Abstract
Soccer analytics often follow one of two approaches: 1) regression models on number of shots taken or goals scored to predict match winners, or 2) spatial and/or temporal analysis of plays for evaluation of strategy. We propose a new model to evaluate skill importance in soccer. Play by play data were collected on 22 NCAA Division I Women’s Soccer matches with a new skill notation system. Using a Bayesian approach, we model play sequences as discrete absorbing Markov chains. Using posterior distributions, we estimate the probability of 35 distinct offensive skills leading to a shot during a single possession.
- 1
The original system is given in Table A.1 in the appendix.
- 2
When comparing skills, we refer to the posterior probability that pscop is greater for one skill than another as the posterior probability of separation between the two skills.
Acknowledgments
We are grateful to the Editor-in-Chief, Associate Editor, referees, and all other editing contributors whose suggestions have enhanced this paper.
Appendix
Additional Tables
Original notation system introduced in Thomas et al. (2009) for identifying and rating the effects of skills performed during soccer matches.
| Pass | |
| Performance score | |
| 7 | The pass results in a scoring opportunity |
| 6 | The pass results in a ball in the “mixer” |
| 5 | The pass results in forward (penetrating) play |
| 4 | The pass results in a square play |
| 3 | The pass results in back play |
| 2 | The pass is deflected out of bounds/player is fouled |
| 1 | The pass results in a 50/50 ball to the opponents |
| 0 | The pass results in an immediate loss of possession |
| Dribble | |
| Performance score | |
| 4 | The dribble results in a scoring opportunity |
| 3 | The dribble is toward the opponent’s goal (penetrating) |
| 2 | The dribble is toward own goal or square |
| 1 | The dribble results in a deflection out of bounds/player is fouled |
| 0 | The dribble results in an immediate loss of possession |
| First touch | |
| Performance score | |
| 5 | The first touch results in a scoring opportunity |
| 4 | The first touch results in penetrating play |
| 3 | The first touch results in a square play |
| 2 | The first touch results in a back play |
| 1 | The first touch is deflected out of bounds/player is fouled |
| 0 | The first touch results in an immediate loss of possession |
| Defensive tactics | |
| Performance score | |
| 8 | Challenge results in possession won; direct play in the attacking third |
| 7 | Challenge results in possession won; direct play in the middle third |
| 6 | Challenge results in possession won; direct play in the defensive third |
| 5 | Challenge results in possession; indirect play/forced errors out of bounds |
| 4 | Challenge with delay results in a ball being played indirectly |
| 3 | Challenge with delay, but the opponents still penetrate |
| 2 | Challenge but no delay, and the opponents penetrate |
| 1 | Challenged a 50/50 ball, but possession is not regained |
| 0 | Player did not provide immediate chase or chase results in a foul |
Note that this system includes defensive skills, which were omitted from our offensive-oriented analysis. Also, the system includes no rating system for shots taken.
All transient states with their possible transitions.
