## Tuesday, 3 July 2012

### Projecting Cross Conversion Rates.

To further demonstrate both the power and the necessity of regressing rate statistics towards the mean if you intend to quote them in evidence for future performance,here's how successful player crossing stats correlate from year to year.

I took every player who had attempted at least 20 crosses in both 2010/11 and 2011/12 and recorded their success rate in both seasons.So for example in 2010/11 Frank Lampard was successful with 26 of his 76 crossing attempts for a conversion rate of 34.2%.I then regressed each player's raw crossing rate towards the mean crossing rate for all the players in the sample(23.4%),the severity of the regression depended on the number of crosses each player had attempted.Lampard crossing ability was subject to 76 trials and his raw average was regressed 37% towards the mean,teammate Florent Malouda attempted 261 crosses,so his numbers were only regressed by 15%.

I therefore had two numbers for 2010/11 for each player,their actual observed rate and a regressed rate that contained an element of the group average that was dependent upon the number of crosses they had made.

I then compared their raw rate from 2010/11 with the raw rate from their next season,2011/12 and likewise repeated the process for the regressed rate.115 players attempted 20 or more crosses and made appearances in the EPL in both seasons and in 77 cases (67%) the regressed conversion rate gave a better indication of what a player was to achieve in 2011/12 than did his raw rate from 2010/11.

I've listed the results for the top 20 cross conversion players from 2010/11 and their subsequent performances in 2011/12.If you were seeking to project a player's 2011/12 performance from the limited knowledge of his performance from the previous year you would have been better advised to use his regressed rate figure in 16 of the 20 cases (80%).

Predicting A Player's Crossing Conversion Rate from One Year to the Next.

 Player. Raw Crossing Success Rate 2010/11 Regressed Crossing Rate. 2010/11. Raw Crossing Success Rate 2011/12. Is the Regressed Rate Closest to the  2011/12 Rate. F Lampard. 34.2 30.2 30.7 Yes S Ricketts. 33.3 28.2 19.2 Yes M Arteta. 32.7 30.8 27.6 Yes M Petrov. 32.2 30.4 24.0 Yes W Routledge. 31.6 28.7 12.3 Yes A Young. 31.2 30.0 20.9 Yes F Malouda. 31.0 29.9 32.2 No D Bilyaletdinov. 30.8 26.1 30.0 No R Taylor. 30.8 26.1 30.1 No B Watson. 30.4 28.6 24.5 Yes R Meireles. 30.0 28.6 30.9 No S Reid. 30.0 25.5 22.9 Yes C Brunt. 29.9 28.8 27.8 Yes L A Valencia. 29.6 27.2 25.3 Yes A Lennon. 29.3 27.7 25.9 Yes J Barton. 29.1 28.4 24.2 Yes J O'Shea. 28.6 25.9 17.6 Yes M Dembele. 28.6 25.1 14.3 Yes Rafael. 28.6 25.9 23.7 Yes A Kolorov. 28.3 27.1 19.3 Yes

On average using the regressed figure gives you a year (N+1) projection that is 15% closer than if you simply use the previous year's raw figure.Additional information such as ageing,injury,splitting the sample by player position,including weighted multiple regression years and change of team is omitted from this simplified approach,but the weakness of projecting with raw figures from one year to the next is highlighted.