Ranking Free Kick Experts. The Pitfalls.

Evaluating player talent has never been more accessible or more prevalent as a result of the raft of individual statistics that are now available. It is therefore important that we fully appreciate the limitations of such analysis and the main areas where confusion and misleading conclusions can arise. The previous season's numbers generated by a transfer target are routinely compared to those of a team's current squad to decide if he will be an upgrade and if so by how much.

I've posted numerous articles aimed at showing the importance of regressing small sample sized chunks of a player's career numbers towards the mean of a group of his peers to better gauge a players real ability levels and provide a better estimation of future performance. What happens over a limited run of games can be largely influenced by luck, with talent taking the minor role. So a player's raw successes and failures should provide just the starting point for an assessment of his true worth. These figures can be improved upon, but even in this new, regressed form they should carry caveats as well.

Below using data from Optapro I've continued the theme of direct free kicks, their effectiveness and the degree to which scoring from such opportunities is skill based. Initially here, I looked at team records for the past four seasons and as teams tend to carry free kick specialists who monopolize such opportunities, it is sensible to look at individual player statistics. Conversion rates from dircet free kicks for the last ten seasons have been combined to provide samples running into the 50's for the majority of the players and into the hundreds for the likes of Ronaldo and Lampard. Also included in the data is the rate at which players hit the target, as well as the rate at which direct free kicks are blocked. A statistics that is sometimes omitted from free kick and open play attempts. 

I initially saw if the observed conversion rates diverge enough from those expected in a purely random process for us to be able to conclude that we are witnessing skilled input from the players. And secondly I've determined the amount of average performance that needs to be included in a team's actual record to improve our estimation of that team's true ability at performing the task we have measured. This analysis assumes that the average difficulty of each chance is broadly similar, it also ignores individual player ageing patterns and any improvement or deteriorating in ability that may come with a player's ability peaking and then declining.

As in the previous post the distribution of success rates among players does indicate that some have more talent at executing a direct free kick than others, but that spread of talent within shooters from the EPL over the last ten seasons is fairly tight. In the table below I've regressed the various conversion rates for every EPL player who has attempted 40 or more shots directly from a free kick since 2002. Scoring from the attempt is obviously the most desirable result, but I've also included the rate at which a player forces an attempted save from the keeper because accuracy can also lead to a valuable second opportunity for a colleague. The ability to avoid the wall with their attempts is included for similar reasons.

Most Proficient Strikers of a Direct Free Kick, EPL 2002-2012.

Player.	Regressed Conversion Rate%.	Conversion Ranking.	Regressed Accuracy Rate%.	Accuracy Ranking.	% Rate of Blocked Attempts.	Blocked Shots Ranking.
Larsson.	8.6	1	44.3	1	27.2	2
Solano.	7.4	2	32.6	6	35.3	16
Henry.	7.2	3	37.3	2	29.8	4
N'Zogbia.	7.2	4	35.2	4	30.1	7
Hasselbaink.	7.1	5	24.9	36	39.9	33
Brunt.	6.7	6	25.8	32	36.3	23
Murphy.	6.7	7	25.7	33	36.5	24
Tevez.	6.6	8	29.8	18	35.4	17
Geremi.	6.4	9	31.9	7	30.4	8
C Jensen.	6.4	10	30.8	14	36.0	19
Ronaldo.	6.4	11	34.0	5	37.9	30
A Young	6.4	12	31.5	9	30.0	6
Giggs.	6.4	13	27.8	25	35.9	18
K Richardson.	6.2	14	26.7	29	30.9	10
Drogba.	6.2	15	31.1	12	30.9	9
R Taylor.	6.0	16	23.3	39	37.2	26
Arteta.	6.0	17	24.6	37	42.8	39
M Taylor	5.9	18	27.0	28	42.0	38
Baines.	5.9	19	24.6	38	37.7	28
Rodallega.	5.8	20	30.1	16	34.7	13
Rochemback.	5.8	21	25.2	34	50.1	40
Bullard.	5.8	22	29.4	20	36.1	21
van Persie.	5.7	23	31.1	11	36.1	20
Pedersen.	5.7	24	29.4	19	39.9	34
Geovanni.	5.7	25	27.5	26	36.7	25
Bentley.	5.7	26	36.8	3	26.8	1
Savage.	5.6	27	31.8	8	34.9	14
Gerrard.	5.6	28	30.4	15	31.7	11
Lampard.	5.5	29	28.1	24	39.4	32
Clement.	5.4	30	21.3	40	41.1	36
L Robert	5.4	31	26.4	30	37.9	29
Nani.	5.4	32	29.2	21	30.0	5
Milner.	5.3	33	28.5	22	39.3	31
Bale.	5.3	34	28.1	23	35.0	15
J Beattie.	5.2	35	30.9	13	36.2	22
Petrov.	5.1	36	31.5	10	34.5	12
Downing.	5.0	37	24.9	35	41.5	37
Barton.	4.9	38	30.1	17	37.2	27
Pennant.	4.8	39	26.1	31	29.0	3
Rooney.	4.7	40	27.2	27	41.0	35

