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Trends in Hat Tricks, 1987-2016 February 9, 2016

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Hat tricks, 1987-2016; bubble size is the number of hat tricks by that year's leader

Hat tricks, 1987-2016; bubble size is the number of hat tricks by that year’s leader

Yesterday’s post on hat tricks raised a question – what’s the historical likelihood of a hat trick? Above is a time series of hat tricks by year, with bubble size weighted by the number of hat tricks scored by that year’s leader. The largest bubble is Mario Lemieux with 9 in 1988-89. The largest since 2000 was Jonathan Cheechoo with 5 in 2005-2006.

This looks like a significant downward trend, and it is; with each passing year, and controlling for games played, the expected number of hat tricks declines by about 1.2 (p = .0147). Meanwhile, adding another game to each team’s schedule seems to increase the number of hat tricks in a season by about .85 (p = .00005). There’s no statistical persistence of the numbers (that is, the lag of hat tricks has a coefficient not statistically different from 0). This downward trend is a bit confusing, since at first glance there hasn’t been a visible decrease in the quality of goaltending. That’s probably my next project.


Islanders Game 51: Okposo’s Hat Trick Helps the Isles Set The Mark February 8, 2016

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In Sunday’s pre-Super Bowl game, the Islanders took out the Pacific division cellar dwellers, the Oilers, in an 8-1 rout. That’s not only tied for the largest goal differential this year, it’s also the most goals scored by any team this year. Kyle Okposo assisted a Nikolai Kulemin goal at the end of the first, scored two in the second about three and a half minutes apart, and sealed the hat trick with the only goal of the third period. Cal Clutterbuck also had a goal and an assist (on Johnny Boychuk‘s game-opening goal). Connor McDavid had the only goal for Edmonton.

Okposo’s hat trick was the 43rd of the season; probably the oddest was a baffling performance by Rasmus Ristolainen in December, in which he scored all three Sabres goals in a losing effort against the terrible Calgary Flames. Mikkel Boedker, John Gaudreau, Zach Parise, and Jeff Skinner each have two hat tricks this year. No one has cracked the three-hat-trick mark this season, although Max Pacioretty and Joe Pavelski each did so in 2013-2014.hattricks

Hat tricks are interesting to model, because there are many complications in scoring them. Like John Scott‘s 2-goal performance in the All-Star game, it’s likely that hat tricks can be massaged along by teammates – feeding a player with two goals the puck in scoring situations, for example – so it’s difficult to argue that they can be poisson distributed (which would require their occurrence to be random). On the other hand, there’s clearly a reason why only 145 players have hat tricks over the last 5 seasons, why so few players have so many (Tyler Seguin with 7, two with 5, six with 4, 13 with 3, 21 with a pair, and the remainder with a single). The graph at right shows how thinly spread hat tricks tend to be over the past 5 seasons.


Sabres Game 53: Seriously? February 7, 2016

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Last night’s Sabres at Bruins ended on a controversial call. NESN described the hooking call on Rasmus Ristolainen as “questionable at best,” but Brad Marchand was awarded a penalty shot 2:32 into the overtime period. Ristolainen was skating hip to hip with Marchand; Marchand flipped Ristolainen’s stick out of his hands while Risto was attempting to play the puck, and Ristolainen followed up with a two-handed shove. Bafflingly, a hook was called, despite Ristolainen’s lack of a stick. In the video below, the “infraction” is signaled at 0:13, well after Ristolainen loses his stick.

