4 96 CHAPTER 4 5. DISCUSSION We provided a roadmap as an approach for causal inference. The roadmap was applied to perform causal inference and examine on the one hand, the performance of TMLE, and on the other hand the accuracy in estimating the effect size between the traditional method GLM and the novel method TMLE. The comparison between GLM and TMLE was made by performing a simulation study on the effect of substitution on the total physical performance of a soccer team. We showed that GLM yields biased estimates of the effect size, whereas TMLE provides more accurate effect size estimations. These findings are consistent with earlier research [2], [11], [34]. Furthermore, we applied the causal roadmap using GLM and TMLE on observed elite soccer data. Our results indicate that a substitution in elite soccer increases the total team performance with 0.0105 to 0.01485 of the total distance covered. Other studies on performance, substitutes, and soccer also show that the performance of a substitute is higher when compared to an entire-match player [3], [4], [16] and that physical performance relates to overall game performance [14]. However, these studies leave out the influence of the substitutions and individual performance on the team performance. The causal roadmap provides a guide for causal inference. It helps to design statistical analyses, answering the causal question while making clear what assumptions are required to provide results with a causal interpretation[35]. Causal inference relates to statistical inference. Where causal inference means reasoning about causation, statistical inference means association reasoning with statistics. Statistical inference aims to assess parameters of a distribution from samples drawn from that distribution [27]. With the parameters, associations among variables and probabilities of future events can be inferred [27]. The associations and probabilities can be updated when new evidence or new data is available [27]. Causal inference aims to go one step further; the aim is to infer probabilities under static conditions and the dynamics of probabilities under changing conditions, for example, a substitution [27]. That is not to say that statistical inference cannot be used to establish causal relationships. Scientific explanations are an example of applying statistical inference, using, for instance, the DeductiveNomological Model of Hempel and Oppenheim [36] applying laws to model statistical relevance designed to establish scientific explanations. Scientific explanations are causal explanations establishing a delicate relationship between statistical inference and causal inference. However, causal inference implies the dynamics of changing conditions where statistical inference does not. The combination of the causal roadmap and TMLE offers an opportunity to study the influence of a changing condition. One limitation of the current study is our application of the causal roadmap. In the first step of this roadmap, it is important to state the knowledge one has about the
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