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Applied Analytics and Data Visualisation Assessment

Thomas Hosty Cundell (77338687)

MSc Sport Performance Analysis

Applied Analytics and Data Visualisation

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Tools and Data

Data analysed was that provided for the assessment for Rugby League
Graphs and diagrams were predominantly built using R Studio with the use of ggplot, dplyr, sjplot and caret libraries.
Path diagram was built in lucidchart

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Castleford Tigers Statistical Season Review

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Path Analysis to Success

With path analysis we can test each relationship, and assess how appropriate a predictive model is and further explore new pathways (Novak, A. R. et al., 2021)

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Attacking Metrics

�Game.Number	Total_PTBs	Carries	Quick_PTBs	Metres	Carries_into_Contact	Tackle_Breaks	Line_Break	Line_Break_Assist
Try	Quality_Kicks	Poor_Kicks	Defensive_Efforts	Defensive_Errors	Points_For	Points_Against	Points_Difference	Opponent_Image
Try_Assist	Forced_Errors	Try_Savers	System_Errors	Breaks_Conceded	Tries_Conceded	Penalties_Conceded	Six_Again_.Conceded	Kicks
Positive_Offload	Linespeed_Efforts	Marker_Efforts	Kick_Pressures	Kick_Chases	Missed_Linespeed	Missed_Kick_Pressure	Ineffective_Marker	X3rd_Man_Retreats
Skill_Execution_Errors	Quality_Supports	Missed_Supports	Tackles	Missed_Tackles	Ineffective_Tackles	PTB_Wins	PTB_Losses	PTB_Non_tackles

�Game.Number	Total_PTBs	Carries	Quick_PTBs	Metres	Carries_into_Contact	Tackle_Breaks	Line_Break	Line_Break_Assist
Try	Quality_Kicks	Poor_Kicks	Defensive_Efforts	Defensive_Errors	Points_For	Points_Against	Points_Difference	Opponent_Image
Try_Assist	Forced_Errors	Try_Savers	System_Errors	Breaks_Conceded	Tries_Conceded	Penalties_Conceded	Six_Again_.Conceded	Kicks
Positive_Offload	Linespeed_Efforts	Marker_Efforts	Kick_Pressures	Kick_Chases	Missed_Linespeed	Missed_Kick_Pressure	Ineffective_Marker	X3rd_Man_Retreats
Skill_Execution_Errors	Quality_Supports	Missed_Supports	Tackles	Missed_Tackles	Ineffective_Tackles	PTB_Wins	PTB_Losses	PTB_Non_tackles

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Correlation Analysis

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Cross Validation

Test Data

Line Breaks	Points For
7	28
3	10
2	18
3	6
1	6
1	13
4	15
3	12
11	60
10	38
11	48
3	22
6	18
4	18
7	38
6	22
5	26
7	18
10	46
4	18
3	14
4	13
5	25
3	6
8	36
1	8
2	8

Training Data

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Points For v Line Breaks

1 Line Break ≅ 4.25 pts

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Path Analysis to Success

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Path Analysis to Success

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Back to the Correlation Analysis

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Multicollinearity

The presence of a relationship between independent variables (Gomez, R. et al., 2022) or our predictors.

We can run a diagnostic that can detect variables where multicollinearity is detected and then remove them from our model as other variables in the data-set may account for and better explain their variance (Parmar, N., et al., 2017)

The result of this multicollinearity diagnostic is a value called Variance Inflation Factor (VIF), if a variables VIF value is > 5 it is tolerable and if it is > 10 it is bad and should be discounted. Ideally, we want our variables to have a VIF value between 1 and 5.

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Variance Inflation Factors

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Principal Components

Creating a value/new variable that encompasses different variables/predictors therefore reducing the dimensionality of data and therefore enhances 2-D visualisation for easier interpretation of the data (McCormack, S et al., 2021).