| State | Possible transitions from the state |
|---|---|
| Pass 5–8 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Pass 4 | Fouled |
| Pass 3 | Deflected OB |
| Pass 1.5 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Pass 1 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Pass 0 | Turnover; Bad Turnover |
| First-touch Pass 7–8 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| First-touch Pass 5–6 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5; Goal Kick; Goal Kick 0, 3; Goalie Throw; Goalie Throw 0 |
| First-touch Pass 4 | Fouled |
| First-touch Pass 3 | Deflected OB |
| First-touch Pass 1.5 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| First-touch Pass 1 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5; Goal Kick; Goal Kick 0, 3; Goalie Throw; Goalie Throw 0 |
| First-touch Pass 0 | Turnover; Bad Turnover |
| Dribbling Touch 5 | Shot 0–3; Pass 0–1, 3–8; First-touch Pass 0–1, 3–8; Dribbling Touch 0–5; Controlling Touch 0–5 |
| Dribbling Touch 3–4 | Shot 0–3; Pass 0–1, 3–8; First-touch Pass 0–1, 3–8; Dribbling Touch 0–5; Controlling Touch 0–5; Goal Kick; Goal Kick 0, 3; Goalie Throw; Goalie Throw 0 |
| Dribbling Touch 2 | Fouled |
| Dribbling Touch 1 | Deflected OB |
| Dribbling Touch 0 | Turnover; Bad Turnover |
| Controlling Touch 3–5 | Shot 0–3; Pass 0–1, 3–8; First-touch Pass 0–1, 3–8; Dribbling Touch 0–5; Controlling Touch 0–5; Goal Kick; Goal Kick 0, 3; Goalie Throw; Goalie Throw 0 |
| Controlling Touch 2 | Fouled |
| Controlling Touch 1 | Deflected OB |
| Controlling Touch 0 | Turnover; Bad Turnover |
| Fouled | Shot 0–3; Free Kick 0–1, 6–8 |
| Deflected OB | Corner Kick; Corner Kick 0–1, 3, 8; Goal Kick; Goal Kick 0, 3; Throw-in 0–1, 3, 5–7 |
| Free Kick 6–8 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Free Kick 1.5 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Free Kick 1 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Free Kick 0 | Turnover; Bad Turnover |
| Corner Kick 8 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Corner Kick | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Corner Kick 3 | Deflected OB |
| Corner Kick 1 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Corner Kick 0 | Turnover; Bad Turnover |
| Goal Kick | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Goal Kick 3 | Deflected OB |
| Goal Kick 0 | Turnover; Bad Turnover |
| Goalie Throw | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Goalie Throw 0 | Turnover; Bad Turnover |
| Throw-in 5–7 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Throw-in 3 | Deflected OB |
| Throw-in 1.5 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Throw-in 1 | Shot 0–3; Turnover; Bad Turnover; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
| Throw-in 0 | Turnover; Bad Turnover |
| Kick-off 6–7 | Shot 0–3; First-touch Pass 0–1, 3–8; Controlling Touch 0–5 |
Posterior mean estimates and 95% HPD credible intervals for expected sequence length in moves for sequences starting at the skill indicated. The 11,573 observed sequences in the data had a mean length of 3.46 and standard deviation of 3.30 moves.
| Expected sequence length | ||
|---|---|---|
| Pass 8 | 2.835 | (2.498, 3.181) |
| Pass 7 | 5.008 | (4.897, 5.116) |
| Pass 6 | 5.228 | (5.129, 5.330) |
| Pass 5 | 4.903 | (4.785, 5.026) |
| Pass 1.5 | 1.171 | (1.049, 1.309) |
| Pass 1 | 2.092 | (1.961, 2.231) |
| First-touch Pass 8 | 2.939 | (2.410, 3.474) |
| First-touch Pass 7 | 5.150 | (5.038, 5.257) |
| First-touch Pass 6 | 4.962 | (4.843, 5.079) |
| First-touch Pass 5 | 4.888 | (4.759, 5.014) |
| First-touch Pass 1.5 | 1.667 | (1.330, 2.029) |
| First-touch Pass 1 | 2.616 | (2.526, 2.706) |
| Dribbling Touch 5 | 3.953 | (3.847, 4.061) |
| Dribbling Touch 4 | 4.489 | (4.382, 4.597) |
| Dribbling Touch 3 | 5.000 | (4.876, 5.124) |
| Controlling Touch 5 | 4.613 | (4.522, 4.707) |
| Controlling Touch 4 | 4.825 | (4.738, 4.913) |
| Controlling Touch 3 | 5.111 | (5.012, 5.208) |
| Fouled | 3.336 | (3.135, 3.537) |
| Deflected OB | 4.238 | (4.069, 4.411) |
| Free Kick 8 | 2.020 | (1.406, 2.706) |
| Free Kick 7 | 5.224 | (4.905, 5.542) |
| Free Kick 6 | 4.990 | (4.584, 5.360) |
| Free Kick 1.5 | 1.153 | (1.059, 1.263) |
| Free Kick 1 | 2.127 | (1.887, 2.376) |
| Corner Kick 8 | 2.067 | (1.615, 2.558) |
| Corner Kick | 4.476 | (3.619, 5.264) |
| Corner Kick 1 | 1.405 | (1.176, 1.661) |
| Goal Kick | 2.179 | (2.063, 2.294) |
| Goalie Throw | 5.506 | (5.296, 5.701) |
| Throw-in 7 | 4.796 | (4.646, 4.950) |
| Throw-in 6 | 5.313 | (5.131, 5.484) |
| Throw-in 5 | 5.401 | (5.162, 5.628) |
| Throw-in 1.5 | 1.720 | (1.136, 2.412) |
| Throw-in 1 | 2.019 | (1.888, 2.154) |
| Kick-off 7 | 4.620 | (4.163, 5.060) |
| Kick-off 6 | 5.273 | (4.762, 5.761) |
Note that these estimates are slightly inflated with respect to the data lengths, as the transition matrix P includes states Fouled and Deflected OB in addition to the skills that led to those states (e.g., Pass 4).