Note that the NHL’s rule on hooking reads (in relevant part):

Hooking – Hooking is the act of using the stick in a manner that enables a player to restrain an opponent.
It’s doubtful Ristolainen committed any infraction at all. He played Marchand closely, but there’s nothing illegal about that. He grabbed Marchand’s jersey and shoved him with two hands, but neither of those actions is a “restraining” or “physical” foul. No boarding, charging, checking from behind (which requires a victim unable to prepare for the hit, and Marchand was clearly aware of Ristolainen), clipping, elbowing, fighting, headbutting, checking to the head, kicking, kneeing, roughing, slew-footing, throwing equipment (that was Robin Lehner after the game), or hooking. At worst, Ristolainen’s jersey grab was a hold. Holding is one of several rules that cross-reference Rule 57.3 (Tripping, Penalty shot), which reads:
The intention of this rule is to restore a reasonable scoring opportunity which has been lost. If, however, the player fouled is able to recover and obtain a reasonable scoring opportunity (or a teammate is able to gain a reasonable scoring opportunity), no
penalty shot should be awarded but the appropriate penalty should be signaled and assessed if a goal is not scored on the play.
“Control of the puck” means the act of propelling the puck with the stick, hand or feet. If while it is being propelled, the puck is touched by another player or his equipment, or hits the goal or goes free, the player shall no longer be considered to be “in control of the puck”.
In order for a penalty shot to be awarded for a player being fouled from behind, the following four (4) criteria must have been met:
The infraction must have taken place in the neutral or attacking zone (i.e. over the puck carrier’s own blue line). (Met)
The infraction must have been committed from behind. (This is a stretch – Ristolainen was skating closely with Marchand.)
The player in possession and control … must have been denied a reasonable chance to score. The fact that the player got a shot off does not automatically eliminate this play from the penalty shot consideration criteria. If the foul was from behind and the player was denied a “more” reasonable scoring opportunity due to the foul, then the penalty shot should still be awarded. (Robin Lehner’s play out of the crease and subsequent poke-check definitely cast doubt on this.)
The player in possession and control (or, in the judgment of the Referee, the player clearly would have obtained possession and
control) must have had no opposing player between himself and the goalkeeper. (Met)
It’s entirely possible that Lehner would have given up a goal eventually, but to award a penalty shot – Marchand’s second this season! – rather than a two-minute minor – if anything at all! – was a seriously questionable call.

Sabres Game 51: Lehner wins it because Condon loses it February 4, 2016

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Despite a rough second period last night, Robin Lehner was in it for the whole game and the Sabres brought home a 4-2 win over the Montreal Canadiens. The Sabres scored 1 goal in the first and 3 (including an empty-netter by Brian Gionta) in the third to come back from a 2-1 deficit.

Peter Llewellyn, USA Today Sports, Photo

Peter Llewellyn, USA Today Sports, Photo

Lehner notched a save percentage of .943, saving 33 of 35 shots on the night. Montreal’s first goal came at 03:19 of the second, 1:08 into a Johann Larsen hooking penalty; it was the first time this season that Lehner allowed a power play goal. The team is 2-4 on the season in Lehner’s starts.

Montreal goalie Mike Condon seemed to lose equilibrium in the third; he faced 10 shots and allowed two goals. In the first two periods, he saved 20 of 21. Condon is 13-15-4 in starts, and the Canadiens are 1-2 in games where he’s come in to relieve Carey Price or Dustin Tokarski. Condon is 4-4 in overtime games, with one of those losses coming in a shootout, so he doesn’t seem to be a guy who gets exhausted and crumbles; he may have just had a nasty period.

The Sabres host Boston tonight; the Bruins have won their last three road games. Lehner will likely start against Tuuka Rask. Boston backup Jonas Gustavsson was placed on the injured reserve list with heart problems on February 1; the Bruins called up Malcolm Subban to serve as backup while Gustavsson is injured, but I’d be surprised to see the 22-year-old Subban (5.76 GAA in one career game) called on to start.

How does scoring affect NHL standings? February 2, 2016

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Lisa Gansky, Photo

Patrick Kane (Lisa Gansky, Photo)

Patrick Kane (right) leads the league in goals and assists (and therefore total points). His Blackhawks are second in the league but lead the Western Conference, and are all but a lock to make the playoffs this season even with 29 games to go. Kane’s 30 goals (and 27.8 goals created) are a touch ahead of the second-place Jamie Benn and Alex Ovechkin, who each have 28 goals. Just how much, though, are those extra goals worth, and would it be better to focus on defense instead? In this entry, I’ll use some econometric modeling techniques to float an answer to that question.

