A goalkeeper’s easiest competitive edge might just be taking a single step to the right. By standing roughly 15 centimeters off-center before a penalty kick — moving slightly to his right hand side against a right-footed kicker — a goalkeeper can fundamentally alter the math of the penalty spot. Here is why this subtle tactical adjustment works and why it could significantly change optimal penalty strategy for both goalkeepers and takers. There is a well-known optimal mixed-strategy for taking penalty kicks as well as saving them, studied extensively by economists Pierre-André Chiappori, Steven Levitt, and Sohyoung Groseclose in 2002. Their study gives the following optimal strategy: a kicker should place 43% of penalties to the left, 24% to the middle, and 33% to the right (assuming a right-footed kicker). Meanwhile, a goalkeeper should dive left (from the kicker’s view) 60% of the time, stay central 9% of the time, and jump right 31% of the time. This payoff matrix shows the probability of a penalty being scored based on shot placement and dive direction, drawn from a dataset of 459 penalties across French and Italian top flights, as used in the mentioned study. goalkeeper \ taker L C R L 0.632 0.812 0.895 C 1 0 1 R 0.941 0.893 0.440 The key observation here is that a right-footed striker should place more penalties to the left than to the right. That comes down to kick biomechanics. A shot to the left carries more accuracy and power, making it more successful even when the goalkeeper guesses correctly and dives the right way. The following image shows an estimate of goalscoring probability based on the horizontal placement of the penalty (for situations where the keeper guesses the side correctly, see the full line). This has been calculated from a different dataset with our own model (details below). As expected, the closer a shot is to a goalpost, the more likely it is to go in. And as established, shots on the left side are more successful than those on the right. Figure 1: Probability of scoring from a penalty based on the horizontal distance of the shot from the middle of the goal. That’s where the new idea appears: What happens if a goalkeeper stops starting dead center and instead moves slightly to their right-hand side (to the left from the striker’s view)? That movement effectively removes several centimeters from the left end of the left line in the previous image, where the goalscoring probability is highest (dashed line on the left), and adds those same centimeters to the right end of the right line (dashed line on the right). The goalscoring probability of this newly added space was estimated by extrapolating our own model. The result is unambiguous: the centimeters you gain on the right are still less dangerous than the centimeters you lose on the left. That difference is the entire source of the advantage. We estimated a new payoff matrix for this noncentral scenario using real data and our own model. Based on that, we calculated how far the goalkeeper should move, as well as the updated optimal strategies for both striker and goalkeeper, which you can see in the following Table. The optimal move distance turned out to be about 15 centimeters. The payoff of shooting left is now almost the same as that of shooting right, meaning that the goalkeeper shift neutralizes the original biomechanical advantage. goalkeeper \ taker L C R L 0.577 0.9 0.933 C 0.833 0 1 R 0.899 0.692 0.4 This noncentral positioning only marginally increases total goalkeeper success once strikers adapt—we estimate a 0.3% increase in save rate, though our sample size was relatively low for this type of analysis and the real number could be higher. However, the change in strategy is substantial. Our results suggest goalkeepers should actually jump to their left (the kicker’s right) much more often—up to 48% of penalties. You can see the optimal strategies in the following Table. L C R Goalkeeper strategy: 42% 10% 48% Taker strategy: 46% 21% 33% Payoff matrix elements: LL: 0.469 RR: 0.461 Although this effect is marginal and carries high statistical uncertainty, the logic behind it is sound. Because shots near the left post are universally known to yield higher success rates than those near the right, shrinking that left-side danger zone inevitably tilts the math in the keeper’s favor. Because this technique takes zero extra effort—it is literally a 15-centimeter step before the whistle—it remains well worth doing. Across tens of thousands of penalty kicks every season in professional football worldwide, even a 0.3% gain translates to over 100 extra saved penalties a year, potentially making the difference in a major tournament final. You can read the full original Substack article here. The technical details can be found in this article, along with the complete code and dataset.   submitted by   /u/Strategist21 [link]   [comments]