Generic temporal features of performance rankings in sports and games

EPJ Data Science

Table 2 Parameter values for fitting process between sports data and ranking models

	Model \(\boldsymbol{m_{1}}\)		Model \(\boldsymbol{m_{2}}\)			Model \(\boldsymbol{m_{3}}\)			Model \(\boldsymbol{m_{4}}\)				Model \(\boldsymbol{m_{5}}\)
	\(\boldsymbol {\log\mathcal{N}}\)	a	\(\boldsymbol{\log\mathcal{N}}\)	a	b	\(\boldsymbol{\log \mathcal{N}}\)	a	q	\(\boldsymbol{\log\mathcal{N}}\)	a	b	q	\(\boldsymbol{\log\mathcal{N}}\)	a	\(\boldsymbol{a'}\)	\(\boldsymbol{k_{c}}\)
ATP	4.51	1.04	4.11	0.626	3.18 ×10⁻³	−1.46	0.816	1.79	4.01	0.628	3.13 ×10⁻³	3.12 ×10⁻²	4.2	0.746	3.004	3.19 ×10²
FIDE	3.46	0.0252	3.46	2.01 ×10⁻²	6.25 ×10⁻⁶	3.32	2.21 ×10⁻²	3.28 ×10⁻²	3.46	0.0202	6.25 ×10⁻⁶	5.05 ×10⁻⁹	3.45	0.016	0.036	1.97 ×10²
OWGR	1.35	0.702	1.05	0.383	2.68 ×10⁻³	−0.928	0.53	0.703	1.023	0.385	2.65 ×10⁻³	1.18 ×10⁻²	1.09	0.452	1.73	2.03 ×10²
GPI	3.75	0.234	3.66	0.144	6.63 ×10⁻⁴	2.54	0.193	0.358	3.66	0.144	6.63 ×10⁻⁴	3.64 ×10⁻⁹	3.65	0.133	0.437	1.08 ×10²
FCWR	4.52	0.529	4.24	0.218	3.06 ×10⁻³	2.19	0.341	0.732	2.93	0.269	1.39 ×10⁻³	0.458	4.35	0.371	3.47	4.26 ×10²
FIFA	3.37	0.473	3.24	0.142	1.02 ×10⁻²	2..30	0.262	0.456	3.15	0.148	9.58 ×10⁻³	4.16 ×10⁻²	3.26	0.227	0.8622	33.86

Table listing parameter values for all models in Eqs. (1)-(3), obtained in the fitting process with empirical data. These values correspond to the model curves in Figure 1 (model \(m_{5}\) not shown there), but are representative of the entire datasets (see Table 3 for further details).