When a team wins a game, they receive 2 points in the standings; a team that loses in regulation receives no points, but a team that loses in overtime or a shootout gets a consolation point for the tie after regulation. Since points, rather than direct win-loss records, are used to determine who makes the playoffs, it’s possible for a playoff team to have fewer points than a team that doesn’t make the playoffs. Though that didn’t happen in 2014-15, the Nashville Predators did finish ahead of the eventual Stanley Cup winning Chicago Blackhawks by having more points (104 to 102) despite having one win fewer (47 to 48). Nashville’s 10 overtime losses to Chicago’s 6 made the difference.

In a previous post, I calculated a pythagorean exponent useful for estimating a hockey team’s win-loss percentage and found a value of 2.11; a similar method to calculate the percentage of available points yields an exponent of 2.09. (That is, win-loss percentage and points percentage are really fairly close, in expectation terms.) Those models make the assumption that a goal against is worth the same as a goal for. Let’s try a couple of things to estimate the usefulness: first, let’s keep the same assumption, and fit a model of Points = a + b*Goals For – b*Goals Against. Using 2014-2015, that gives us an optimal model of Points = 92.2 + .357*Goals For – .357*Goals Against, with a sum of squared errors of 557.355.

Relaxing that assumption – allowing a goal for to be worth a different amount than a goal against – is theoretically justified by the fact that a losing team not only scores no points but loses the opportunity to score an overtime point, too. If we allow that flexibility, 2014-2015 gives us an estimated Points = 88.2 + .366*Goals For – .347*Goals Against, with a sum of squared errors of 555.594.

Since 88.2 points are expected in a season of 0-0 games, the expected points at the beginning of a game are approximately 88.2/82 = 1.076. Someone scores two, but the point given to the eventual losing team for a regulation tie pulls that average up a smidge.

The upshot of all of this? Defense is important, but since the expected points for a goal are higher than the expected penalty for allowing the other team to score, a team at the margin should consider signing a roving defenseman rather than a strictly defensive player – and it wouldn’t be crazy for a losing team to play four attackers and one defender for the last few minutes of the game, even before pulling the goalie.

NHL Luck and Playoffs through February 1 February 1, 2016

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Following the technically brilliant performance of John Scott in last night’s All-Star Game,1 the NHL is slightly past its midway point in the season. Most teams have played 49 of their 82 games, and while the Buffalo Sabres haven’t been mathematically eliminated yet, winning every game for the remainder of the season would only get them as many points as last year’s third-place finisher in the Eastern conference.

In other words, it’s spring.

Currently, the Eastern Conference would send Florida, Tampa Bay, and Detroit automatically to the playoffs from the Atlantic division, along with Washington and both New York teams. The wild cards would be Boston and New Jersey, with the latter at 52 points. The Sabres have 44.

The Western Conference would send Chicago, Dallas, and St. Louis from the Central and Los Angeles, San Jose, and Arizona automatically from the Pacific. Both wild card slots would come from the Central, going to Nashville with 56 and Colorado with 57. Minnesota (55) would be edged out, though they’d have made the playoffs instead of Arizona under last year’s system.

That’s a pisser for the Wild, who are actually playing about 3.3 wins below expectation; in other words, for their goals for and goals against, we’d expect about 26.3 wins, but they only have 23. Arizona, meanwhile, is at 24 wins, but “should” have only about 21.7. Though Minnesota can overtake Nashville or Colorado relatively easily, it looks like the more competitive Central division is going to lead to someone being excluded from the playoffs who would have made it under last year’s system.

Luck numbers through the All-Star Break follow.

