Why is it so hard for good teams to get better? Looking at the value of a marginal goal

Posted on July 3, 2014 by Matt Cane — Leave a comment

We’re now three days into free agency and with most of the marquee names on the market already signed on for the coming year and beyond, teams and fans alike are starting to look over their rosters trying to figure out whether they’re sitting in a better position than they were on June 30th. With some teams the improvement is fairly obvious: after finishing 8th in the West last year the Dallas Stars have added Jason Spezza and Ales Hemsky and looked poised to take a run at the Blues and Blackhawks for Central Division supremacy. The Anaheim Ducks also made a big splash, bringing in Ryan Kesler from the Canucks while only sacrificing Nick Bonino and Lucas Sbisa. Having added a big name to take some of the pressure off of Ryan Getlaf, should we expect a similar bump to elevate the Ducks to President’s Trophy champions next year?

This type of situation comes up frequently not just in the NHL but across professional sports: fringe team adds a few key pieces and turns into championship contenders, while a team that finished the previous year on the edge of winning it all can’t turn their added potential into dominance. Ultimately, what this comes down to is that the value of a given player isn’t the same to each team: adding on additional goals (or allowing fewer goals, depending on which way you look at it), has different effects on a team’s record depending on how good they were before. Adding Brad Richards to the Blackhawks isn’t the same as adding Brad Richards to the Blue Jackets would be. To put it another way, the value of a marginal goal decreases as a team’s goal differential increases (and in a non-linear manner, as we’ll see later).

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2014 Free Agent Preview: Forwards

Posted on June 26, 2014 by Matt Cane — Leave a comment

It’s almost free-agent season, the time of year when most fans are salivating over all the possible superstars their team might add, while the analytics fans of the world are mostly hoping their GM’s don’t screw up too badly. In celebration of this most joyous terrifying time of year, Puck++ is proud to present our First Annual Puck++ Players for Purchase at a Premium Price Preview™.

Rather than going through every available free-agent though (since in the time it would take me to write up most of them will end up signing), I’m going to focus on 15 forwards and 10 or so defencemen (to be determined when/if I get around to writing part 2) who are likely to garner significant interest, or at least significant media attention.

For each player I’m going to present 3 sets of data: 1) His traditional stats from the last 3 seasons (G, A, Pts., +/-); 2) His xGF20, xGA20 and xGD20 numbers for the last 3 seasons (the details on how these numbers are calculated can be found here and here); and 3) His 5 most comparable players, using xGF20 and xGA20 for the past 3 years. The comparable players are determined by looking at which players had seasons most similar from an xGF20 and xGA20 point of view over the past 3 years. As an aside, if you want a quick cheat sheet to evaluate xGD20 numbers, here are the average numbers based on ice-time in the 2013-2014 season:

Line xGD20
1 0.09
2 0.05
3 0.00
4 -0.05

All salary data quoted below is from CapGeek. All standard stats from HockeyDB. Blame them (or my poor transcription) for any errors.

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Context Neutral Player Evaluation: Examining Defence and Calculating xGD20

Posted on June 23, 2014 by Matt Cane — 1 Comment

A few months ago I wrote about xGF20, my attempt to isolate a player’s offensive ability from his teammates abilities and the luck involved in shooting percentages in small samples. At its core, xGF20 is based on 3 reasonably repeatable individual measures:

1) A player’s rate of individual shot generation;

2) A player’s rate of altruistic shot generation (that is, the shots he generates for his teammates); and

3) A player’s individual shooting ability (regressed based on position)

Using these three metrics, xGF20 presents a player’s expected on-ice goals for per 20 minutes of ice-time, assuming his teammates shoot at a league-average rate. While the calculation is slightly more complicated than what I’ve just presented, it does allow us to make comparisons between players without worrying about who their linemates were. If you put Jason Spezza on a line between my brother and I (sorry Ben), you’d expect his on-ice GF20 to drop dramatically through no fault of his own. Although xGF20 is very similar in theory to Relative CF20, taking into account a players own shooting ability allows us to differentiate between those who just throw the puck at the net without purpose (David Clarkson) and those who take more shots because they’re better at it (Alex Ovechkin).

