## Simulating Rink Bias

I ran some simulations to see if rink bias really matters. It does not seem to make much difference.

Baseline Model

Typical goalie with a save percentage of 0.920 facing 1500 shots in a season. I ran 10,000 seasons.

Goals allowed was determined using a pseudo-random number generator.

Mean 1380 Minimum 1335 Maximum 1417

90% confidence interval is 1363 to 1397 Save percentage 90% CI is 0.908666 to 0.931333

95% confidence interval is 1360 to 1401 Save percentage 95% CI is 0.906666 to 0.934000

Rink Bias Model

Once again, a goalie with a save percentage of 0.920 faces 1500 shots. The number of goals determined by using a pseudo-random number generator. However, the number of shots at home was assumed to be undercounted or overcounted by 5% or 10%. (750 shots at home adjusted up or down by 37 or 75.) Saves were then computed from shots minus goals. Save percentages were computed, and compared to the confidence intervals above. I ran 50,000 seasons for each of the 4 possibilities.

 Scenario # < 0.906666 # < 0.908666 # > 0.931333 # > 0.934000 5% over 663 1297 4119 1910 5% under 2955 4923 1559 626 10% over 251 663 6749 2812 10% under 3923 6818 786 341 Control 1304 2461 2911 1260

In the 5% over scenario 94.854% of the computed save percentages fell in the 95% CI. 89.168% of the computed save percentages fell in the 90% CI.

In the 5% under scenario 92.838% of the computed save percentages fell in the 95% CI. 87.036% of the computed save percentages fell in the 90% CI.

In the 10% over scenario 93.874% of the computed save percentages fell in the 95% CI. 85.176% of the computed save percentages fell in the 90% CI.

In the 10% under scenario 91.472% of the computed save percentages fell in the 95% CI. 84.792% of the computed save percentages fell in the 90% CI.

In the validation control 94.872% of the computed save percentages fell in the 95% CI. 89.256% of the computed save percentages fell in the 90% CI.

In this simulation of rink bias, despite a systematic miscounting of shots of 5% or even 10%, the vast majority of observed save percentages fall within the range you would see if there were no rink bias.

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