are the factors that on their own and as a combination are correlated with good results, Refusals, EL, Horse Fall, Unseated Rider? Age of horse and rider, barely qualified, previous results, competing at international level since when, average number of successful / unsuccessful competitions per year at that level, number of competition as a combination, Are there parameters that significantly alter the probability of a fall? Homework: questions from the audience during the seminar

5 2. The data file Excel file with data on each international starter rows and 650 columns Profile of rider: age # different horses # starts 1*, 2*, 3*, 4* # MER 1*, 2*, 3*, 4* Profile horse: age # different horses # starts 1*, 2*, 3*, 4* # MER 1*, 2*, 3*, 4* Profile of competition CCI or CIC Star-level SJ before XC Speed Distance Result Dressage: pen XC: pen, EL (R, Fall) RET,WD SJ: pen, EL, RET,WD Identifications, Date, Officials, Profile of fall 38 columns 944 rows Multidimensional highly correlated dataset PCA, FA Low dimensional uncorrelated dataset File: but focus on 2013

6 The principal component analysis = Data reduction due to correlations Bumpus data set : measures of birds PC1 97% of variation in data is along PC1 Reduction of 2-dim data point (body length, length of wings) To 1-dim data point= Projection on PC1 Only 3% loss of variation! Noise! Birds with a large body length do have a large length of wings + negation.

7 Competition profile as illustration of PCA- technique Component Matrix a Component Starlevel CCIorCIC SJbeforXC Course length Speed Competition number of starters 1 2 3,834 -,802,667,890,803,994

8 Component Matrix a Component Starlevel CCIorCIC SJbeforXC Course length Speed Competition number of starters 1 2 3,834 -,802,667,890,803,994

9 Fall Analysis

10 Fall characteristics FALSE TRUE valid %FALSE %TRUE Combination ,4 0,6 Fence Type Option ,0 0,0 Frangible ,9 0,1 Portable ,4 45,6 Related to water ,3 21,7 Terrain ,0 57,0 Ground Line ,2 75,8 Off a Bend ,1 32,9 Air Jacket worn ,7 63,3 Air Jacket activated ,0 46,0 Frangible break 7 Horse fell or tread on Rider ,3 4,7 Accident Type ,2 30,8 Horse slipped? ,0 Wind ,3 12,7 Poor Visibility ,9 0,1 Horse refused? Horse hit Fence? ,0 51,0 Horse tipped portable? 5 Horse broke fence? ,5 3,5 Horse somersaulted? ,3 4,7 Inexperience ,1 41,9 Rider fatigue ,6 0,4 Horse out of control ,7 3,3 Horse too fast Horse too slow ,9 7,1 Light situation ,9 4,1 Horse impaired by health ,8 0,2 Horse fatigued ,7 2,3 Horse distracted ,7 1,3

11 Five possible classes of falls related to a fence Component Fall Fence Combination Fall Fence Portable Fall Fence Related to water Fall Fence Ground line ,663,461,681 Fall Fence Off a bend Did horse fall on or tread on athlete,418,397 Did the horse slip Wind,437 Did horse refuse Did horse hit the fence Did horse break the fence Did horse somersault Inexperience Athlete impaired by fatigue -,697,704,476,419,407 Horse out of control Horse too fast Horse too slow Horse fatigued Horse distracted,685,730,631,519,544 NB: 82 falls not related to fence are not included in this analysis

12 Falls and type of fences In total 817 falls related to fences C. square spread E. brush F. round No normalization by the number of times the type of fence is jumped!