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Adjusting Save Percentage for Team Effects

Posted on May 29, 2014 by Matt Cane — Leave a comment

As anyone who’s looked at evaluating goalies before knows it’s not a pleasant task. Even ignoring the inherent extreme variability in game to game or year to year statistics, a goaltender’s numbers can be heavily influenced by the 5 skaters in front of him. While when we look at forwards ordefencemen we can get around this issue by looking at WOWY or Relative numbers, we don’t have that same luxury with goalies. Even if we were to compare a goalie to how his team did when he had the night off our analysis is complicated by the fact that most teams tend to use only a small number of goalies each season. While we may be able to say that a team posted a better save percentage with their starter than their backup that doesn’t give us a good sense of whether the starter was great or the backup was terrible – we’re still stuck trying to isolate the team effect.

One method we can use to get an estimate of the team effect is their skill at shot prevention. Teams that are better defensively are likely to give up fewer shots, although somewhat paradoxically those shots are more likely to go in. But what if we looked at things from a different point of view: what if rather than focusing on a team’s ability to prevent shots in general we adjusted for who was taking the shots? After all, shots by defencemen tend to go in less than half as often as shots by forwards, so it stands to reason that if a team can prevent opposing forwards from putting the puck on net that their goalie would likely experience a higher save percentage because of that.

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Round 2 Preview and Round 1 Review

Posted on May 1, 2014 by Matt Cane — Leave a comment

The second round of the Stanley Cup playoffs begin tonight (in 37 minutes at the moment I started writing this, to be precise), and after an exciting first round it’s nice not to have to wait even one night to get back into the action. In the first round our model had a good showing, correctly predicting the winners of 5 of 8 series while missing on the Avs (incredibly high shooting percentage), Lightning (replacement level backup playing for Vezina candidate) and Blue Jackets (not really clear that either team was trying to win the series).

While some might not view 5 of 8 as a great percentage, from the point of view of the model it was actually spot on. Since our model picks not only the winners but also the probability of each team winning, we have to look at the predictions it makes in the context of each team’s predicted winning percentage. After all, the model was much more confident in its pick of Anaheim (71.8%) than of Columbus (53.6%). Because our predicted win probabilities aren’t 100%, we shouldn’t get all of the series right and we should actually be worried if it does: if we’re able to consistently pick all of the winners even if we don’t view them as 100% favourites it means that our model is actually underestimating the probability, and not giving us a good view of each team’s odds.

To illustrate this further, imagine we predicted 5 series: in 3 of them we predicted that the favourite would win 66% of the time (2 out of 3 times), while in the other two we viewed each team as having equal odds (50%). In this world we’d expect to get 3 games right: 2 of the 3 66% series, and 1 of the two coin flips. We can get an estimate of how many games we think we should get right by simply adding up the probability of the favourites (0.66 + 0.66 + 0.66 + 0.5 + 0.5 = 3)

Looking back at our model, we can estimate how many series we should have predicted correctly by applying a similar analysis. Using our round 1 odds for all of our favourites our expected number of correct predictions is: 0.685 + 0.556 + 0.536 + 0.594 + 0.634 + 0.635 + 0.718 + 0.549 = 4.91. So when we got 5/8 right, we’re actually right around where we’d expect to be (admittedly due to the  small sample size we won’t always be that close, but you get the point).

All of which is to say that the model did a pretty good job at round 1, perhaps better than it would appear at first glance. With that beings said, let’s take a look at what we expect to happen in Round 2.

Team 3rd Round Stanley Cup Win Cup
Boston Bruins 80.0% 64.6% 37.9%
Montréal Canadiens 20.0% 10.2% 2.7%
Pittsburgh Penguins 54.7% 14.5% 4.1%
New York Rangers 45.3% 10.7% 2.5%
Minnesota Wild 17.8% 4.5% 1.2%
Chicago Blackhawks 82.2% 48.7% 28.2%
Anaheim Ducks 62.9% 32.5% 17.3%
Los Angeles Kings 37.1% 14.3% 6.0%

Looking at the numbers, if you’re a fan of the exciting, close series we saw in round 1 you’re likely in for a bit of a disappoint. Both Boston and Chicago are viewed as overwhelming favourites by the model, with each team coming in above 80% to move on to the conference finals. Unsurprisingly, the Hawks and Bruins are also heavy favourites to take home the Cup at this point, with the model seeing only a 34% chance that Lord Stanley’s mug won’t end up in Beantown or the Windy City.

