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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%.