Team pythwins luck GP W L PTS
Arizona Coyotes 21.7 2.3 49 24 20 53
Los Angeles Kings 28.0 2.0 49 30 16 63
Washington Capitals 33.2 1.8 47 35 8 74
St. Louis Blues 26.2 1.8 52 28 16 64
Chicago Blackhawks 31.5 1.5 53 33 16 70
Colorado Avalanche 26.0 1.0 52 27 22 57
Ottawa Senators 22.1 0.9 50 23 21 52
Philadelphia Flyers 20.1 0.9 47 21 18 50
Anaheim Ducks 21.1 0.9 47 22 18 51
Dallas Stars 30.2 0.8 50 31 14 67
Calgary Flames 20.4 0.6 48 21 24 45
Detroit Red Wings 24.5 0.5 49 25 16 58
New Jersey Devils 24.5 0.5 50 25 20 55
New York Rangers 27.0 0.0 49 27 17 59
Edmonton Oilers 19.1 -0.1 50 19 26 43
Winnipeg Jets 22.2 -0.2 49 22 24 47
Carolina Hurricanes 23.2 -0.2 51 23 20 54
San Jose Sharks 26.3 -0.3 48 26 18 56
Nashville Predators 24.4 -0.4 50 24 18 56
Florida Panthers 29.5 -0.5 49 29 15 63
Tampa Bay Lightning 27.5 -0.5 49 27 18 58
Pittsburgh Penguins 24.6 -0.6 48 24 17 55
Buffalo Sabres 20.7 -0.7 50 20 26 44
New York Islanders 26.0 -1.0 47 25 16 56
Montreal Canadiens 25.0 -1.0 50 24 22 52
Vancouver Canucks 21.1 -1.1 50 20 19 51
Boston Bruins 27.1 -1.1 49 26 18 57
Toronto Maple Leafs 20.0 -3.0 48 17 22 43
Minnesota Wild 26.3 -3.3 49 23 17 55


1Since I will never be able to type that phrase again, I figured I’d use it while I could.

Islanders’ Kill Streak Continues Despite Loss December 28, 2015

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Despite losing 3-1 (one empty-net goal) on December 27, the New York Islanders continued a penalty kill streak that goes back to November 25, when they gave up a power play goal to Claude Giroux off a goaltender interference call against Josh Bailey. In the 14 games since, the Islanders have killed off 94 minutes of penalties and run to an 8-4-2 record (with three shootout wins and a shootout loss at Ottawa on December 5). By contrast, their opponents have been less disciplined: they’ve taken 114 penalty minutes and allowed the Islanders to score 8 power play goals. Over that span, the Islanders have outscored the opposition 35-31, allowing 2 shorthanded goals but scoring none.

That is, without question, a very strong 14-game stretch. Part of it is certainly luck – a team should theoretically lose half of its shootouts, but the Isles are 3-1 in shootouts and 1-1 in overtime since November 27. If you subtract the goals granted for shootout wins, they’re about .53 wins above expectation, which is a fairly large proportion for a small stretch. In addition, they’ve been outshot 426-393 over that stretch. In wins, oddly, they’ve still been outshot 257-218, and in losses they’ve outshot their opponents 175-169.

With numbers like that, it’s unsurprising they’re regressing a bit to the mean. However, they’re still 19-12-5 on the year with 43 points; that places them third in the Metropolitan, but would put them tied for second in the Atlantic or Pacific. The Central is tough, with Dallas, St. Louis, and Chicago’s high point totals, but the relatively anemic Eastern Conference is allowing the Islanders to shine. They’re likely to make the playoffs; even if the Devils or Penguins knock them out of third, the Atlantic Division’s weak performance will allow them to make a wild card play on points.

The penalty differential that the Islanders have cultivated is likely to play a large role, if they can continue it. In the 2014-2015 season, a power play translated to about 3.4 extra shots on goal for the team with the advantage, while being shorthanded tended to cost the team about 1.8 shots. Those numbers are likely to hold up this season as well. In addition, they’ve been ecumenical in their production: Josh Bailey, Kyle Okposo, Marek Zidlicky, Mikhail Grabovski, and Ryan Strome each have 7 points over the 14-game stretch. With Jaroslav Halak battling an upper body injury, Thomas Greiss has given the Islanders little cause for concern. In short, they seem set up to do well in the immediate term.

