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Table 3 Goodness of fit measures

From: Generic temporal features of performance rankings in sports and games

  

\(\boldsymbol{m_{1}}\)

\(\boldsymbol{m_{2}}\)

\(\boldsymbol{m_{3}}\)

\(\boldsymbol{m_{4}}\)

\(\boldsymbol{m_{5}}\)

ATP

\(\langle R^{2} \rangle\)

0.222

0.982

0.879

0.982

0.964

D

0.433

0.044

0.08

0.038

0.077

\(\sigma_{R^{2}}\)

0.0969

0.01652

0.009

0.0124

0.0288

\(\sigma_{D}\)

0.211

0.0126

0.0672

0.0128

0.0287

p

0.01

0.17

0.0

0.12

0.0

FIDE

\(\langle R^{2} \rangle\)

0.777

0.936

0.657

0.936

0.991

D

0.477

0.2

0.188

0.2

0.141

\(\sigma_{R^{2}}\)

0.0071

0.0053

0.0028

0.0054

0.0035

\(\sigma_{D}\)

0.0072

0.0048

0.0166

0.0048

0.0005

p

0.0

0.0

0.0

0.0

0.0

OWGR

\(\langle R^{2} \rangle\)

0.631

0.981

0.943

0.982

0.97

D

0.316

0.046

0.088

0.043

0.088

\(\sigma_{R^{2}}\)

0.0264

0.0388

0.0138

0.0381

0.0391

\(\sigma_{D}\)

0.1292

0.0165

0.0192

0.0152

0.0104

p

0.0

0.92

0.0

0.89

0.0

GPI

\(\langle R^{2} \rangle\)

0.791

0.978

0.937

0.978

0.985

D

0.531

0.201

0.149

0.201

0.202

\(\sigma_{R^{2}}\)

0.01029

0.0115

0.0044

0.0115

0.0459

\(\sigma_{D}\)

0.01612

0.0039

0.0048

0.0039

0.00533

p

0.0

0.0

0.0

0.0

0.0

FCWR

\(\langle R^{2} \rangle\)

0.727

0.986

0.981

0.997

0.947

D

0.295

0.115

0.057

0.055

0.172

\(\sigma_{R^{2}}\)

0.0186

0.0183

0.0098

0.0112

0.0268

\(\sigma_{D}\)

0.02833

0.0046

0.0052

0.00128

0.0104

p

0.0

0.0

0.0

0.0

0.0

FIFA

\(\langle R^{2} \rangle\)

0.833

0.993

0.981

0.996

0.979

D

0.387

0.076

0.071

0.041

0.155

\(\sigma_{R^{2}}\)

0.0277

0.0324

0.0135

0.0114

0.0413

\(\sigma_{D}\)

0.02888

0.004

0.007

0.002

0.0147

p

0.0

0.99

0.0

0.99

0.02

  1. Table listing mean values \(\langle R^{2} \rangle\) and 〈D〉 (and their associated standard deviations \(\sigma_{D}\) and \(\sigma_{R^{2}}\)), averaged over all time slices available, for the fitting process between the six sports and five theoretical rank distributions used here. We also include values of the Kolmogorov-Smirnov index p for the single time slice of Figure 1. Higher \(\langle R^{2} \rangle\) and lower 〈D〉 imply better fits. Since \(\sigma_{D}\) and \(\sigma_{R^{2}}\) are small, the fits shown in Figure 1 are representative of the entire datasets. The best fits for each sport are shown in bold.