Fenwick Error

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:

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:

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%.