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JOHN SCOTT AND… OTHERS: THE 2016 NHL ALL-STAR GAME

Annika Balk

MTH412

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“NHLSTATS” Data Set in R

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Points of Players From the 2016 NHL All-Star Game

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Buffalo Native Patrick Kane

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Buffalo Native Patrick Kane

2016 All-Star MVP John Scott

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This is John Scott

Amassing only 1 point and playing only 11 games Scott made it to the game and won every fan over.

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Question Posed: Is the observed difference in points between the Eastern and Western Conference Statistically Significant?

H0: µE= µW

HA: µE< µW

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Question Posed: Is the observed difference in points between the Eastern and Western Conference Statistically Significant?

H0: µE= µW

HA: µE< µW

​

To see if John Scott impacted this question I resampled the data with and without him by removing his data point in my R “NHLSTATS” dataset.

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First I subset the data into East and West

Atlpt <- POINTS[DIVISION == "Atlantic"]

Metpt <- POINTS[DIVISION =="Metropolitan"]

pte <- sum(Atlpt, Metpt)

meaneast <- pte/18

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Observed mean of Eastern Conference:

57.5

Pacpt <- POINTS[DIVISION == "Pacific"]

Cenpt <- POINTS[DIVISION == "Central"]

ptw <- sum(Pacpt, Cenpt)

meanwest <- ptw/18

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Observed mean of Western Conference:

63.94

So our observed test statistic of (meanwest- meaneast) is 6.44

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First I subset the data into East and West

Atlpt <- POINTS[DIVISION == "Atlantic"]

Metpt <- POINTS[DIVISION =="Metropolitan"]

pte <- sum(Atlpt, Metpt)

meaneast <- pte/18

​

Observed mean of Eastern Conference:

57.5

Pacpt <- POINTS[DIVISION == "Pacific"]

Cenpt <- POINTS[DIVISION == "Central"]

ptw <- sum(Pacpt, Cenpt)

meanwest <- ptw/18

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Observed mean of Western Conference:

63.94

So our observed test statistic of (meanwest- meaneast) is 6.44

But is this by random chance?

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In R for Resample…

  • Used the replicate function and indexed points to make all the points randomized.
  • Index- [-index] of points yielded a normally distributed histogram.
  • Abline at observed test difference
  • P-Value = 0.1492185
  • Conclusion: Not enough evidence to suggest the points between East and West is statistically significant

Fail to reject

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Question Posed: Is the observed difference in points between the Eastern and Western Conference Statistically Significant?

H0: µE= µW

HA: µE< µW

​

Now John Scott has been removed

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Subset data without Scott

Atlpt <- POINTS[DIVISION == "Atlantic"]

Metpt <- POINTS[DIVISION =="Metropolitan"]

pte <- sum(Atlpt, Metpt)

meaneast <- pte/18

​

Observed mean of Eastern Conference:

57.5

Pacpt <- POINTS[DIVISION == "Pacific"]

Cenpt <- POINTS[DIVISION == "Central"]

ptw <- sum(Pacpt, Cenpt)

meanwest <- ptw/17

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Observed mean of Western Conference:

67.65

So our observed test statistic of (meanwest- meaneast) is 10.15

*To remove Scott in R:

NHLWOJS <- NHLSTATS[-32,]

attach(NHLWOJS)

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Subset data without Scott

Atlpt <- POINTS[DIVISION == "Atlantic"]

Metpt <- POINTS[DIVISION =="Metropolitan"]

pte <- sum(Atlpt, Metpt)

meaneast <- pte/18

​

Observed mean of Eastern Conference:

57.5

Pacpt <- POINTS[DIVISION == "Pacific"]

Cenpt <- POINTS[DIVISION == "Central"]

ptw <- sum(Pacpt, Cenpt)

meanwest <- ptw/17

​

Observed mean of Western Conference:

67.65

So our observed test statistic of (meanwest- meaneast) is 10.15

But is this by random chance?

​

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In R for Resample…

  • Used the replicate function and indexed points to make all the points randomized.
  • Index- [-index] of points yielded a normally distributed histogram.
  • Abline at observed test difference
  • P-Value = 0.0236
  • Conclusion: With a P-Val <.05 there is enough evidence to reject the null and state that there is a statistical significant difference in points between the western and eastern conference.

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Conclusions

  • Scott’s low scoring season played a role in the significance in points scored on average between the Eastern and Western players.
  • In reality it seems that a typical All-Star caliber Western player outperformed an All-Star caliber Eastern player on average in points for the 2015-2016 season.
  • This surprised me!

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Bootstrap of Mean Points John Scott included

  • Blue line represents observed mean
  • Calculated Bootstrap Bias
  • BiasBoot(ɵ̂Boot)= E[ɵ̂Boot]-ɵ̂= .0407
  • Relatively close to zero which indicates the parameter is fairly unbiased.
  • Also indicating the sampling distribution is centered around parameter.
  • Data looks very normal and by CLT this makes sense as N increases

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95% Confidence Interval Of Points

Bootstrap CI

  • Using R bootstrapping the points I calculated a 95% confidence interval
  • I found an interval of [54.778, 66.556]

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Theory Calculation CI

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  • Used above formula with a Z score of 1.96.

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  • I found an interval of [54.76106, 66.68339]

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Theory matched the bootstrap sample!

*John Scott included in both calculations

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THANK YOU!