# Spatial Analysis of Corners

By Daniel Silberwasser

Jose Mourinho, one of the most successful soccer managers of all time, onceÂ asked: â€śHow many countries can you think of where a corner kick is treated with theÂ same applause as a goal?â€ť The self proclaimed â€śspecial oneâ€ť answered his ownÂ question: â€śOne. It only happens in Englandâ€ť (Anderson 24). Watching any soccer matchÂ confirms Mourinhoâ€™s observation. When the linesman points his flag at the corner, theÂ crowd roars in anticipation.

However, multiple studies have revealed the corner kickâ€™s inefficacy. In a paperÂ presented at the Fifth World Congress on Science and Football, students from theÂ Department of Sports Science and the University of Wales performed a notationalÂ analysis of twenty English Premier League matches and suggested that only 2.7% ofÂ corner kicks resulted in goals. In the bestselling book Soccer by the Numbers,Â Professor Chris Anderson from Cornell University and Professor David Sally of the TuckÂ School of Business argue that corner kicks lead to shots, but not to goals. In a sampleÂ of 134 English Premier League matches, Sally and Anderson found that only 2.2% ofÂ corner kicks result in goals (Anderson 26).

The purpose of this study is to use spatial data from the 2011-2012 English Premier League collected by high speed cameras installed in various stadiums to both reexamine previous studies of corner kicks and provide new insight into Â how a corner kickâ€™s curvature and landing location contribute to its success.Â The data used in this study comes from Opta Sports’ geospatial data, which gives the (X,Y) coordinate position of each corner kick and the final (End_X,Â End_Y) coordinate position where the ball is first touched by a player on the field.

Because not every soccerÂ pitch has the same length and width, the X coordinateâ€™s units are the percentage of theÂ fieldâ€™s length and the Y coordinateâ€™s units are the percentage of the fieldâ€™s width (variation in pitch dimension is quite small so this is unlikely to bias the results). Afterwards, this data is coded for the curvature of the corner kick and the result of the corner kick. The result of each of the 1000 corner kicks analyzed is either â€śno shot,â€ť â€śmiss,â€ť â€śon target,â€ť â€śpost,â€ť or â€śgoal.â€ť Unless explicitly statedÂ otherwise, the data used in the methods below has been filtered for outliersâ€”corner kicks that land too far and corner kicks passed short.

A logistic regression model is appropriate with this data because a regression will expose and compare how a corner kickâ€™s curvature and final coordinates impact a binary result: a goal. Because goals are such rare events, occurring in this data set at a rate of .022 per corner kick, a rate similar to those found in previous studies, a correction for rare events is needed. Fortunately, Professor Gary King of Harvard University released a rare events logistic regression package for R that includes such a correction. The explanatory variables included in the model are a dummy variable indicating the ballâ€™s curvature, the End_X and End_Y coordinates where the ball was first contacted, and the squared terms of said End_X and End_Y coordinates.

When looking at all filtered data from both left and right corner kicks, the only significant variables in the model with the lowest akaike information criterion were the ballâ€™s final X coordinate (X represents the length of the pitch) and the final X coordinateâ€™s squared transformation. An increase in the final X coordinate was found to have a negative impact on the probability of a goal. However, this probability was found to be minimized when X = 90%, evident in the below figure.

The same regression was run using dataÂ from only left corner kicks and yielded similar results. The final Y coordinate of the ball was insignificant, as was its swing. The final X coordinate minimized probability once again at 90.299%. When the rare events logistic regression was run with data from corner kicks coming from the right side of the pitch, no significant variables were found.

Now I reran the regression with success defined as a shot on target. Because 18% of corner kicks lead to shots and 10% lead to shots on target, a rare events correction is unnecessary in this case. When looking at corner kicks from both the left and the right, only the final X coordinate of the kick and its square were found to be significant at a level of 95%. The final X coordinate minimized probability at 93.6%.

When only using results of corner kicks coming from the left side, both the final Y coordinate and the indicator signifying a straight corner kick as opposed to an inwardÂ swinging corner kick were statistically significant. According to the model, kicking a corner kick without any curvature increases the odds of a shot on target by 3.44. The final Y coordinate of the ball at first contact maximized the probability of a shot on target at 52.51%, about halfway between the two corners. The data from corner kicks from the right yielded no significant results.

The data seems relatively consistent on where in terms of the width of the field a player should put the ball in order to maximize shots and shots on target. In all cases where the ballâ€™s final Y variable was statistically significant at an alpha level of .05, the model indicated that the probability of a shot or shot on target would be maximized within 2% of the center of the pitch. The model suggests that teams should not try to put the ball by the near post nor the back post. This makes sense because a player narrows the angles with which he can reach the goal if he connects with the ball away from the center.

Interpreting the final X coordinateâ€™s impact on success confirms what many soccer coaches and fans already know about corner kicks: as a player moves farther away from the goal, itâ€™s easier to shoot, but harder to score. When a player moves towards the goal, itâ€™s harder to actually get a shot off but the probability of scoring from said shot is higher. The final X coordinate minimizes the probability of scoring a goal when X is 90%. Thus, as the ball is contacted closer to the goal, the probability of scoring increases.Â  When success is defined as a shot on target, the final X coordinate minimizes probability when X is 93.6%. The probability of a shot on target increases as the player moves into the area where the probability of scoring was minimized. The final X coordinate minimizes the probability of a shot when X is 95.08%, even closer to the goal. This isnâ€™t surprising because as one moves closer to the goalie, the goalie can prevent a player from even touching the ball. As a player moves into the area where the probability of scoring and shooting on target was low, their probability of getting a shot off increases.

Coaches can use these interpretations in various ways depending on the game situation. The data suggests a coach should attempt more straight corner kicks into the middle of the pitchâ€™s width. If a coach desperately needs a goal, a risky but necessary decision might be to kick the ball closer to the goalie. If a coach is happy to settle with a shot on target or even just a shot, then farther out preferable. If teams start following these strategies, maybe the fansâ€™ uproarious response to a corner kick will one day be justified.