# Automated Discovery of Successful Strategies in Association Football
## 2 Materials and Methods
### Preparing and Representing Corner Kick Event Data
#### 2.1.1 Play Extraction and Preprocessing  
Similar to previous works [2; 25], we divide the log into sequences of related events, which we call _plays_. However, our focus is on corner kick plays; we define a corner kick play begins with the occurrence of a Free kick event whose subevent type is Corner. On the other hand, a corner kick ends upon the occurrence of either of the following four conditions: (1) the occurrence of a terminal event (Foul, Clearance, Interruption, Offside); (2) a significant period of inactivity (for consistency with [2], a time delta between contiguous events of more than 10 s); (3) a change in ball possession; or (4) when the ball leaves the field. Furthermore, we observed that the data set can contain invalid position information (e.g., the same initial and final positions for certain events). Therefore, plays where events contain invalid position information are removed from our data set. Given that our tactics focus on how the ball moves toward the scoring zone, we remove all non-pass events (Duel, Others on the ball, Free kick, Interruption, Shot, Foul, Save attempt, Offside, Goalkeeper leaving line) from our plays, effectively converting them into pass sequences. Nevertheless, the occurrence of the removed events in the plays is stored as play metadata. Some of this metadata (e.g., number of duels) will be used as contextual information, whose impact on the outcome of a play is considered as part of the analysis described in Section 2.3. Recall that, initially, the first event of our plays was a Free kick event whose subevent type was Corner. This event can essentially be considered a type of pass. Therefore, before removing all Free kick events, Free kicks whose subevent type is Corner are changed into Pass events. Additionally, for two contiguous pass events in a pass sequence, the second pass either begins at the same location where the first pass ends, or begins at a different location (e.g., as a result of the receiving player running with the ball or a loose ball). These two possibilities are illustrated in Figure 1 which, for ease of reference, shows a non-corner kick play. Notice that in the first scenario (Figure 1a), all passes in the sequence are taken from the final position of the preceding pass; describing at all times how the ball moves toward its final destination. However, in the second scenario (Figure 1b), the pass sequence fails to describe how the ball moves from the final position of the first pass (\(fp_{1}\)) to theinitial position of the second pass (\(ip_{2}\)). In general, we refer to this scenario as a position mismatch, and it is caused by an implicit movement of the ball. Implicit ball movements in our plays prevent us from creating uninterrupted sequences of events that describe how the ball travels toward the scoring zone. Tactics extracted from such sequences will not be able to describe the step-by-step movement of the ball. Therefore, we capture the implicit movements of the ball by introducing a synthetic _Ball movement_ event whenever a position mismatch is detected. A typical player sprint is on average 14 m long [41]; we define a position mismatch occurs whenever the Euclidean distance between (\(fp_{i}\)) and (\(ip_{i+1}\)) is greater than ten units, which roughly matches this distance. We assign the initial position of the synthetic event to be equal to (\(fp_{i}\)) and its final position to be equal to (\(ip_{i+1}\)). Figure 2 shows how this event is added to address the position mismatch shown in Figure 1b. Due to the high level of redundancy between the initial and final positions in the enhanced sequence, we only keep the final position information. Figure 1: Pass sequence examples with and without a position mismatch. A blue circle indicates an event’s initial position, while a smaller one indicates its final position. A blue dotted line connects the initial and final positions for ease of visualization. (**a**) Example play showing no position mismatch. (**b**) Example play showing a position mismatch.