The Islanders are idle tonight and will see the Maple Leafs again tomorrow night.

NHL Pythagorean Luck through December 10, 2015 December 11, 2015

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Below is a plot of NHL teams’ Pythagorean luck through games played on December 10. The bubbles are scaled to the number of wins each team has.


Shockingly, the 12-16 Calgary Flames are 2.4 wins above their expectation, meaning that they should really be a 10-18 or 9-19 team right now. Meanwhile, the Canucks are suffering at 3.4 wins below expectation; at 11-19, they could easily be a .500 team if a few pucks had bounced differently.

Lucky wins for each team follow:

Team Lucky Wins
Dallas Stars 2.97
Montreal Canadiens -1.23
Washington Capitals 1.58
New York Rangers -1.24
Los Angeles Kings 1.38
New York Islanders -0.77
Detroit Red Wings 1.09
St. Louis Blues 1.08
Nashville Predators 0.30
Ottawa Senators -0.21
Chicago Blackhawks -0.29
Boston Bruins -0.60
Minnesota Wild -0.23
Florida Panthers -0.93
Pittsburgh Penguins 1.28
New Jersey Devils -0.66
Tampa Bay Lightning -1.65
Philadelphia Flyers 1.41
Winnipeg Jets 0.58
Vancouver Canucks -3.40
San Jose Sharks 0.39
Anaheim Ducks 0.13
Arizona Coyotes 1.50
Edmonton Oilers -0.19
Calgary Flames 2.40
Buffalo Sabres -1.26
Toronto Maple Leafs -1.58
Colorado Avalanche -1.38
Carolina Hurricanes 0.23
Columbus Blue Jackets -0.70
League Average 0.00

After 20 Games, How Are The Sabres Distributing Ice Time? November 23, 2015

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On Saturday, the Sabres managed to turn another close game into a decisive loss, and once again the game turned on the power play. Down 1-0 entering the third against Lindy Ruff‘s 16-4 Stars, Tyler Ennis took a crucial holding penalty to allow the Stars onto the power play. Though the Sabres had killed a trio of second-period penalties, they couldn’t take advantage of Dallas’s three penalties (including 51 seconds on the two-man advantage to start the second period). Jamie Benn knocked it in on the power play and then followed up less than two minutes later with a second goal; Antoine Russel had the go-ahead for Dallas in the first period.

Chad Johnson was back in net and saved 29 of 32, but the Sabres only took 22 shots on net. Dan Bylsma is on record as saying the quality, not the quantity, of shots is his aim. Bylsma certainly hasn’t rewarded a high proportion of shots while on ice; he’s rewarded players like Rasmus Ristolainen and captain Brian Gionta, both of whom are well below the 50% mark (meaning that the opposition takes more shots than the Sabres while Ristolainen or Gionta are on the ice), but Ristolainen is averaging almost 23 minutes per game and Gionta is hovering just below 18. In general, more minutes lead to more shots, of course, but there’s little informative about that.

Below is a bubble chart with Fenwick For% on the x-axis; Fenwick For% is the percentage of the total shots taken and attempted while the player is on-ice that were taken by the Sabres. On the y-axis is minutes per game. The bubbles are scaled by shots attempted by the player divided by total time on the ice, to show how influential each individual player’s shooting is on his own numbers.

Bubbles are scaled by shots taken per minute on ice.

Bubbles are scaled by shots taken per minute on ice.

