Shooting Percentage: Expected vs Actual Based on Time since Last Shot

I spend a lot of time making lists and obscure statistical arguments about playoff-bound teams these days, but I rarely look at what I like to call "basic research".  Well, here's one for my more statistically-inclined readers.

Since the early days of the "shot quality" concept, people have been aware that rebounds are more dangerous than other shots taken from the same location.  In particular, shots taken 1, 2 or sometimes 3 seconds after the last shot are proportionally more dangerous than all other shots.  You can see that in this table, which shows the expected number of goals and shooting percentage - based on shot location - vs the actual number of goals.  The ratio of the two is the "relative danger" of a given even-strength shot:

 

Time # Sh Expt Goals Actl Goals Ex S% Act S% Rel S%
0 3665 293 580 7.99 15.83 1.98
1 6292 636 1105 10.11 17.56 1.74
2 7174 681 1335 9.49 18.61 1.96
3 5995 443 662 7.40 11.04 1.49
4 6568 411 450 6.26 6.85 1.09
5 7301 433 351 5.93 4.81 0.81
6 7604 441 377 5.80 4.96 0.86
7 7656 442 390 5.78 5.09 0.88
8 7519 431 365 5.73 4.85 0.85
9 7422 417 329 5.61 4.43 0.79
10 6743 386 355 5.73 5.26 0.92
11 6630 378 365 5.70 5.51 0.97
12 6178 344 339 5.57 5.49 0.99
13 5817 337 304 5.79 5.23 0.90
14 5625 314 282 5.59 5.01 0.90
15 5495 299 320 5.45 5.82 1.07
16 5116 285 287 5.57 5.61 1.01
17 5118 284 284 5.54 5.55 1.00
18 4940 276 259 5.58 5.24 0.94
19 4881 268 237 5.50 4.86 0.88
20 4666 260 268 5.57 5.74 1.03

 

There are a couple of interesting phenomena here.  First, I was surprised to see that shooting percentage is significantly lower than expected for shots taken 5-9 seconds after the last shot, while for 10+ seconds there's no difference.  I don't see a good reason why shots would be less dangerous in that time frame - while they're not rebounds, they still imply that the attacking team recovered the puck and got an opportunity to shoot on net.  I don't doubt that the collective wisdom of my readers will present an obvious explanation for what's baffling me at the moment.

The second thing that surprised me is the "zero-second" rebound.  In other words, two shots taken in such quick succession that no time elapsed on the clock.  We've seen bias in pretty much every other subjective measure recorded by NHL scorers, so it's no surprise that there's a 3.5-1 variation in "zero-second" rebounds across the league:

 

fla 250 dal 121 buf 87
nyi 222 col 118 pho 86
det 213 nj 116 cls 82
sj 187 nyr 107 edm 79
van 171 ott 104 la 79
tor 170 bos 101 min 79
atl 160 ana 100 mon 78
chi 156 was 99 nsh 75
cgy 152 phi 97 car 74
tb 141 stl 89 pit 72

 

Tom Awad had previously pointed out the irregularities in Florida.  There's much less variation in other recorded shots:

 

Time 0 1 2 3 4 5
Max/Min 3.5 2.4 2.4 2.0 1.9 1.9

 

The ratio of the highest-shooting rink to the lowest-shooting rink on non-rebound shots is approximately 1.3, which is slightly larger than what we'd expect given how many shots are taken in games played by the highest-pace teams vs the lowest-pace teams, but it doesn't indicate a massive recording bias.  But there is a huge amount of variation in the total number of rebounds recorded in each rink:

 

fla 1299
car 1172
col 1152
mon 1126
edm 1116
nyi 1115
tor 1071
sj 1069
nyr 1062
ott 1061
tb 1052
nsh 1010
la 994
was 992
atl 985
pho 978
buf 976
phi 974
cgy 955
pit 955
ana 928
min 915
stl 893
van 889
dal 862
det 852
nj 832
bos 816
cls 815
chi 778

 

Rebounds were considered to be all shots that were taken 0-4 seconds after a previous shot.  The difference between Florida and Chicago is about 125 shots per season (I used 2005-09 in my database) which amounts to something like extra goals expected goals per season.  It's possible that the rebound total variations aren't due to scorer bias, but I have my doubts.  I'll check into that at some future date.

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