Robert Snodgrass attempted 16 direct free kicks in his 2012 BPL campaign, scoring on 3 occasions – a league-best. In a season where only 33 goals were scored from direct free kicks in 577 attempts – a 5.7% overall conversion rate – Snodgrass' 18.8% individual conversion rate is spectacular and the best in the league for players with at least 10 samples. But, does this mean that Snodgrass is the best free-kick taker in the BPL?
If we construct an experiment that assumes all direct free kicks have a 5.7% chance of resulting in a goal, a player attempting 10 shots is expected to score 0.57 goals (10 * 5.7%). For this experiment, we will also assume that goalscoring can be modeled as a Poisson distribution – a mechanism commonly employed by soccer analysts. A Poisson distribution is a discrete probability distribution that expresses the probability of a certain number of events happening given that the events happen independently at a known average rate.
Given these conditions, a player attempting 10 direct free kicks will score 3 or more goals roughly 2% of the time. With only 17 players attempting at least 10 free kicks in 2012's BPL, it's fair to assume Snodgrass' status as an outlier is more than dumb luck. Even players that have a "true" expected conversion rate of 10% won't score a single goal from 10 shots almost 40% of the time. In a world of exceptionally small sample sizes, we are forced to get more creative. For evaluating free kick specialists, we must step away from a binary result set and start leveraging the value of more detailed data.
Opta collects the origin and destination coordinates of every free kick in major competitions. First, we calculate the distance between the end coordinate of each free kick and the closest point inside the nearest goalpost. The destination of all non-blocked free kicks taken in the 2012 BPL season are illustrated below. The shot coordinates are wrapped over an axis fixed on the center of the goal (12 feet from either post). For clarity, free kicks that hit the top-right or top-left corner of the goal would be marked at the same location (coordinate 0,0).
Since not all free kicks are taken from the same angle or distance, it is important calculate the angle of error between the shot destination and the "intended" target location. The green line below represents a hypothetical path of an off-target shot. The accompanying black line between the top-left corner of the goal and the shot origin is the "intended" shot path. The angle between these two paths is the "error angle" – which represents the amount of additional accuracy that would have been required for the hypothetical shot to hit the "intended" shot target precisely.
The average angle of error for all direct free kicks in since 2011's BPL season has been 14.1°. On goal-scoring direct free kicks, this average angle reduces to 6.1° – considerably more precise.
Here are the 10 most accurate free kick takers in the BPL since the beginning of the 2011 that attempted at least 15 shots:
Seb Larsson not only has the lowest average angle of error since the beginning of the 2011 season, he also had the third smallest standard deviation of angle (most precise) in the league. Charlie Adam was the league's most precise but was not adequately accurate enough to make this list. As average angle of error is more repeatable year-over-year than free kick conversion rate, Larsson's 2012 BPL performance of 0 goals in 11 shots performance seems rather unlucky. Larsson also happened to lead the league in accuracy during his goal-less 2012 campaign.
It's important to point out the shot blocking percentages, especially those of our most-accurate Seb Larsson and our 2012-goal-scoring Snodgrass (10th on our list). Since the beginning of the 2011 BPL season, 38% of all direct free kicks were blocked. Watching a player hit the wall with a free kick may be frustrating, but it seems to happen to the very best. No player having taken at least 15 direct free kicks in the BPL since 2011 has had less than 15% of their shots blocked. Since the margin between a goal-bound strike and a wall-bound shot can often be so thin, I would advise against using shot blocking percentages as a pure representation of quality. Percentage of blocked shots is useful anecdotal evidence for extreme outliers, but probably not much more.
By stepping away from binary result sets and augmenting small sample sizes, it's possible to find players who are perhaps undervalued and overlooked because they're currently caught in a unlucky series of encounters with firm woodwork, close calls, and exemplary goalkeeping. In the Barclay's Premier League, where just a few goals can close the thin margin between relegation and survival, finding a few cheap goals can prove to be quite valuable.