Evander Kane is hovering up around the 20 minute mark; he’s a clear outlier in terms of number of shots per minute, at 64 shots and averaging around 20 minutes per game. He’s also up on top of the Fenwick For%, at 56.0. As far as shots per minute, the decision seems to be hit and miss; of course Zach Bogosian is going to get some ice time to reacclimate despite not taking tons of shots, and Jack Eichel, Tyler Ennis, and Gionta are clustered around the 15-20-minute mark despite their low Fenwick numbers because of their relative importance to the team. Oddly, Josh Gorges is clustered right in there with them; like Ristolainen, his low Fenwick numbers seem to raise flags about his defense. Still, the shots per minute on ice seem to be scattered fairly randomly throughout the lineup.

Not every player is a scorer. It’s distressing, though, to see a player like defenseman Cody Franson taking 75 shots and averaging 18:27 over 20 games when he doesn’t seem to be preventing all that many shots; his 47.6 Fenwick For% is well below the 50-50 mark we’d hope for. Meanwhile, Chad Johnson’s .901 save percentage ranks him 50th out of 68 goalies in the NHL and he’s sporting a 117 GA%, meaning he’s allowed 17% more goals than average. (Linus Ullmark has an 87.) Ullmark may not maintain this consistency, but the Sabres have to protect Johnson if they’re going to keep these tight games from breaking open.

St Louis visits Buffalo tonight. Ullmark will start; his counterpart will likely be Jake Allen, who has a .930 save percentage to Ullmark’s .926 and an 82 GA%. Allen, 25, is a solid young goalie, but so is Ullmark. This one will depend on solid defense …. and, hopefully, avoiding power plays.

Sabres Game 19 Recap: Penalties are costly November 20, 2015

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Despite a solid performance by rookie goaltender Linus Ullmark, the Sabres dropped a shootout loss to the St. Louis Blues last night. Going into the shootout, the teams had played 65 minutes of 2-2 hockey. Sam Reinhart and Ryan O’Reilly scored at even strength for the Sabres; both Blues goals, by Kevin Shattenkirk and Vladimir Tarasenko, came on the power play. Those power plays were costly; Tyler Ennis was penalized 5 minutes for boarding at 5:00 into the first, and Shattenkirk’s goal followed 34 seconds later. In the third period, Jake McCabe was called for hooking 3:24 in, and Tarasenko’s goal came at 4:26. Alex Steen scored the only shootout goal for Saint Louis; O’Reilly, Ennis, and Evander Kane shot and missed for Buffalo. Meanwhile, the Blues’ penalties came in bunches, and the Sabres were woefully unable to take advantage of brief 2-man-advantage conditions in periods 2 and 3.

The Sabres aren’t a bad team on the power play – against a league average of 19.21% of power plays converted, the Sabres convert 22.58% of opportunities into goals. They’re much, much worse defensively, though: the league average penalty kill percentage is 80.79%1, but the Sabres kill only 72.92% of penalties. Buffalo has a miserable 96 power play PDO, which is an awful name for a great stat. In general, save% plus shooting% should average out to about 100, or so goes the theory; teams with lower scores are unluckier, and teams with higher scores are luckier. 96 in power play situations puts then 27th in the league. While shorthanded, they have an abysmal 92.3 PDO, 23rd in the league.

Some of that is mitigated by the Sabres’ low (thus far) penalty numbers – the average team has allowed 62 power play opportunities and the Sabres have allowed only 48 – but the Sabres have allowed 13 goals in those 48 opportunities while the league average is 12 goals on 62 opportunities. Just imagine if the Sabres were chippier and allowed more power plays.

The Sabres have fixed some of their early-season issues with shots, outshooting the Blues 34-29, and Ullmark (minion mask and all) managed to lower his goals against average to 2.31. He’s been remarkably consistent. He can’t, though, carry the team on his back. As a developing rookie, he needs his skaters to take advantage of those 2-man advantage situations. The Sabres had 2:35 of two-man advantage and couldn’t convert. A single goal would have put a second point on the board for the Sabres and another win in Ullmark’s record.

1 Obviously, the league average PP% and PK% have to add up to 100%.