Figure 1.
Flow chart of the state transition model exemplified on a rally starting with service for player A.
Figure 2.
Example of a simulated change of the transition probability (%) between FOSA-S – Point B (Error) as well as the resulting winning probabilities (%) from the bronze medal match Lin vs Ovtcharov.
Figure 3
Transition matrix for the men’s final of the Tokyo Olympics 2020 between Fan Zhendong and Ma Long (4–11, 12–10, 8–11, 9–11, 11–3, 7–11).
Table 1.
Descriptive statistics of the performance relevance per state transition.
| State Transitions | Mean | Median | Max. | Min. | Std. | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| m | w | m | w | m | w | m | w | m | w | |
| Serve-Def * | 0.32 | 0.13 | 0.27 | 0.08 | 2.12 | 1.59 | −1.08 | −1.34 | 0.60 | 0.58 |
| Serve-FOS-S | −0.22 | −0.06 | −0.18 | −0.05 | 1.56 | 1.61 | −2.12 | −1.54 | 0.65 | 0.57 |
| Serve-P | 0.56 | 0.55 | 0.52 | 0.53 | 1.45 | 1.60 | 0.24 | 0.22 | 0.18 | 0.20 |
| Serve-E | −0.67 | −0.66 | −0.62 | −0.59 | −0.24 | −0.30 | −1.71 | −1.57 | 0.23 | 0.24 |
| Def-Def * | 0.44 | 0.25 | 0.37 | 0.19 | 2.64 | 1.31 | −0.71 | −0.55 | 0.49 | 0.33 |
| Def-FOS-D | 0.12 | 0.24 | 0.08 | 0.20 | 1.40 | 1.62 | −1.27 | −1.63 | 0.49 | 0.56 |
| Def-P | 0.52 | 0.51 | 0.49 | 0.46 | 1.81 | 1.24 | 0.16 | 0.04 | 0.24 | 0.25 |
| Def-E | −0.91 | −0.87 | −0.84 | −0.80 | −0.12 | −0.04 | −2.17 | −2.18 | 0.39 | 0.46 |
| FOS-S-FOS+1 | 0.82 | 0.85 | 0.77 | 0.88 | 2.27 | 2.72 | −0.31 | −0.35 | 0.54 | 0.54 |
| FOS-S-P | 0.43 | 0.39 | 0.36 | 0.34 | 1.33 | 1.46 | 0.01 | 0.04 | 0.29 | 0.27 |
| FOS-S-E | −1.11 | −1.07 | −1.09 | −1.02 | −0.06 | −0.04 | −2.62 | −2.72 | 0.55 | 0.55 |
| FOS-D-FOS+1 | 0.61 | 0.66 | 0.55 | 0.66 | 2.01 | 1.91 | −0.81 | −0.52 | 0.56 | 0.52 |
| FOS-D-P | 0.54 | 0.46 | 0.52 | 0.41 | 1.30 | 1.20 | 0.06 | 0.06 | 0.32 | 0.28 |
| FOS-D-E | −1.07 | −1.01 | −1.02 | −1.02 | −0.09 | −0.12 | −2.45 | −2.01 | 0.49 | 0.50 |
| FOS+1-FOS+2 | 1.53 | 1.62 | 1.48 | 1.58 | 3.17 | 3.69 | −0.24 | 0.15 | 0.72 | 0.73 |
| FOS+1-P | 0.90 | 0.82 | 0.85 | 0.71 | 2.69 | 1.96 | 0.04 | 0.20 | 0.47 | 0.40 |
| FOS+1-E | −2.12 | −2.13 | −2.07 | −2.10 | −0.35 | −0.62 | −4.07 | −4.02 | 0.76 | 0.75 |
| FOS+2-FOS+3 | 0.77 | 0.89 | 0.69 | 0.85 | 2.66 | 2.06 | −0.57 | −0.13 | 0.53 | 0.46 |
| FOS+2-P | 0.46 | 0.45 | 0.43 | 0.38 | 1.55 | 1.30 | 0.04 | 0.03 | 0.27 | 0.29 |
| FOS+2-E | −1.07 | −1.15 | −1.03 | −1.12 | −0.04 | −0.16 | −2.87 | −2.49 | 0.50 | 0.53 |
| FOS+3-Off | 0.50 | 0.58 | 0.48 | 0.55 | 1.56 | 1.48 | −0.44 | −0.29 | 0.37 | 0.41 |
| FOS+3-P | 0.32 | 0.31 | 0.29 | 0.25 | 1.06 | 1.20 | 0.01 | 0.02 | 0.23 | 0.24 |
| FOS+3-E | −0.72 | −0.78 | −0.67 | −0.67 | −0.02 | 0.00 | −1.88 | −2.00 | 0.42 | 0.43 |
| Fin-Fin * | 1.10 | 1.31 | 0.99 | 1.20 | 3.58 | 3.59 | 0.08 | 0.00 | 0.66 | 0.74 |
| Fin-P | 0.66 | 0.65 | 0.60 | 0.52 | 2.07 | 1.78 | 0.03 | 0.00 | 0.43 | 0.48 |
| Fin-E | −1.51 | −1.66 | −1.31 | −1.58 | −0.27 | 0.00 | −4.05 | −4.24 | 0.78 | 0.97 |
Figure 4.
Performance relevancies of transitions to following shots as well as error from FOSs and subsequent shots as absolute mean values.