Posterior mean estimates of absorption probabilities to Shot Opportunity (pscop), Turnover (TOV), and Bad Turnover (BTOV) with 95% HPD credible intervals.
| pscop | TOV | BTOV | ||||
|---|---|---|---|---|---|---|
| Pass 8 | 0.350 | (0.278, 0.422) | 0.448 | (0.381, 0.516) | 0.047 | (0.039, 0.055) |
| Pass 7 | 0.050 | (0.044, 0.057) | 0.838 | (0.829, 0.846) | 0.089 | (0.083, 0.095) |
| Pass 6 | 0.052 | (0.047, 0.058) | 0.831 | (0.822, 0.839) | 0.089 | (0.083, 0.095) |
| Pass 5 | 0.053 | (0.045, 0.060) | 0.831 | (0.821, 0.841) | 0.088 | (0.082, 0.093) |
| Pass 1.5 | 0.022 | (0.004, 0.044) | 0.942 | (0.905, 0.975) | 0.034 | (0.010, 0.063) |
| Pass 1 | 0.011 | (0.009, 0.014) | 0.898 | (0.881, 0.915) | 0.084 | (0.068, 0.100) |
| Pass 0 | 0.889 | (0.875, 0.903) | 0.111 | (0.097, 0.125) | ||
| First-touch Pass 8 | 0.387 | (0.275, 0.501) | 0.490 | (0.388, 0.595) | 0.052 | (0.041, 0.064) |
| First-touch Pass 7 | 0.044 | (0.040, 0.049) | 0.844 | (0.837, 0.852) | 0.090 | (0.085, 0.096) |
| First-touch Pass 6 | 0.052 | (0.045, 0.059) | 0.837 | (0.827, 0.846) | 0.089 | (0.084, 0.095) |
| First-touch Pass 5 | 0.049 | (0.042, 0.056) | 0.841 | (0.832, 0.851) | 0.088 | (0.082, 0.093) |
| First-touch Pass 1.5 | 0.036 | (0.006, 0.077) | 0.900 | (0.837, 0.956) | 0.046 | (0.015, 0.088) |
| First-touch Pass 1 | 0.016 | (0.014, 0.018) | 0.900 | (0.892, 0.909) | 0.076 | (0.068, 0.084) |
| First-touch Pass 0 | 0.901 | (0.889, 0.912) | 0.099 | (0.088, 0.111) | ||
| Dribble 5 | 0.078 | (0.067, 0.088) | 0.797 | (0.784, 0.810) | 0.087 | (0.081, 0.094) |
| Dribble 4 | 0.058 | (0.051, 0.066) | 0.824 | (0.814, 0.835) | 0.090 | (0.083, 0.096) |
| Dribble 3 | 0.044 | (0.039, 0.049) | 0.841 | (0.832, 0.850) | 0.091 | (0.085, 0.097) |
| Dribble 0 | 0.882 | (0.861, 0.902) | 0.118 | (0.098, 0.139) | ||
| Controlling Touch 5 | 0.071 | (0.063, 0.079) | 0.808 | (0.797, 0.819) | 0.088 | (0.081, 0.094) |
| Controlling Touch 4 | 0.055 | (0.049, 0.061) | 0.829 | (0.820, 0.838) | 0.090 | (0.084, 0.097) |
| Controlling Touch 3 | 0.046 | (0.041, 0.051) | 0.839 | (0.831, 0.848) | 0.091 | (0.085, 0.098) |
| Controlling Touch 0 | 0.906 | (0.894, 0.917) | 0.094 | (0.083, 0.106) | ||
