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# Fenwick Error

Fenwick has the same estimation error problem as Corsi. Fenwick for a full season has a 95% Confidence interval of about 43.5% to 56.5%.

Monte Carlo with Variable Fenwick Rates

Like Corsi, players produce Fenwick events at variable rates. I pulled the actual 5v5 shift-by-shift event counts for all the Blues. For each Blues player I created 10,000 seasons of 1804 shifts broken into 82 games. I picked each game at random and used the player's Fenwick counts as the offense table and the opponent's corresponding Fenwick counts as the defense table from that game. I then calculated the variation across those 10,000 seasons. The results:

 Player Std Dev ARNOTT 4.94606 BACKES 5.29088 BERGLUND 4.65374 COLAIACOVO 4.76238 JACKMAN 6.28369 LANGENBRUNNER 4.6193 MCDONALD 4.93661 NICHOL 6.25261 OSHIE 4.64261 PIETRANGELO 4.24851 POLAK 5.50802 REAVES 5.78662 SHATTENKIRK 5.09614 SOBOTKA 5.28241 STEEN 3.98272 STEWART 5.26295 HUSKINS 5.3452 GRACHEV 3.9228 PORTER 4.96594 COLE 4.63169 RUSSELL 6.82199 PERRON 4.25887 CROMBEEN 6.78321 DAGOSTINI 5.10153 AVERAGE 5.14108

With an average standard deviation of 5.14 the average 95% confidence interval of Fenwick/60 is about +/- 10.07.

Fenwick is normally reported as a percentage. Converting +/-10.07 to a percentage gives a 95% confidence interval of 43.1% to 56.9%

Season-to-Season Variation

Players with 5 Seasons on 1 Team

There are 146 players who played with one team all five full seasons from 2007-08 through 2011-12. For these players, the mean square error of Fenwick% is 8.98. A sample of size n underestimates the population variance by a factor of n-1/n. Correcting for this gives an estimated population variance of 11.225. This gives an estimated population Standard Deviation of 3.35 and a 95% Confidence Interval of 43.43% to 56.57%.

Players with 2 Seasons on 1 Team

If we look at seasons 2010-11 and 2011-12, and look only at players who played for the same team both seasons and who played at least 900 minutes in both seasons, we get a mean square error for Fenwick% of 4.743. Comparing mean square errors of all players with 900 minutes or more across all 4 pairs of seasons we get:

 Mean Sq 2007-08 2008-09 2009-10 2010-11 Average > 900 min 4.137 6.908 3.740 4.743 4.882

With a sample size of 2 and an average sample mean square error of 4.882, the estimated population variance is 9.764. This gives an estimated population standard deviation of 3.125 and a 95% Confidence Interval of 43.88% to 56.12%.

Conclusion

Fenwick% for a full season has a 95% Confidence Interval of about 43.5% to 56.5%.