Whenever an NHL team carries two high-scoring centers there is inevitable discussion of the top pivot drawing the tough matchups while the second benefits from facing weaker competition on a game-by-game basis. This topic has been magnified in the past few months as rookie Mathew Barzal achieved incredible success from the New York Islanders’ second scoring line, en route to his Calder crowning, behind puck-wizard John Tavares.

There are statistics that measure strength-of-competition at 5v5, but it is difficult to apply such numbers as context to on-ice performance due to multiple complexities; there is no one-size-fits-all adjustment for raw on-ice performance stats.

An alternate strategy for analysis is to classify groups of similar competition and see how the two players performed against the same opponents. The 62 defensemen below are organized by ice time per-game at 5v5. Although this is not a perfect measure of quality, generally better defensemen play more minutes. More importantly, we can now compare how two forwards, in this case Tavares and Barzal of the Islanders, performed against defined groups of competition in the 2017-18 regular season.

Overall the D1 group features plenty of high-end defensemen while D2 boasts impressive talent in its own right, including Hampus Lindholm, Duncan Keith, and P. K. Subban.

(Note that Sami Vatanen of the Devils and Ryan McDonagh of the Rangers were traded during the season. Each reached 800 minutes while leading his primary team in 5v5 minutes per-game. Their stats with the Ducks and Lightning, respectively, are not figured in.)

On average D1s played 33% of 5v5 time-on-ice with D2s as their partner, so there is not as much overlap as one might expect, between the two groups. This is due to many factors, such as unfortunate injury, coaches intentionally shuffling pairs, and similar minutes played at 5v5 by two or even three pairs, causing a D1 to be paired with a D3 or D4. (Calgary is an example of the latter, as T. J. Brodie-- paired with Travis Hamonic-- edged out Dougie Hamilton and Mark Giordano for the most 5v5 minutes per-game.)

The Final 30 Games

Midway through the season Tavares’s time-on-ice versus D1s and D2s topped out above seven minutes per-game, whereas Barzal clocked in under five minutes.

In the last 30 games, however, Tavares descended below 6.5 minutes while Barzal closed in on 5.5. By the end of the season Barzal was facing off against D1s for roughly eighty percent as many minutes per-game as Tavares. He was no longer a sheltered rookie. In fact, in the closing 30 games Barzal played 428 minutes of 5v5 hockey to Tavares’s 411, for the Islanders. Tavares still drew more time against stronger opposing defensemen, but the disparity was shrinking.

As a measurement of 5v5 on-ice performance I am using Natural Stat Trick score-and-venue adjusted shot attempts (HDCFs, SCFs, and CFs). The shots are weighted by their general conversion rate (shooting percentage), using stats from all 31 NHL teams during the 2017-18 regular season, so that higher-danger attempts are worth more than lower-percentage attempts. The resulting formula, an NST-based on-ice expected goals-for percentage (xGF%), is fully explained at the bottom of this article along with its three-bin limitation.

Tavares’s xGF% against D1s was largely stable, between 43% and 48%, over the course of the season. The modest percentage is not as damning as it may appear at first glance since (a) this largely embodies his ice time versus the toughest defensive opposition and (b) the Islanders struggled mightily as a team at 5v5 in terms of allowing scoring chances, particularly December through February, when Tavares’s rate dipped below 45%.

In contrast, Barzal’s 5v5 on-ice xGF% increased over the course of the last 50 games of the regular season, most noticeably against D1 competition. Over the last 34 games his xGF% soared well above 50% against D1 and D2 competition, after plunging down to sub-40 for a good chunk of the first half of the season versus D1s.

Keep in mind that linemates play a large part in a center’s on-ice performance. Barzal certainly benefited from his right winger Jordan Eberle, who was in many respects the Islanders’ best winger at 5v5. Andrew Ladd and Anthony Beauvillier took turns on the rookie’s left side, adding different elements to the line. Meanwhile capable forwards Anders Lee and Josh Bailey typically flanked Tavares after Bailey and Eberle swapped right wing spots in the top-6 the last week of October.

Overall the Islanders’ 5v5 play took a tumble after four players vanished from the lineup before Christmas. The team lost Calvin de Haan for the season at the tail end of the 33rd game, while hosting the Kings. A few games later fellow defenseman Johnny Boychuk left the ice. He would return in seven weeks, but appeared to be still ailing at times, leading up to surgery in April. Left wing Nikolay Kulemin’s season came to a close due to a November injury while right wing Joshua Ho-Sang was demoted to the AHL in mid-December, despite sharing some 5v5 success with Casey Cizikas in terms of on-ice performance and penalties drawn.

Cizikas’s fourth line never recovered, while the third line only began to hold its own once Tanner Fritz was re-introduced to Brock Nelson for the closing 25 games of the season. (Nelson was 50% xGF with Fritz at 44% zone-starts in 214 minutes.... Nelson and Ladd were 39% xGF without Fritz in 56 minutes, for what it’s worth, in the last 25 games, with slightly steeper 41% zone-starts.)

Barzal’s xGF% versus top competition increased despite the Islanders failing to break 46% as a team (against all competition) over a 30-game stretch in the second half of the season, until the final game. (The gray line below includes Barzal’s contributions, which help account for its subtle ascension games 60 to 82.)

Much of Barzal’s increase in xGF% was due to the Islanders’ improvement in high-danger scoring-chance shot-attempt (HDCF) percentage with Barzal facing top opposing defensemen. While the Isles were slaughtered versus D1s in terms of HDCFs over the first 48 games with Barzal on the ice, they posted a commanding 58% over the last 34 games of the season. Shot quality drove the change in xGF% as much as shot quantity.

