The Randomness of Shooting: 6 Games of the Blues

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.