The only other team with a decent shot at the cup, at least according to our predictions, are the Anaheim Ducks, who enter their series against the comeback Kings as 63% favourites. Los Angeles obviously cares not for the rules of probability though, as they were down to 8% odds to move on and less than 1% to win the cup after losing 3 straight to start their series with the Sharks. While the Ducks struggled at times versus the Stars, the model still favours their high shooting percentage game over the pure volume effort that the Kings tend to put forward.

The closest series, and the one this author is most excited for, is the Penguins-Rangers series set to start tomorrow in Pittsburgh. While the Pens definitely struggled at times in their series versus Columbus, and while Marc-Andre Fleury has done little to combat his reputation for choking in the clutch (not that clutch play is really a thing, but that’s another story) the team led by the Cole Harbour Kid enters their series as slight favourites over the Blue Shirts. Similar to the Ducks-Kings series this looks to be another quality versus quantity matchup, with the Pens relying on Sid the Kid and Evgeni Malkin to drag their woeful bottom 6 past New York’s Fenwick machine (oh and perhaps the greatest goalie of his generation, Henrik Lundqvist).

Coming back to our little probability exercise that we started with, let’s take a look at how many series we expect the model to get right this round. Taking the expected win probabilities of the Bruins, Penguins, Ducks and Blackhawks we should get approximately 2.8 series correct, or roughly all but 1. So there you have it: you’re now prepped for Round 2, and there’s actually still time left to grab a beer before the anthem!

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2014 Playoff Predictions

Posted on April 15, 2014 by Matt Cane — Leave a comment

Tomorrow night marks the start of the NHL playoffs and so to continue an annual tradition (once is a tradition, right?) I’ve put together the World Famous PuckPlusPlus Playoff Prediction Preview (hurray, alliteration). In the lockout shortened season, our model managed to do fairly well, correctly predicting all of the conference finalists as well as the eventual Cup winner and runner-up so we’ve set a pretty high bar for ourselves for this year.

Our model last year was relatively straightforward, looking at each team’s Fenwick For %, Shooting Percentage, and Save Percentage to determine the probability of winning an individual game. For this season our model still uses the same variables, but I’ve slightly tweaked how they’re fed into the model: rather than looking at each team’s save and shooting percentage individually, the model now looks at the home team’s “Shooting Advantage” and “Save Advantage”, which are simply the difference between the home team and the visiting team’s shooting and save percentages respectively.  The rationale for making this change was to ensure that the shooting percentages for each team were given the same weight in determining the outcome of the game (and likewise for each team’s save percentage). I’ve also set up the model to use the save percentage of the expected starter for each team, to remove the effect of the back-up goalies on our predictions.

With all that explanation out of the way, let’s take a look at what the model thinks is going to happen over the next few weeks. The table below shows each teams odds of advancing to a given round of the playoffs, as well as their odds of being the eventual Cup champions. Winners of the 1st round are also highlighted in bold

Team 2nd Round 3rd Round Stanley Cup Win Cup
Boston Bruins 68.5% 53.7% 43.0% 27.1%
Chicago Blackhawks 63.5% 47.4% 29.8% 18.8%
Anaheim Ducks 71.8% 47.2% 26.9% 15.7%
St. Louis Blues 36.5% 22.2% 10.7% 5.3%
Detroit Red Wings 31.5% 19.0% 11.9% 5.1%
Los Angeles Kings 54.9% 24.2% 10.4% 4.9%
Colorado Avalanche 63.4% 22.3% 9.3% 3.9%
Columbus Blue Jackets 53.6% 31.9% 11.2% 3.9%
Tampa Bay Lightning 55.6% 16.0% 8.8% 3.0%
San Jose Sharks 45.1% 17.0% 6.6% 2.7%
Pittsburgh Penguins 46.4% 26.8% 8.5% 2.7%
New York Rangers 59.4% 26.3% 7.4% 2.1%
Montréal Canadiens 44.4% 11.3% 5.8% 1.8%
Dallas Stars 28.2% 11.7% 3.9% 1.5%
Minnesota Wild 36.6% 8.1% 2.4% 0.7%
Philadelphia Flyers 40.6% 14.9% 3.3% 0.7%