13 Unseated Riders: 599 (73%) Horse Falls: 218 (27%) Significant difference between the distribution of Unseated riders and horse falls (chi-square p=0.017)

14 Distribution Unseated riders and horse falls over the fence types Relative more Horse Falls than Unseated Riders on type C Relative more Unseated Riders than Horse Falls on type G (corner) and J(step)

15 Number of fence where the fall occurs Total number of fences No significant tendency Fatigue of horse/rider

16 Falls and star-level Significantly higher relative number of Unseated Riders in the 1* level To do: Normalization with the number of starters per star level

17 Falls and ground conditions

18

19 Results Analysis

20 Rider profile 79% variation explained with 3 PC s Did Finish YES or NO Athlete age at time of competition Component atstarts104to12,654 Athlete number of starts 1* 2013 atstarts204to12 Athlete number of starts 2* 2013 atstarts304to12 Athlete number of starts 3* 2013 atstarts404to12 Athlete number of starts 4* 2013 atnumhor0412,765,726,798,616,613,922,877,631,629 Athlete number of different horses ridden 2013,604 atmer10412 Athlete MER 1* 2013 atmer20412 Athlete MER 2* 2013 atmer30412 Athlete MER 3* 2013 atmer40412 Athlete MER 4* 2013,786,928,625,634,693,809,618,601,927,880,903 PC1: 3* and 4* PC2: 2*, 3* and a lot of horses PC3: 1* NB: success rate, code 1-7, correlated with finish

21 Horse profile Horse profile Did Finish YES or NO Only 55% variation explained with 3 PC s Component Horse age at time of competition hostart10412 Horse number of starts 1* 2013 hostart20412 Horse number of starts 2* 2013 hostart30412 Horse number of starts 3* 2013 hostart40412 Horse number of starts 4* 2013 homer10412 Horse MER 1* 2013 homer20412 Horse MER 2* 2013 homer30412 Horse MER 3* 2013 homer40412 Horse MER 4* ,850 -,757,758,522,798,592,827,884 -,611,714,557,821,565,720 PC1: old 1* and 2* PC2: old 3*, 4* PC3: new 2*, 3* and no 1* Neg. correlated with finish

22 Preliminary summary ResultCode PC1rider PC2rider PC3rider PC1horse PC2horse PC3horse XC-clear Mean SE XC-20pen Mean SE No experienced 1 and 2* horses XC-40pen Mean SE XC-60pen Mean SE No 2 and 3* rider, Not many horses No experienced 1 and 2* horses XC-EL-R Mean SE No 2 and 3* rider, Not many horses No experienced 1 and 2* horses XC-EL-FR Mean SE No 1, 2 and 3* rider, Not many horses XC-EL-FH Mean SE XC-RET Mean SE XC-WD Mean SE No 1* rider Horse start in 2 and 3* 2and 3* rider with one horse Horse start in 2 and 3* Total Mean SE

23 Dressage score Result code, Starlevel Total Std. ResultCode N Mean Deviation XC-clear XC-20pen XC-40pen XC-60pen XC-EL-R XC-EL-FR XC-EL-FH XC-EL-OT XC-RET XC-WD Total * 2* 3* ANOVA: the ResultCode has an influence; no difference for different Star-levels

24 SJ score Result Code, Starlevel ResultCode N Mean Std. Deviation XC-clear XC-20pen XC-40pen XC-60pen XC-EL-R XC-EL-FR XC-EL-FH XC-EL-OT XC-RET XC-WD Total Source Type III Sum of Squares df Mean Square F Sig. Corrected Model a Intercept ResultCode Starlevel ResultCode * Starlevel Error Total Corrected Total ANOVA: the ResultCode has an influence; no difference for different Star-levels

25 Age of Rider, Horse Result Code, Star-level Mean Starlevel Horse age at time of competition Athlete age at time of competition 1 9,67 28, ,37 31, ,64 34, ,62 36,52 Total 10,27 30,44 Mean ResultCode Horse age at time of competition Athlete age at time of competition XC-clear 10,19 30,48 XC-20pen 10,24 29,84 XC-40pen 10,36 29,92 XC-60pen 10,03 28,41 XC-EL-R 10,39 29,03 XC-EL-FR 10,60 29,33 XC-EL-FH 10,49 29,91 Age of horse and age of the athlete are significantly different in the different starlevels XC-EL-OT 10,64 33,04 XC-RET 10,66 32,15 XC-WD 10,62 32,91 Total 10,27 30,44 The mean age of the athletes is significantly In the different results classes; not the age of the horse.

26 Acknowledgements FEI-eventing department: Giuseppe, Catrin, Nathalie FEI-IT department: Jérôme Begey and Gaspard Dufour