Corsi Error: Part 3

Jared Wickerham

Monte Carlo suggests that the 95% Confidence Interval for Corsi/60 for a full season is about +/-13.7. Season to season variation suggests the 95% Confidence Interval is about +/- 14.3.

David Backes is David Backes is David Backes. Eric Staal is Eric Staal is Eric Staal. So let's see how much their Corsi production varies from season to season.

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. The mean square error of Corsi/60 is 41.00. 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 51.25. This gives an estimated Standard Deviation of 7.16 and a 95% Confidence Interval of +/- 14.03.

For David Backes, we get a mean of 5.976 and a sample standard deviation of 4.692. For Eric Staal, we get a mean of 5.610 and a sample standard deviation of 6.002.

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, we get a mean square error for Corsi/60 of 99.65. If we remove players with fewer than 150 minutes we get a mean square error for Corsi/60 of 41.16. Comparing mean square errors of all players, players with 150 minutes or more, players with 300 minutes or more, etc. across all 4 pairs of seasons we get:

Mean Sq

2007-08

2008-09

2009-10

2010-11

Average

all

91.50

112.20

121.90

99.65

106.31

> 150 min

40.05

42.49

48.35

41.16

43.01

> 300 min

33.34

35.52

41.26

35.66

36.45

> 600 min

26.22

32.42

27.76

32.18

29.65

> 900 min

22.67

34.46

25.24

30.51

28.22

With a sample size of 2 and an average sample mean square error of 28.22, the estimated population variance is 56.44. This gives an estimated population standard deviation of 7.51 and a 95% Confidence Interval of +/- 14.72.

Conclusion

The analysis of season to season variation suggests that the Corsi of individual players playing a full season has a 95% Confidence Interval of about +/- 14.03 to +/- 14.72. This is similar to the +/- 13.7 suggested by Monte Carlo analysis.

In This Article

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