In the Eastern Conference, and looking at the battle for the Cup in general, the Bruins appear to be the heavy favourites at nearly even money to make the cup and roughly 1 in 4 odds to win the whole thing. Boston’s high odds are driven by 2 things: 1) They’re a really good hockey team, backstopped by arguably the best goaltender in the league; and 2) The Eastern Conference is much weaker than the West this year. The East is so weak in fact, that the model believes the Bruins toughest battle before the cup will be their first round opponents, the Red Wings, who still only have a 31.5% chance of taking down the President’s Trophy winners. After Detroit, there’s not a single team in the East who the model views as having better than a 25% chance of beating the Bruins.

On the Western Conference side, things are a bit tighter: Chicago and Anaheim are a close 2nd and 3rd in overall odds, although neither team has even a 50% chance of getting to the conference finals. The Ducks in particular are a tough team to figure out given their goaltending situation. The probabilities shown above assume that Frederik Andersen starts for the Ducks but if we re-run the numbers with Jonas Hiller in net the Ducks overall odds decrease to 8.1%, while their odds of even getting out of the first round drop 8.5 points to 63.3%.

Speaking of team’s whose odds change dramatically based on who’s in net, the Tampa Bay Lightning definitely need Ben Bishop to get better fast if they want to have any hope of taking home the cup at the end of the year. With Anders Lindback in net, the model views them as only a 55% favourite to get past the Habs in the first round, while with Bishop manning the crease their odds increase to 62.6% (admittedly, Bishop won’t make much of a difference on their Cup odds increasing them by only ~2% as they’d still have to get by the Bruins).

The most interesting teams in my opinion are the Columbus Blue Jackets and Detroit Red Wings. While the Wings are heavy underdogs, if they are able to get past the Bruins in round 1 their odds will skyrocket and they would definitely be the favourites to represent the East in the Cup Finals. Although the model may view a defeat of the Bruins as being less than likely, it is important to note that the Wings seem to be getting healthy at the right time, and may be being underestimated in our predictions.

Columbus, on the other hand, go into the first round as surprising favourites against the Pittsburgh Penguins (Marc-Andre Fleury, this one’s on you). The Blue Jackets are struggling with injury issues of their own however, and unless they can get Nathan Horton, R.J. Umberger and Nick Foligno back they could be in trouble against a Penguins team that is getting some big names back for the start of round 1. Should ‘Lumbus get through the first round though, they’d likely be strong favourites to take on the Bruins in the Conference finals, as they’re predicted to come out ahead in matchups against either the New York Rangers of Philadelphia Flyers.

The least likely team to move past the first round is one that many are predicting to pull off an upset in the first round, the Dallas Stars. Dallas is ultimately a heavy underdog due to the fact that they’re only slightly ahead of the Ducks on the puck possession side, while trailing them heavily both on the shooting percentage and goaltending fronts. Of course as we mentioned above the Ducks advantage in the model is primarily due to Frederik Andersen-facing off against Jonas Hiller, the Ducks are viewed as having roughly the same likelihood of advancing as the Blues and Wild (one of those should offer comfort to Stars fans, while the other-not so much).

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Introducing xGF20: A Context Neutral, Corsi-Based Goal Creation Metric

Posted on March 27, 2014 by Matt Cane — Leave a comment

If you follow the hockey analytics world at all (and since you’re reading this, I’m assuming you do), you likely have a pretty good understanding of, and appreciation for, Corsi. Analysts like to use Corsi because it’s a better predictor of future success than simple goal-based metrics because of the much larger sample that you get to work with. While a team might ride the percentages to score and win more in the short-run, if you really want a good sense of where a team is going to end up you’re better of looking at their Corsi % (more specifically, at their Even Strength Corsi % in close games).