As everyone probably knows, Seb Larsson in his intermittent Premiership career with Arsenal, Birmingham and latterly Sunderland is widely regarded as the best direct free kick specialist. The regressed numbers appear to confirm this, not only is he comfortably ahead of second placed Nobby Solano, he is also the most accurate and second as the least likely to see his shot blocked.

Everyone likes lists, so hopefully the table will be of interest. However, the main point of this post is to try to simulate how easy it is to take one seasons worth of samples and arrive at conclusions that aren't confirmed by future or more extensive datasets.

Shots from direct free kicks for individuals are relatively rare events, especially if the kicking duties are shared out between players. Larsson, who tops the group has double figure attempts in four of his five EPL seasons, the exception being his year at Arsenal when he barely played, but even he doesn't make it into the twenties. Rooney who lies last in the "best of the best" group has only taken double figure attempts since Ronaldo's departure.

So if we restrict our analysis to a single, most recent season for direct free kick analysis we are going to be looking at small sample sizes and that means a lot of luck.Regression towards the mean can avoid drastic over or under inflation of true individual ability by dragging results towards more realistic long term outcomes, but how likely are we to place an inferior practitioner of a particular talent ahead of his superior ?

Broad assumptions have to be made in most new football analysis and if we pretend that Larsson's and Rooney's chances of scoring an individual direct free kick mirrors our estimation of their true conversion average, we can construct a simulation of how often the inferior Rooney, conversion rate 4.7%  would outscore the superior Larsson, conversion rate 8.6% over one (generous) season of 20 attempts each.

In 1,000 simulations, "Rooney" scored more goals directly from free kicks than "Larsson" in just over 20% of the "seasons". So in a rare, but skill based talent in football a player with a conversion rate of under 5% can record a better season long record than one with a conversion rate in excess of 8% about a fifth of the time even when we grant them an inflated number of attempts. Coincidentally, Rooney out converted Larsson in one season out of the four in which they were both playing in the EPL. If the "best" can beat the "worst" a significant number of times over a number of trials, we should be taking great care before we come to solid and forthright opinions about the relative merits of two or more players, even when those conclusions are backed up with real, but raw data.

In short, raw figures are merely the precursor to evaluating player talent, but especially in rare events where talent spreads are narrow we have to acknowledge the real possibility that the rankings may not even fully reflect the true capabilities of the individuals listed.

Direct Free Kicks. Always Take Your Best Shot.

The ball was carefully placed just right of the centre of the pitch and almost 38 yards from goal. An apprehensive wall was assembled 10 yards outside of the penalty area and Barthez barked out his instructions as Roberto Carlos prepared his run up that had stretched to beyond the arc of the centre circle. Seconds later the most iconic free kick of all time had been scored in an inconsequential friendly tournament in France. Ferociously struck with the outside of his left boot, the ball swerved from a trajectory 5 yards wide of Barthez's left hand post, dipped, before slamming against the inside of the upright and burying itself in the net.

A brilliant, majestic free kick that is unlikely to be repeated, certainly Roberto Carlos never came close to emulating his own feat, often struggling to even trouble the keeper despite constant repeated efforts. And there lies the paradox surrounding direct free kicks, as Roberto Carlos demonstrated in Le Tournoi and subsequently, they provide unforgettable moments, but they much more frequently fail to produce goals.

