When early season trends don’t fit in with expectations in sports, people will reference regression more quickly than when Colin Miller won both the Hardest Shot and Fastest Skater at the 2015 AHL All Star Game in Utica (I was going to fit that nugget of information in no matter what this article was about. 105.5 MPH!). Statistically, of course they’re right to say that regression is a possibility, whether positively or negatively, but that’s not interesting to talk about for a player or their team.

Telling an NHL player, “Yeah don’t worry you’ll score more eventually” or, “It’s been a good run, but expect it to run dry soon enough” is kind of pointless. Scientifically, a hockey season is not observational for the players and coaches, meaning that there are things that they can change as a season goes on. If a player is scoring more, they’ll want to know if those results are sustainable and how they can continue to maintain production. If a player is going through a cold spell, they’ll be very eager to figure out if there is a fix to why their production is lacking.

If there’s things a hockey team can control, they’ll want to take those measures instead of waiting on luck to determine their path, and part of the process is understanding the data behind that which they can control. Moneypuck’s data of every recorded shot since 2007 can give us insight into shooting talent with the result of every shot as one of the hundreds of variables in their shot datasets.

This is how we’re going to seek out insight to understand why Jeff Skinner and Taylor Hall have a combined 1 goal between them through the first 10 games of the season.

Shot Profile

After the elongated offseason, any skill or physical trait would be subject to some amount of rust, including shot accuracy. Let’s look at how the accurate the NHL is at shooting, starting with a baseline of every shot taken from 2007-08 through the 2019-20 season.

While players have different levels of shooting talent, looking at the baseline shot result distribution gives an idea of what to anticipate. Plus, we can compare it to the how the league has fared in this first month of the 2021 season.

Here, the best indicator of rusty shot accuracy would be a substantially higher percentage of shots that miss the net. More saved shots could also be an indicator, but the scope of the data doesn’t consider the goalie facing each shot. Since the 27.24% of shots to miss the net this season is a minuscule difference from 27.82% from 2007-2020, there’s nothing pointing to a league wide trend of inaccurate shooting.

Expected Goals

Expected goal models give a probability that a single shot results in a goal. An broad definition, yes, but for this exercise, a single shot probability is the parameter needed to run simulations, which can give more insight on the context of goal totals. Like the exercise of flipping a coin over and over a whole bunch of times, we can simulate taking a shot a large number of times. The only difference is that instead of the probability of flipping heads or tails being 50%, the probability of scoring is the output for the shot from the expected goal model. Empirically, if we use the 6.57% from the 2007-2020 shot profile for the percentage of shots to result in a goal, for every 100 shots, the expectation is between 6 and 7 goals. If we shoot 100 shots a large number of times, such as 10,000, 6 and 7 goals will be the most frequently accomplished totals.

The result of the simulation showed what we expected, the average number of goals scored in each simulations was 6.5371, hovering around 6.57. Not only does the simulation give an estimated number of goals, but also the estimated probability that the player’s sample of shots would result in different numbers of goals.

But what’s the point of this? Well, in hockey, not all 100 shots would have the same probability of being a goal, so this simulation technique will be important to knowing what amount of goals can be expected with a player’s shot profile.

Case Study 1: Jeff Skinner

For Skinner, the polarizing differences between his first and second seasons of production power the high-wattage spotlight on the 28 year old in 2021, and it only gets warmer as each game goes by that he doesn’t score his first goal of the season.

The lack of goals for Skinner is mostly showing itself in an increase in shots being saved, so there’s room there for Skinner to expect some pucks will start finding the back of the net soon, especially with the consistency that he gets shot attempts in high danger areas. Let’s also look at the previous two seasons to see if there was anything that stood out between the two shot profiles.

Initial glimpses at his previous two seasons of shots suggest to me that Skinner has been a more accurate shooter in terms of hitting the net during his tenure with the Sabres, setting up the possibility that he was both lucky in 2018-19 and unlucky in 2019-20; they don’t need to be exclusive events. Simulating his expected goals in these seasons, then, could give insight into what that the most likely middle ground is for Skinner’s shooting talent.

Note that the solid blue line for these simulation plots represents the player’s actual goal total while the dotted line is the average goal total for the simulations being plotted.

For his career, Skinner is a near expectation shooter, ranking in the 44th percentile for his 256 goals scored on 3187 shots in this simulation: only a few goals away from the expectation of about 258 goals for a career that started in 2010. Now let’s look at just his shots from the previous two seasons.