This, however, is problematic for many traditional hockey-types. A common criticism of analytics from the “haters”, is that Corsi doesn’t take into account shooting percentage or the play of teammates and that it isn’t a “be-all-end-all” statistic (not that anyone ever said it was). To a degree, these criticisms are fair: we know that teammates have a large effect on play, that’s why we look at stats like Corsi Rel. In addition, there’s at least some convincing evidence that higher or lower on-ice shooting percentages are sustainable over the longer term. Critics of analytics will argue to no end that goal creation, not shot creation is the key to success. Their view is that the “Corsi Hockey League” and the NHL where goals are scored are different worlds which can’t be bridged by silly things like numbers.

Luckily for those of us more in touch with reality, numbers are actually really good at building bridges (admittedly, this metaphor is going a bit far). Creating a metric that measures goal-creation ability isn’t straightforward, but it definitely can be done. So hold on to your hats as I explain in as long-winded a fashion as is humanly possible, xGF20.

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Breaking Down Corsi: Looking Into Shot Blocks and Misses

Posted on February 11, 2014 by Matt Cane — Leave a comment

The willingness to block shots is one that’s often touted by the media as being the difference between winning and losing. Players who put their bodies on the line are held in the highest regard and with good reason: Fenwick, which excludes blocked shots tends to be a better predictor of future victories than Corsi, which includes them. The key question around blocked shots, as with anything that correlates well with winning, is whether they’re actually repeatable. We know that blocked shots are valuable, but we want to know whether they tend to happen at random or with some predictability.

A few years ago Sunny Mehta looked into shot blocks and misses over the 2008-2009 season and found that there seemed to be an element of skill in blocking shots, while both shot attempts for blocked, and shot attempts for and against missed seemed to be mostly luck. I wanted to update his study, looking at data from the 2008/09 through to the lockout shortened 2013 season and examining to what degree teams had control over blocked and missed shots. I also wanted to take a look at how each metric broke down between forwards and defenseman, to see whether rates varied the groups. Before we start looking at repeatability though let’s go through some high-level numbers.

Goals Shots Corsi MS BS Sh% FSh% BS% MS%*
F 20531 213655 368133 75971 78507 9.6% 7.1% 21.3% 26.2%
D 3087 72347 161722 34534 54841 4.3% 2.9% 33.9% 32.3%
All 23620 286009 529865 110508 133348 8.2% 5.9% 25.2% 27.8%

*(Fenwick-Shots)/Fenwick

Forwards score on roughly 5.5% more of their shots than defensemen, and roughly 4.2% more of their Fenwick attempts. This is an important fact to keep in mind-blocking a forward’s shot is much more valuable than blocking a defenseman’s. With that being said, defensemen tend to have more of their shots blocked, and tend to miss the net more often on the shots that don’t get blocked. This, of course, makes sense-forwards tend to take shots from closer in, leaving less of a chance to get a leg in the way, or to put it wide or high.

We can also look at the numbers another way, breaking down what percentage of each event comes from shot attempts taken by either forwards or defensemen. While forwards take 74.7% of the shots, they only record 68.7% of the missed shots and 58.9% of the blocked shots, while accounting for 86.9% of the goals scored.

Goals Shots Corsi Missed Shots Blocked Shots
F 86.9% 74.7% 69.5% 68.7% 58.9%
D 13.1% 25.3% 30.5% 31.3% 41.1%

With all that in mind, let’s get down to the more detailed stats: first off, let’s look at whose shots are being blocked and who’s doing the blocking.

Shooter Blocked By % of Shooter % Total
F F 21.3% 12.5%
F D 78.7% 46.3%
D F 56.9% 23.4%
D D 43.1% 17.7%
All F 35.9%
All D 64.0%

The results we see aren’t exactly surprising: the majority of the time when a forward takes a shot and it’s blocked it’s a defenseman doing the blocking (78.7% of the time). Similarly, when a defenseman’s shot is blocked, it’s more likely to be blocked by a forward (56.9%) than an opposing defenseman (43.1%). In total, defenseman are doing most of the blocking, accounting for 64.0% of the total shot blocks, with the majority of these blocks coming on shots taken by forwards.

