Searching For A Winger.

The last post highlighted the need to treat small sampled sized rate statistics with a lot of caution.Football managers,both real or imaginary are currently looking at the numbers produced by last year's crop of professionals with a view to adding them to their actual or fantasy lineup for the 2012/13 campaign.As a result of the readily available source of more in depth individual statistics,the first stop for the aspiring SAFs is the data provided by the numerous Opta re sellers.

And there will almost certainly be a bite sized chunk of numerical data to give form to whichever quality you are looking to invest in with your new signing.A tackle rate of 89% from 30 total tackles may indicate that some of the success enjoyed by last year's defence was down to this precise individual contribution,but once that figure starts being used to predict future performance,then the picture becomes much less clear.A tough tackling defender may be just what your fantasy or real team needs,but do these kind of raw numbers give you much confidence that this is what you will get if you press the "buy" button.

Let's imagine you want to purchase a throwback winger from the 80's,possessed of dribbling skills and the ability to pick out a cross with pin point accuracy.A Mark Chamberlain,proud father of The Ox,for example.EPL Index usefully provide the number and success rate of crosses for all players from last season's EPL as well as their total dribbles and their success rate in that category.

We saw in the previous post that sample size in these type of success or fail statistics can quickly compromise the predictive quality of these rate figures.Less attempts mean a larger proportion of random variation in the observed figures,so to produce a figure that better represents expected future performance we have to add a fairly hefty portion of league average to the observed rate.The larger the number of trials,the less we need to regress toward the mean of the whole sample.

Regressed Crossing Rate Stats from 2011/12 EPL.

Player.	Total Crosses.	Accurate Crosses.	Observed Success Rate %.	Regression Rate.	"True"  Rate %.
David Fox.	92	38	41.3	34%	35.1
Luka Modric.	122	46	37.7	29%	33.6
James Morrison	84	33	39.3	37%	33.5
Mark Gower.	95	35	36.8	34%	32.3
Barry Bannan	100	35	35	33%	31.2
A'thony Pilkington	108	37	34.2	31%	30.9
Michael Knightly	108	35	32.4	31%	29.6
Wes Hoolahan.	55	19	34.5	47%	29.3
Florent Malouda.	93	30	32.2	34%	29.2
Jermaine Pennant.	228	68	29.8	18%	28.7
Stilian Petrov.	65	21	32.3	43%	28.5
Chris Eagles.	161	48	29.8	23%	28.3
Population Average.			23.4

Above are the top ten most successful crossers taken from EPL data for 2011/12.Some are midfielders,whilst others are more traditional wide players.The top ranked cross efficient player was Norwich's David Fox who was successful with over 41% of his 92 attempts compared to a sample average success rate of 23.4%.Around 50 crossing attempts are needed for the contribution from random chance to equal that from player talent and so Fox's 92 crosses implies that his cross conversion rate is more heavily influenced by his talent.The make up of the population from which Fox's score is taken indicates that his observed conversion rate needs to be regressed about 34% towards the group mean.So in Fox you my get the EPL's most accurate crosser of a ball,but you are extremely unlikely to get a conversion rate anywhere near his observed 41.3% in 2012/13.

The effect of applying a regression not only pulls the more extreme results toward more realistic levels,but also the ranking order also changes in cases where impressive conversion rates have been achieved over relatively large sample sets.For example Pennant's corrected rate leapfrogs that of Petrov because the latter's higher raw rate was achieved in only 65 trials compared to Pennant's 228 observations.Pennant's observed numbers are regressed only 20% compared to nearly 50% for Petrov.

Regressed Dribbling Rate Stats 2011/12 EPL.

Player.	Total Dribbles.	Successful Dribbles.	Observed Success Rate %.	Regression Rate.	"True"  Rate %.
Steven N'Zonzi	25	22	88.0	29%	76.7
Mikel Arteta	23	20	87.0	30%	75.3
Mark Davies	60	46	76.7	14.5%	72.7
Ramieres	59	43	72.9	14.5%	69.4
Sandro	22	17	77.3	31%	68.3
Joe Allen	50	36	72.0	17%	68.1
Ryan Giggs	30	22	73.3	25%	67.1
Nigel Reo Coker	42	30	71.4	19%	67.0
Assou-Ekotto	44	31	70.5	18.5%	66.4
Patrice Evra	75	51	68.0	12%	65.7
Nani	79	53	67.1	11%	65.0
Charlie Adam.	36	25	69.4	22%	64.9
Population Average.			48.7

Applying the same technique to the 2011/12 dribbling statistics sees Steven N'Zonzi's small sample sized 88% conversion rate dragged down to 76.7% and Ramieres and Nani's larger sample size rate allows them to leapfrog Sandro and Adam respectively in the rankings.

Top Combinations of Crossing and Dribbling Stats,2011/12 EPL Players.

Player.	"True" Dribbling Success Rate.	Dribbling Ranking.	"True" Crossing Success Rate.	Crossing Ranking.
Luca Modric.	60.6	22	33.9	2
Joe Allen.	65.7	5	27.2	27
Mikel Arteta.	70.0	3	26.4	37
Wes Hoolahan.	58.7	32	29.6	9
Tomas Rosicky.	62.1	13	26.8	30
Maynor Figueroa.	56.8	38	30.7	7
Benoit Assou-Ekotto.	63.4	9	25.8	48
James Morrison.	54.6	55	33.8	3
Jermaine Pennant.	55.3	48	28.8	11
Stilian Petrov.	55.1	49	28.7	12
Leighton Baines.	55.6	42	27.4	22
Gareth Barry.	55.4	44	27.4	23
Florent Malouda.	52.2	73	29.4	10
Juan Mata.	59.5	27	25.5	57
Ryan Giggs.	63.9	10	24.4	82
Seb Larsson.	56.0	41	25.8	52
Kieren Richardson.	50.6	83	27.6	19
Gylfi Sigurdsson.	53.6	65	26.2	41
Alejandro Faurlin.	55.3	47	25.2	60
Branislav Ivanovic.	52.1	75	26.4	38

Having dampened down unrealistic expectations and reshuffled the respective leader boards,all that's required to draw up a shortlist of potential wingers is to combine the crossing and dribbling ranking tables.As this post is more about demonstrating the effect of regressing observed values,I've simply arranged the players according to their combined ranking from each discipline.Of the top twenty combined outfielders WBA's James Morrison is the top ranked player who has operated in a wide role in 2011/12 and his particularly impressive projected crossing percentage gets him the vote in front of Stoke's Jermaine Pennant.

Seasonal player statistics perfectly describe what has occurred,but their predictive value often leads to inflated expectations if they are used in raw "as is" form.