Season	Actual Goals	Average Goals in Simulation	Actual Goals Percentile on Simulation	Approximate Number of Goals If 44th Percentile
2018-19	40	31.96	94.76th	31.21
2019-20	14	16.17	27.82nd	15.61

So we see that 2018-19 was above player expectation and average for Skinner, while 2019-20 was below player expectation and average. Skinner’s 40 goal season ranking in about the 95th percentile show what most casual observers would consider: he had a career year that season. With that being said, before anyone thinks that automatically should’ve disqualified him from his contract extension, the estimated probability that Skinner exceeded 30 goals is close to two-thirds, so while the cap hit wouldn’t have reached $9M in that case, the Sabres still would have had every reason to pay him top goal scorer money.

In the contrast of last season, even with the shortened season, it’s difficult to picture what reaching 20 goals would’ve looked like for Skinner, and if we look further, while his frequency of high shot quality stayed similar for the most part of the two seasons, Skinner took a higher frequency of low probability shots.

With extra contextual pseudo-variables considered, Skinner having to drive the scoring on his own line with lesser talented players than, say, Jack Eichel or Sam Reinhart, hurt his goal totals last season.

Now let’s see what this season looks like through 10 games for Skinner.

It’s a much different (and cooler if we’re being honest with ourselves) looking plot for the limited 32 shots Skinner has taken in 2021 because there’s a much smaller range of possible goal totals from the simulation. The average simulation result has Skinner at an expected goal total of between 2 and 3 through 10 games. An advantage of the early season sample is being able to tabulate the results of the simulation much more neatly, so let’s look at those by goal total:

Goal Total	Instances In The 10,000 Simulations	Percent of The 10,000 Simulations
0	897	8.97%
1	2407	24.07%
2	2804	28.04%
3	2051	20.51%
4	1139	11.39%
5	473	4.73%
6	170	1.7%
7	46	0.46%
8	11	0.11%
9	1	0.01%
12	1	0.01%

Skinner’s shots resulted in 0 goals less than 1 of every 10 simulations and reached 2 or 3 goals in nearly half of them. This information combined with the heavy volume of net-front shots here in the early season make me confident that Skinner will start catching up to a closer-to-expected goal total. Of course, I’d have more confidence in saying that with some line tinkering that puts him aside Jack Eichel, but that’s for a different day. Now it’s time to look at Eichel’s current most frequent left wing.

Case Study 2: Taylor Hall

Through 10 games, Taylor Hall is point short of a point per game pace. Good!

Through 10 games, Taylor Hall has one goal. Not good!

Through 10 games, Taylor Hall has three 5v5 points, all assists. Could be better!

Through 10 games, the Sabres have 59.2% of the shot attempts and 65.52% of the expected goals (Per Natual Stat Trick) when Taylor Hall is on the ice for the Sabres at 5v5. Very good! This is a long way to get to saying that I think Hall’s fortune is going to turn favorably in February.

I’m encouraged by the Charting Hockey shot chart for Hall above because, like Skinner, Hall has a concentrated volume of shots in high danger areas. Let’s see how he’s shooting:

Hall has taken 46 shots so far this season, and an extra 1 of about every 8 of them have missed the net. Has Hall’s shooting accuracy ever been something that comes and goes from season to season?

Season	Percent of Shots To Miss The Net
2010-11	29.01%
2011-12	25.09%
2012-13	24.26%
2013-14	23.55%
2014-15	26.98%
2015-16	22.28%
2016-17	21.26%
2017-18	24.17%
2018-19	26.41%
2019-20	25.07%

So since Hall hasn’t exceeded 27% for shots missing the net in a season since his rookie year, there’s precedence to expect Hall will finish the season at a more accurate clip in the final 46 games, and with that, some of those shots will begin hitting the net, whether it’s from rust going away or more fortunate bounces like not hitting the post on a penalty shot. Onto expected goals:

For his career leading into this season, he is only about 6 goals short of the expected total (220 goals compared to 226 expected goals), which, for a guy in his 11th NHL season, is an extra goal here and there every other year.

Goal Total	Instances In The 10,000 Simulations	Percent of The 10,000 Simulations
0	363	3.63%
1	1307	13.07%
2	2164	21.64%
3	2414	24.14%
4	1807	18.07%
5	1090	10.9%
6	533	5.33%
7	240	2.4%
8	66	0.66%
9	12	0.12%
10	4	0.04%

The mean goal total of the simulation is centered just over 3 expected goals to this point in the season, with about 3 of every 5 simulations having Hall anywhere from 2 to 4 goals. For Hall, Skinner, and any player in the NHL right now, even the players with the most shot attempts through two and a half weeks of games aren’t going to be too far from their expectation even if they’ve yet to score this season. If shot accuracy continues to be an issue for Hall in February, then it’ll need to be something he works more on in practices and pregame. Otherwise, the former league MVP’s best chance for more goals is to keep shooting. 

So as a conclusion, it’s not yet time to panic with goal totals from individual players all around the league. Some new line combinations probably need to enter the mix, but that’s a different story for a different day. Thanks for reading!

Photo Credit: Sara Schmidle/NHLI via Getty Images