Now let’s look at the repeatability of blocked and missed shots. What we want to get a sense of is whether the ability to block shot attempts or to force a shooter to miss the net is more ability or luck. Similarly, we want to know whether certain teams or players are better at hitting the net than others, and if this is a persistent ability, or random variation. To look into these, I’ve run split half correlations at the team level for each of our four variables of interest (SAF Blocked %, SAF Missed %, SAA Blocked % and SAA Missed %). Split half correlations simply look at to what degree the numbers a team puts up in the odd numbered games predict the numbers for that team in the even numbered games. A higher correlation implies that a particular number is more skill than variance, while a lower number implies the exact opposite. In each table I’ve looked at the overall correlation as well as the correlation for shot attempts taken by forwards and defenseman.

Correlation 2008-2013 Correlation 2008-2012
SAA Blocked (All) 0.71 0.72
SAA Blocked (F) 0.62 0.66
SAA Blocked (D) 0.64 0.61

We’ll start by looking at SAA Blocked %, the percentage of total shot attempts against that a team manages to block. Our results here show a fairly strong correlation, in agreement with what Sunny found around the skill involved in blocking shots. We also see that a team’s ability to block shots from opposing forwards appears to be slightly more persistent than their ability to block their shots from defensemen (note that when we include the lockout shortened 2013 season these numbers flip, but I’m more inclined to leave it out of split-half comparisons due to sample size constraints).

What about at the other end of the ice though? To what degree can teams control how many of their shot attempts for are blocked?

Correlation 2008-2013 Correlation 2008-2012
SAF Blocked (All) 0.57 0.59
SAF Blocked (F) 0.55 0.60
SAF Blocked (D) 0.34 0.34

Once again, we seem to see a fair amount of repeatability in the number, although it’s definitely less than for SAA Blocked. Our data here does seem to differ from Sunny’s conclusions, although the breakdown between forwards and defensemen is much more important in this case. While the split-half correlation is reasonably high for forwards SAF blocked, for defensemen it’s significantly lower.

What this means is that forwards do seem to have some influence over whether or not their shots are blocked, while for defensemen it’s much more random. At a glance, I think these numbers make a lot of sense intuitively: a defenseman is often taking shots from further out than a forward, and while they can obviously avoid firing the puck directly into a forwards shinpads, they don’t have a lot of control over whether a shot hits an opposing defenseman nearer to the net. On the other hand a forward will generally only have to get a shot by one or zero players, which leads to a lot less luck influencing their results.

Correlation 2008-2013 Correlation 2008-2012
SAA Missed (All) 0.46 0.46
SAA Missed (F) 0.39 0.40
SAA Missed (D) 0.26 0.22
SAF Missed (All) 0.48 0.49
SAF Missed (F) 0.38 0.40
SAF Missed (D) 0.31 0.31

Looking at missed shots we see that the repeatability of both SAA Missed and SAF Missed seem to be significantly lower. While the overall and forward missed shots percentages show a higher correlation than defenseman SAF blocked %, the numbers aren’t that encouraging. Knowing the missed shot percentages in the odd-numbered games helps us explain less than 25% of the variance in the even-numbered games. While it may make intuitive sense that some players would be better at hitting the net than others, the numbers don’t really back up that conclusion. Forwards may be able to avoid the maze of legs and bodies in front of them, but once the puck gets by that maze whether it hits the net or not is up to lady luck to decide.

One important thing to note with this analysis is that we’ve only looked at team level data, and only looked at numbers within seasons. What that means is that we can’t really make any conclusions about individual player’s ability to block shots or avoid blocks themselves. Without examining the individual level data, we can’t know whether the repeatability is due to the system a coach has put in place, or some innate ability of the players themselves. We can speculate of course: if I had to bet I’d lean towards blocking shots being a product of a team’s system with there being more of an individual focus on avoiding shot blocks. But without the data to back up the theories that’s all they are-until we can dig down into the details, we just can’t reach any conclusions.

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What’s the cost of icing the puck?