| Fouled | 0.089 | (0.064, 0.115) | 0.820 | (0.788, 0.851) | 0.047 | (0.038, 0.059) |
| Deflected OB | 0.048 | (0.036, 0.060) | 0.859 | (0.843, 0.875) | 0.069 | (0.063, 0.076) |
| Free Kick 8 | 0.428 | (0.223, 0.643) | 0.421 | (0.228, 0.612) | 0.042 | (0.022, 0.062) |
| Free Kick 7 | 0.046 | (0.039, 0.053) | 0.843 | (0.833, 0.854) | 0.089 | (0.083, 0.095) |
| Free Kick 6 | 0.082 | (0.050, 0.124) | 0.766 | (0.710, 0.817) | 0.081 | (0.072, 0.089) |
| Free Kick 1.5 | 0.013 | (0.000, 0.037) | 0.964 | (0.930, 0.991) | 0.023 | (0.006, 0.048) |
| Free Kick 1 | 0.010 | (0.007, 0.014) | 0.936 | (0.916, 0.955) | 0.048 | (0.032, 0.068) |
| Free Kick 0 | 0.960 | (0.918, 0.994) | 0.040 | (0.006, 0.082) | ||
| Corner Kick 8 | 0.428 | (0.296, 0.564) | 0.320 | (0.204, 0.436) | 0.033 | (0.021, 0.046) |
| Corner Kick | 0.230 | (0.098, 0.370) | 0.613 | (0.469, 0.745) | 0.063 | (0.047, 0.078) |
| Corner Kick 1 | 0.034 | (0.005, 0.070) | 0.940 | (0.895, 0.978) | 0.012 | (0.005, 0.018) |
| Corner Kick 0 | 0.984 | (0.939, 1.000) | 0.016 | (0.000, 0.061) | ||
| Goal Kick | 0.010 | (0.008, 0.012) | 0.940 | (0.932, 0.948) | 0.045 | (0.038, 0.053) |
| Goal Kick 0 | 0.937 | (0.885, 0.982) | 0.063 | (0.018, 0.115) | ||
| Goalie Throw | 0.058 | (0.051, 0.065) | 0.829 | (0.817, 0.840) | 0.086 | (0.079, 0.093) |
| Goalie Throw 0 | 0.583 | (0.230, 0.920) | 0.417 | (0.080, 0.770) | ||
| Throw-in 7 | 0.035 | (0.031, 0.039) | 0.856 | (0.848, 0.864) | 0.091 | (0.085, 0.096) |
| Throw-in 6 | 0.044 | (0.039, 0.049) | 0.846 | (0.837, 0.854) | 0.090 | (0.084, 0.096) |
| Throw-in 5 | 0.050 | (0.044, 0.057) | 0.837 | (0.827, 0.846) | 0.089 | (0.083, 0.095) |
| Throw-in 1.5 | 0.006 | (0.000, 0.012) | 0.907 | (0.789, 0.988) | 0.084 | (0.011, 0.204) |
| Throw-in 1 | 0.009 | (0.007, 0.011) | 0.909 | (0.892, 0.926) | 0.078 | (0.062, 0.095) |
| Throw-in 0 | 0.953 | (0.918, 0.985) | 0.047 | (0.015, 0.082) | ||
| Kick-off 7 | 0.037 | (0.029, 0.044) | 0.855 | (0.843, 0.866) | 0.092 | (0.086, 0.099) |
| Kick-off 6 | 0.042 | (0.032, 0.051) | 0.849 | (0.837, 0.863) | 0.089 | (0.084, 0.095) |
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