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# The Randomness of Shooting: 6 Games of the Blues

I fire up the random number generator and see how the Blues are doing.

Through 6 games this season the Blues had 6 goals on 155 5v5 shots. That's a lowly 3.47% shooting percentage. Let's run some simulations and see whether that's within the range of expected outcomes.

Level 1

Let's just assume a simple Binomial. All shots are created equal, 8% chance of scoring. In all these first two tables, Upper95 is the upper end of the 95% Confidence Interval for observed shooting percentage. Lower95 is the lower end. Upgoals is the upper end of the 95% Confidence Interval for observed number of goals. Lowgoals is the lower end.

 Type Events shootpct misspct sd upper95 lower95 upgoals lowgoals SOG 155 0.08 0.92 0.022 0.123 0.037 19 6

Level 2

We know all shots are not created equal. Distance, time relative to last shot, shot type, etc. all impact shooting percentage. We know from my goalie work that observed Confidence Intervals are wider than the Binomial model predicts. At 5 games, they're about 10% wider. Plugging that in we get:

 Type Events shootpct misspct sd upper95 lower95 upgoals lowgoals SOG 155 0.08 0.92 0.024 0.127 0.033 20 5

Level 3

Let's take one step back. The Blues have 215 Fenwick events. Teams normally miss about 27.2% of their 5v5 shots. Starting with 215 Fenwick events, I used a random number generator to determine how many shots hit the net, and a second random number generator to determine how many score.

 stat mean sd 0% 2.5% 50% 97.5% 100% Goals 12.4901 3.68408187 1 6 12 20 28 Shots 156.5386 6.451176 130 144 157 169 182 ShPct 0.0798 0.0233 0.0062 0.0375 0.0789 0.1282 0.1728

So, the observed number of goals ranges from 1 to 28, with a 95% Confidence Interval of 6 to 20. Shooting percentage similarly ranges from 0.6% to 17.3%, with a 95% Confidence Interval of 3.75% to 12.8%.

Level 4

Let's take another step back. The Blues have 295 Corsi events. Teams normally have about 25.5% of their 5v5 Corsi events blocked. Starting with 295 Corsi events, I used a random number generator to determine how many shots get blocked, a second random number generator to determine how many of the unblocked shots hit the net, and a third to determine how many score.

 stat mean sd 0% 2.5% 50% 97.5% 100% Fenwick 219.8419 7.53665606 192 205 220 234 245 Goals 12.7469 3.82396426 1 6 13 21 28 Shots 160.0404 8.59192353 124 144 160 177 196 ShPct 0.0796 0.0235 0.0062 0.0364 0.0788 0.1287 0.1742

Here the observed number of goals ranges from 1 to 28, with a 95% Confidence Interval of 6 to 21. Shooting percentage similarly ranges from 0.6% to 17.4%, with a 95% Confidence Interval of 3.63% to 12.87%.

Level 5

The Blues have played 278:20 at 5v5. For this simulation, I used a random number generator to determine how many Corsi events get generated, a second random number generator to determine how many shots get blocked, a third random number generator to determine how many of the unblocked shots hit the net, and a fourth to determine how many score.

 stat mean sd 0% 2.5% 50% 97.5% 100% Corsi 231.966 16.48700173 175 200 232 265 297 Fenwick 172.9072 13.93784827 124 146 173 201 227 Goals 10.0574 3.48208526 0 4 10 17 26 Shots 125.8389 11.67725921 85 103 126 149 170 ShPct 0.0799 0.0267 0.0000 0.0308 0.0789 0.1351 0.2016

The 95% Confidence Interval for goals is 4 to 17, but the average number of Corsi events is only 232. The Blues are well above that. This shows 295 events as outside the 95% Confidence Interval for 278:20 of 5v5 hockey, which it would be if Corsi rates were fixed. Anyway, I tweaked the numbers to give an average Corsi production of 295. What I got there was:

 stat mean sd 0% 2.5% 50% 97.5% 100% Corsi 293.9789 18.80410099 226 258 294 332 364 Fenwick 219.0358 15.9165402 158 189 219 251 280 Goals 12.7333 3.84752537 0 6 13 21 30 Shots 159.3506 13.32719179 115 134 159 186 211 ShPct 0.0799 0.0232 0.0000 0.0360 0.0793 0.1267 0.1772

In this simulation, the observed number of goals ranges from 0 to 30, with a 95% Confidence Interval of 6 to 21. Shooting percentage similarly ranges from 0.0% to 17.7%, with a 95% Confidence Interval of 3.597% to 12.66%.

Conclusions

Through 6 games, the Blues generated more offensive Corsi events than an average team would be expected to generate. The number of goals scored was on the low end of expectation but within the range of random variation seen in these simulations. The Blues shooting percentage was on the low end of expectation but within the range of random variation.