## Goalie Stats: Coin Tossers and Confidence Intervals

Rob was nice enough/crazy enough to ask me to contribute some articles to "Blues By The Numbers"

If you toss a coin 100 times, on average you will get heads 50 times. But you might get 55 or 47. The "confidence interval" is a range in which the number of heads is likely to fall. When tossing a coin, it is easy to calculate the confidence interval. In the above example, there is a roughly 90% probability that the number of heads will be between 42 and 58. That is the "90% confidence interval". The 95% confidence interval is 40 to 60. The 95% confidence interval is wider, so you can be more "confident" that the number lies in this range.

Goalies are coin tossers.

If you take an average shot at an average goalie, there is a 92% chance he saves it and an 8% chance you score. If you shoot 100 times, he might make 92 saves, but he might make 96 or 87. Once again, it is easy to calculate a range of how many saves you expect an average goalie to make. Here the 95% confidence interval is 87 to 97.

Now, if a goalie saved 97 of the last 100 shots he faced, people would talk about him being "hot" or "lucky". No luck here. This is just randomness.

More shots = Narrower confidence intervals.

If we increase the number of shots, the confidence interval narrows. At 1000 shots, the 95% confidence interval is 903 to 937.

We can use confidence intervals in two ways. The first answers the type of question "How good is Halak?" The second answers the type of question "If Halak is a 0.925 goalie, what can we expect this season?" Looking at the first question, Halak has seen 4904 even strength shots in his career and has saved 4535 of them. That's a 0.925 save percentage. We can calculate the 95% confidence interval. It is 0.917 to 0.932. So there is a 95% probability that his true ability is between 0.917 and 0.932.

We can also calculate what we should see this season. If he faces 1200 even strength shots, the 95% confidence interval for the save percentage we will see is 0.910 to 0.940

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