(HDCFs are typically located in the crease and low slot area. See visual at the bottom of this article.)

By this point I can hear the skeptics clamoring, “The crude binning of data may result in misleading values!” It is true that categorizing all shot attempts into three tiers of danger-level and then applying values with a broad stroke is not as useful as classifying shot-attempts into dozens of precise bins. Consider, though, that while a more refined xGF% may steer Barzal’s rate in the closing 34 games down toward 50%, it may instead boost it up, approaching 56%. For those concerned with the method, they can take heart in the fact that the Islanders out-attempted opponents 175 to 160 (52.3%) in the last 34 games of the season with Barzal on the ice against D1 competition, after adjusting for score and venue, while Natural Stat Trick data suggest that it is likely New York had at least a slight edge in shot-quality as well.

The 58% zone-starts for Barzal works out to 14 extra offensive-zone faceoffs in 164 minutes of 5v5 ice time: 50 in the o-zone, 36 in the d-zone. The advantage is notable, but one extra o-zone faceoff every 12 minutes of 5v5 action is typically not enough to swing xGF by more than one or two percentage points.

We can’t draw too heavy a conclusion from 34 games of data, but for a 20-year-old rookie it is encouraging as young centers often struggle at 5v5, particularly against high-quality competition. After being sent back to the WHL 16 months prior, it is a remarkable feat for Barzal to merely hold his own facing some of the NHL’s best defensemen over a decent stretch of games the end of this season. To be clear, this is merely an indication that Barzal can succeed against the best in the league. If he excels for 400 or 500 minutes against D1s in the 2018-19 season then his strong finish this past season will be further substantiated.

Might this be a case of Barzal facing an assortment of less-capable D1s (or their mediocre teams) in the last 34 games of the seasons? It does not appear to be. There were 10 games that largely drove Barzal’s expected goals-for percentage above 50% in the second half of the season. Of those 10, five were at home in Brooklyn, in which Barzal’s line faced Seth Jones (CBJ, x2), Mattias Ekholm (NSH), Jeff Petry (MTL), and Dmitri Orlov (WSH). His away games included four defensemen who achieved largely successful seasons: Jake Gardiner (TOR), Sami Vatanen (NJD), Darnell Nurse (EDM), and T. J. Brodie (CGY), as well as Alex Goligoski for the struggling Coyotes. In sum they are a formidable, if unheralded, group of D1s, who collectively finished the season above 50% for xGF while logging heavy minutes at 5v5.

Eberle played nine of these ten games at right wing, while Beauvillier lined up on Barzal’s left for six of the ten. Notably, Anders Lee took a spot at left wing for games against Jones and Ekholm in the first week of February.

This isn’t to say that we should put much stock into these ten games in isolation. For almost any NHL center we can find 10 games in which his xGF% is above 55% over the course of the season. Rather, the chart above is intended to merely dispel the notion that Barzal’s xGF% was driven due to a soft spot in the schedule.

Does this mean that Barzal would hold his own as the top center for the Islanders next season, should Tavares sign with another franchise? Much like a backup goalie transitioning to being the starter, I am not sure that question can be answered solely with statistics. Sometimes players step seamlessly into bigger roles (see Vegas Golden Knights for examples), while other times the weight of increased responsibility proves too much. Even if Barzal does become a capable top center next season, the Islanders still have a large hole on the other top-6 line without Tavares. Comparing the two centers is likely trivial if Tavares leaves, in regards to next season; having two high-quality centers is a lot better than having one.

The Formula

Natural Stat Trick separates shot attempts into different categories: high-danger scoring-chance shot attempts (HDCFs), scoring-chance shot attempts (SCFs) and all shot attempts (CFs). The site provides a visual in the glossary for the categorizations, but it lacks on-ice markings. The picture below is an approximation of the boundaries for HDCF and SCF, based on shot locations from NST game-logs.

Note that some shots are downgraded if they are blocked by opposing skaters, while they are upgraded if they stem from rushes or result from rebounds. The categorizations are not entirely based on shot location, but all shot attempts ultimately fall into one of three bins.

An HDCF is marked down as an SCF and a CF, while an SCF is also marked down as a CF. After all of the math, it breaks down to the following for the 2017-18 regular season 5v5:

A: 12.57% shooting for HDCFs (2762 goals for 21,979 attempts)

B: 4.00% shooting for SCFs that are not HDCFs (1404 goals for 35,094 attempts)

C: 1.21% shooting for CFs that are not SCFs (737 goals for 60,677 attempts)

Thus, the formula for expected goals is:

(A*0.1257) + (B*0.0400) + (C*0.0121)

Note that SCFs that are not HDCFs are the same as “medium-danger” shot attempts on NST. CFs that are not SCFs are similar to “low-danger” attempts, but also include attempts from outside the offensive zone, while “low-danger” only accounts for offensive-zone shot attempts.

I believe the formula is useful, but organizing into three bins admittedly leaves for a large range of quality within each categorization. For instance, further classification of SCFs (ones that are not HDCFs) might group some attempts in a more precise bin ranging from 6% to 7% conversion rate, whereas another subset of SCFs could potentially be classified into a bin ranging from 3% to 3.5% conversion rate. Thus, one shot attempt placed in the SCF bin may be twice as likely to result in a goal than another attempt placed in the same SCF bin. The formula is an estimation, but generally ought to be more useful than simple shot-attempts percentage for determining on-ice play over a couple hundred minutes of 5v5.