## 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 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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