On winning the penalty shoot-out in soccer
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Bibliographic record
Abstract
The penalty shoot-out is used to break tied games in the knock-out stages of soccer competition. The shoot-out, which consists of an alternating series of penalty kicks, is won by the team with the highest goal tally after n kicks per team (n = 5). In the event of a tie after five penalty kicks each, the shoot-out progresses to 'sudden death' by increasing n in iterative fashion (i.e. n = n + 1) until one team obtains a higher goal tally than the other after an equal number of kicks per team. The team to strike first is determined at the end of extra time by the toss of a coin. As each on-field player can be awarded only a single penalty kick, the line-up order in which the penalty kicks are taken allows for the possibility of tactical influence on the final outcome. Consequently, we report a probability analysis of the penalty shoot-out in soccer from which we identify the following pre- and post-game strategies. The best five ranked penalty takers from the on-field players should be assigned to the first five penalty kicks in their reverse order of ability. That is, the fifth best penalty taker should take the first penalty kick, the fourth best penalty taker should take the second penalty kick, and so on. In the event of sudden death, the next highest ranked on-field player should be assigned to the next penalty kick until the shoot-out ends. For this tactic to be successful, players should be ranked a priori on their penalty-taking ability. Similarly, goalkeepers should be ranked a priori on their penalty-stopping ability. These findings indicate that the tactical substitution of on-field players for higher ranked penalty takers, including higher ranked penalty stoppers (i.e. goalkeepers), with a view to an impending penalty shoot-out should be given due consideration. These results are of practical importance in that they are shown to maximize the likelihood of winning the penalty shoot-out under certain initial conditions.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it