Goal attempts from direct free kicks are relatively rare beasts. The permanent members of the EPL since 2008-09 have averaged just under 20 such events per season and those teams average just over a goal and a half a season from direct free kicks. Below I've listed the each team's scoring record in such situations since 2008, the raw figures are taken from the EPLIndex website.


Conversion Rates For Direct Free Kicks For EPL Teams, 2008-2012.

Team.	Direct Free Kicks.	Goals Scored from Kick.	Conversion Rate %.	Regressed Rate %.
Arsenal.	86	5	5.8	7.2
Aston Villa.	66	4	6.0	7.3
Blackburn.	76	5	6.6	7.4
Bolton.	84	6	7.1	7.6
Chelsea.	130	7	5.4	6.8
Everton.	71	9	12.7	9.1
Fulham.	69	6	8.7	8.0
Hull.	46	5	10.9	8.4
Liverpool.	67	5	7.5	7.7
Man City.	70	8	11.4	8.8
Man Utd.	91	10	11.0	8.8
Newcastle.	56	3	5.4	7.2
Stoke.	44	2	4.5	7.2
Sunderland.	61	8	13.1	9.1
Tottenham.	88	3	3.4	6.4
WBA.	49	6	12.2	8.7
WHU.	63	2	3.2	6.6
Wigan.	92	10	10.9	8.8
Wolves.	39	1	2.6	6.9

Before we can begin to quantify the value of direct free kicks, we need to take each team's actual performance record and use it to estimate the spread of talent with the group. Wolves have the lowest conversion rate at 2.6% and Sunderland the highest at 13.1%, but these percentages could fluctuate wildly with the addition or subtraction of one or two goals, such is the paucity of scores from relatively few attempts. The average conversion rate for all teams is just under 8% and such is the spread of conversion rates for all teams we can conclude scoring from a direct free kick is a talent, but the spread of talent is quite narrow. It's likely that the teams who have played in the EPL since 2008 would need to take upwards of 200 direct free kicks before we can begin see a separation of talent with the best having highest actual conversion rates. That's around ten seasons worth of shots.

3...2...1...Jump.

Therefore we should be very wary about taking any of the conversion rates posted by teams at face value, even over four seasons the actual results posted by each team will be very heavily influenced by random chance. Roberto Carlos was obviously an extremely talented striker of a football, but the combination of biomechanics needed while completing the shot, the alignment of the defensive wall, the angle at which the ball struck the post and Barthez's (non) reaction time are each variables that can align or combine to produce a goal or just a marvelous failure. His Le Tournoi goal was certainly the product of skill, but randomness also played a significant role in that one attempt.

We must accept that even four years of direct free kick trials will be predominately the product of luck and will not come near to representing the true qualities of each team. Sunderland are way ahead of Wolves in recorded performance, but the true gap between their respective shooting abilities will certainly be much narrower. To get our best estimate of each side's true ability we need to add a large amount of league average conversion rates to each side's actual records.

I've done this in the final column of the table and my best estimate of the true conversion rates for EPL sides is much tighter than the actual record each has shown over the last four years. The worst sides are likely to convert direct kicks at around 7%, while the best are only a few ticks higher at 9%. We can now use these more representative figures to continue to evaluate direct free kicks.

Average conversion rates for all shots attempted in open play are well into double figures, so direct free kicks are inferior by comparison. However, once we start to compare open play shots taken from similar distance to typical direct free kicks, the picture changes. Direct free kicks must be taken from at least 18 yards from the goal line and on average they appear to originate from well into the mid twenties. Open play shots from similar areas of the field are only converted around 4% of the time. So even the poorest of EPL free kick takers will outshoot an average open play attempt from the same position. It appears that allowing a player to compose himself and a team to present their best striker of a ball as the taker more than compensates for the presence of a defensive wall.

For a team to profitably spurn the opportunity to shoot directly from a free kick they must instead be able to manufacture an open play attempt with similar chances of success. Shots taken in an arc approximately 16 yards from goal during open play have predicted conversion rates of around 7%, so a team will have to be capable of creating such a chance on average from every direct free kick they spurn to gain comparable value. In reality this won't be possible, nor would the chance be equivalent to a normal open play shot because the penalty area will be much more populated with defensive players.

Direct free kicks may be rare events where goals are infrequently scored, but given the choices, a shot is always the best course of action.