When compilating principal components we produce a component per the amount of variables we input. I.e. we have 5 variables (Line Break Assist, Poor Kicks, Positive Offloads, Quality Supports and Tackle Breaks) so we will get 5 different PCs.

Each PC captures a certain amount of variance of data, and we can investigate how much of each variable is captured within a PC.

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Principal Component Analysis

PC	Percentage Variance
1	45.907429
2	18.078482
3	16.412684
4	11.833012
5	7.768393

= 80.4

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Cross validation results of new model

RMSE: 1.73
Rsquared: 0.8602261, 86% of the variation

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Model Predictions v Actual

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Model Predictions v Actual

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Model Predictions v Actual

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Principal Component Analysis

	PC1	PC2	PC3
Line_Break_Assist	-0.3726419	0.112721125	-0.87241869
Positive_Offload	-0.2858663	0.900121356	0.28943013
Quality_Supports	-0.5166228	-0.348283030	0.29817146
Tackle_Breaks	-0.5011170	-0.236157239	0.24761989
Poor_Kicks	0.5112740	0.002045057	0.06995711

	PC1	PC2	PC3
Line_Break_Assist	-0.3726419	0.112721125	-0.87241869
Positive_Offload	-0.2858663	0.900121356	0.28943013
Quality_Supports	-0.5166228	-0.348283030	0.29817146
Tackle_Breaks	-0.5011170	-0.236157239	0.24761989
Poor_Kicks	0.5112740	0.002045057	0.06995711

Each PC captures a certain amount of variance of data, and we can investigate how much of each variable is captured within a PC by observing the eigenvectors.

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Tackle Breaks

Red ribbon – mean +/- swc which is 0.2 of a standard deviation, meaning we can only be confident if performance falls outside of that, that it’s an over or under performance��The error bars on each data point, is the confidence interval +/- which is then range in which if everything was to be sampled again for tackle breaks, 95% of the values recorded would fall in that range��-Not 100% ideal that those ranges exceed the average ribbon across the middle as when a value falls inside the ribbon we still can’t be confident that the metric gathered is accurate to be an average performance��Ideally these averages and metrics would be collated using the other 11 teams season data too, this way we could see how we’re performing not just against ourselves but against the league and really see where we need to improve on.

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Quality Supports

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Poor Kicks

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KPI Conclusions

Improve volume of Quality Supports/Improve overall quality of Support play (S&C work to maintain fitness towards end of season to allow high energy levels to keep up support play)
Increase Tackle Breaks
Work on Kicking game to cut out Poor Kicks (End of season focus)

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Reference List

Gomez, R. M., Garcia, C. B. G., Sanchez, A. R., and Garcia, C. G. (2022) Limitations in Detecting Multicollinearity due to Scaling Issues in the mcvis Package. R Journal, 14 (4) December, pp. 264-279.

Novak, A. R., Impellizzeri, F. M., Garveyb, C., and Fransen, J. (2021) Implementation of path analysis and piecewise structural equation modelling to improve the interpretation of key performance indicators in team sports: An example in professional rugby union. JOURNAL OF SPORTS SCIENCES. [Online]. 39 (22), pp. 2509-2516. Available from: <https://doi.org/10.1080/02640414.2021.1943169> [Accessed 1 May 2023].

McCormack, S., Jones, B., Scantlebury, S., Collins, N., Owen, C., and Till, K. (2021) Using Principal Component Analysis to Compare the Physical Qualities Between Academy and International Youth Rugby League Players. International Journal of Sports Physiology and Performance. pp. 1-8. ISSN 1555-0265 Available from: <https://doi.org/10.1123/ijspp.2021-0049> [Accessed 4 May 2023].

Parmar, N., James, N., Hughes, M., Jones, H. and Hearne, G. (2017) Team performance indicators that predict match outcome and points difference in professional rugby league. International Journal of Performance Analysis in Sport. [Online]. 12 (6), pp. 1044-1056. Available from: <https://doi.org/10.1080/24748668.2017.1419409> [Accessed 4 May 2023].