How do psychological and physiological performance determinants interact within individual athletes? An analytical network approach

Figures & data

Table 1. Data collection.

Time of the day	Measured factor	Self-report question	Measurement scale	References
T1: In the morning up to 30 minutes before the first training session or match	Recovery	How good is your recovery?	CRS from 6 (very, very poor recovery) to 20 (very, very good recovery)	(e.g., Brink et al., 2010; Kenttä & Hassmén, 1998)
	Self-efficacy	How confident are you that you can perform maximally today?	VAS from 0 (not at all confident) to 100 (very confident)	(e.g., Bandura, 2006; Moritz et al., 2000)
	Motivation	How motivated are you to perform maximally today?	VAS from 0 (not at all motivated) to 100 (maximally motivated)	(e.g., Barte et al., 2019; Blanchard et al., 2007)
	Mood	How much are you in the mood to train/play the match today?	VAS from 0 (not at all in the mood) to 100 (very much in the mood)	(e.g., Cohen et al., 2006; Totterdell, 2000)
T2: During the training session or match	Distance		Meter	(e.g., Bourdon et al., 2017; Mara et al., 2015)
	Average speed		Km/h	(e.g., Akenhead & Nassis, 2016; Fortin-Guichard et al., 2022)
	Average heart rate		Beats per minute	(e.g., Akenhead & Nassis, 2016; e.g., Bourdon et al., 2017)
T3: At the end of the day up to 30 minutes after the last training session or the match	RPE	How hard was the training/match?	CRS from 6 (very, very light) to 20 (very, very hard)	(e.g., Borg, 1982; Brink et al., 2010)
	Perceived performance	How well did you perform today?	VAS from 0 (very bad (far below my capabilities)) to 100 (maximally (to the best of my capabilities))	(e.g., Cohen et al., 2006; Totterdell, 2000)
	Enjoyment	How much did you enjoy the training session(s)/the match today?	VAS from 0 (not at all) to 100 (very much)	(e.g., Puente-Díaz, 2012; Van Yperen et al., 2022)

Note. T = time point, CRS = Category-Ratio Scale, VAS = Virtual Analogue Scale, RPE = Rating of Perceived Exertion.

Figure 1. The time-varying autoregressive effect of motivation (left) and the cross-lagged effect of recovery (right) of Player 2.

Note: The solid line shows the strength of the effect over time, whereas the dashed lines correspond to the 95% Bayesian Credible Intervals (i.e., the uncertainty of the smooth function). The horizontal line serves as guidance for an effect of 0. t–1 represents the previous point in time and t the current point in time.

Figure 2. Network graph of Player 1.

Note. The network remained stable across the season (i.e., no changes in effects). The green/solid edges represent positive effects and the thickness reflects the absolute value of the parameter estimate, that is, the magnitude of the effect (thicker edges display stronger effects and thinner edges display weaker effects). The self-loops show the autoregressive effects and the direct edges represent cross-lagged effects. We used NodeXL (https://nodexl.com/) with the Furchterman-Reingold layout to visualise the graphs.

Figure 3. Network graph of Player 2.

Note. The network changed across the season. The green/solid edges represent positive effects, the red/dashed edges represent negative effects and the thickness reflects the absolute value of the parameter estimate, that is, the magnitude of the effect (thicker edges display stronger effects and thinner edges display weaker effects). The self-loops show the autoregressive effects and the direct edges represent cross-lagged effects. Changing effects (cf. Figure 1) are highlighted by a yellow/glowing shade around the edges. We used NodeXL (https://nodexl.com/) with the Furchterman-Reingold layout to visualise the graphs.

Table A1. BIC Scores of the Time-Invariant and Time-Varying Models of Player 1.

Model (GAM)	Time-invariant	Time-varying
Recovery	299	312
Self-efficacy	281	295
Motivation	341	365
Mood	309	330
Distance	272	314
Speed	285	326
Heart Rate	290	315
Load	329	356
Perceived Performance	325	347
Enjoyment	335	371

Note. The better model fit is marked in bold.

Table A2. BIC Scores of the Time-Invariant and Time-Varying Models of Player 2.

Model (GAM)	Time-invariant	Time-varying
Recovery	363	361
Self-efficacy	291	310
Motivation	285	276
Mood	364	386
Distance	362	394
Speed	369	407
Heart Rate	365	402
Load	370	396
Perceived Performance	358	367
Enjoyment	367	411

Note. The better model fit is marked in bold.

Table A3. Significant Time-Invariant Parameters of Player 1

Model (GAM)	Parameter	Estimate	Std. Error	t	p
Self-efficacy	Self-efficacy	0.271	0.118	2.307	.023
Motivation	Motivation	0.282	0.127	2.217	.029
Mood	Mood	0.281	0.112	2.501	.014
Distance	Self-efficacy	0.793	0.174	4.569	<.001
Speed	Self-efficacy	0.570	0.189	3.024	.003
Heart Rate	Self-efficacy	0.457	0.187	2.444	.016
Perceived Performance	Self-efficacy	0.451	0.157	2.879	.005
Enjoyment	Self-efficacy	0.453	0.151	2.991	.003

Table A4. Significant Time-Invariant Parameters of Player 2.

Model (GAM)	Parameter	Estimate	Std. Error	t	p
Self-efficacy	Self-efficacy	0.439	0.071	6.212	<.001
	Perceived Performance	0.505	0.099	5.100	<.001
Mood	Mood	0.269	0.090	3.007	.003
	Load	−0.310	0.113	−2.735	.007
	Perceived Performance	0.243	0.123	1.983	.049
Distance	Recovery	−0.270	0.130	−2.078	.040
	Mood	0.398	0.105	3.807	<.001
Speed	Recovery	−0.291	0.133	−2.181	.031
	Speed	0.229	0.085	2.698	.008
Load	Mood	0.246	0.107	2.290	.024
Perceived Performance	Self-efficacy	0.260	0.114	2.276	.025
	Perceived Performance	0.248	0.106	2.342	.021
Enjoyment	Self-efficacy	0.233	0.111	2.094	.038
	Mood	0.294	0.107	2.756	.007

Table A5. Significant Time-Varying Parameters of Player 2.

Model (GAM)	Parameter	edf	F	p
Recovery	Load	2.000	3.453	.0353
Motivation	Motivation	6.175	4.727	<.001

Note. edf = effective degrees of freedom.

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Data availability statement

The R code has been made publicly available at DataVerseNL and can be accessed at https://dataverse.nl/privateurl.xhtml?token = eaf92882-1755-42df-86f5-d430f45b9dad [https://dataverse.nl/dataset.xhtml?persistentId=doi:10.34894/HNA8QQ]. The data contains sensitive information about the subjects and is therefore restricted from openly sharing it. Requests can be made by researchers affiliated with universities or independent, non-commercial research institutes via the same repository.