Posted on December 20, 2013 by Matt Cane — 4 Comments

Following the 2004-2005 lockout, the NHL introduced a variety of rule changes intended to increase scoring and bring fans back to the rink. One of these changes which prevented a team that ices the puck from changing their defenders, was aimed at stopping the practice of pinned-in teams from sending the puck down the ice simply to get a line change and a fresh set of legs out. The idea being that giving the offensive team a chance to change and face a set of tired defenders would create a significant offensive advantage. Defensive zone faceoffs are the last place you want to start a shift, with Michael Schuckers estimating that starting in your defensive zone is worth approximately -0.0055 goals. The question that naturally comes up from this idea though is whether there is an incremental cost to a team icing the puck, and what that incremental cost is. Is the penalty for icing the puck simply the defensive zone faceoff, or does the fatigue factor play a significant role?

Using the NHL’s Play-by-Play files from 2010-2013, I identified all icing calls and who the offending team was by looking at the faceoff immediately following the icing and inferring the offending team from the faceoff zone and faceoff winner. After that, I followed Schuckers THoR methodology and calculated how often the team that iced the puck scored a goal in the next 20 seconds (see (a) below) and how often their opponents scored a goal in the next 20 seconds (see (b) below). I should note that this is a major simplification of Schuckers regression model which takes into account numerous other factors when determining the value of an event, but for the purposes of coming up with a rough estimate it should do.

Event Goals
(a) Icing P20

0.0071
(b) Icing Against P20

0.0160
(c) Icing NP20 ((a)-(b))

-0.0090
(d) Zone Start

-0.0055
(e) Icing Fatigue Cost ((c)-(d))

-0.0035

With these two numbers, we can then calculate the net probability of a goal from the point of view of the team that iced the puck, given in (c) above as -0.0090. What that’s saying is that each time a team ices the puck, they’re essentially costing themselves -0.009 goals in the long run. The cost of icing the puck though is made up of two factors though: the cost of taking a faceoff in the defensive zone, and the cost of having tired players on the ice. We know that a zone start is worth about -0.0055 goals from Schuckers work that I mentioned above, so the fatigue cost of an icing is simply the difference between the Icing NP20 (c) and the zone start cost (d), or -0.0035 goals.

This may not seem like a lot, but it’s roughly 3 times the per-play value of home ice advantage as given by the THoR model. What tempers the impact of icing is that icings are a relatively rare occurrence-within our sample there were an average of 6.7 icings per game, which isn’t game changing, but over the course of a full season a team that consistently ices the puck could see this effect add up. Jan Hejda was on the ice for 50 net icings in 2011-2012, which cost his team nearly half a goal between the zone-start and fatigue effects.

Now obviously our estimate doesn’t tell the whole story-there may be some gain to the team that iced the puck that we’re not capturing, as teams often ice the puck when they’re under a lot of pressure in their own zone. But it does illustrate the importance of accurate passing when starting on the attack, and how a missed connection when a team is moving up the ice can end up being more costly than just the lost offensive opportunity.

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The Benefits of the 4-Forward Powerplay

Posted on November 10, 2013 by Matt Cane — 3 Comments

On Friday night I wondered aloud why coaches don’t play a 3F/1D setup during overtime, given the unpredictable nature of the shootout and the single point they’d already guaranteed themselves. And so naturally, as I often do, I started to look into an entirely different (although in this instance at least somewhat related) problem: why do coaches almost always play with a 3 forward/2 defenseman approach when on the powerplay? To me, this seemed like it might be a case of the old wisdom taking precedence over analytical thought. After all, in baseball bunting with a runner on first still remains a popular play, while in football coaches are still hesitant to going for it on 4th down, even though both of these strategies have been shown analytically to be poor decisions in most cases. Perhaps the decision to ice a standard powerplay lineup is another example of coaches playing too conservative when the numbers suggest a non-conventional approach is superior.

And with that, I started to dive into the data to look whether playing 4 forwards on the powerplay really did provide an advantage over the standard 3 forward approach. To do this, I started out by looking at the shooting percentage of teams playing under both approaches from the 2010-2011 season through to the 2012-2013 season. I broke the stats down into 5v3 and 5v4 situations to eliminate any potential contamination from the 2-man advantage situations. While this analysis doesn’t look at whether or not the 4 forward approach generates more or less offensive chances, given the number of shots we’re looking at it should give us a decent sense of whether the 4 forward approach is generating higher quality chances and/or chances taken by higher percentage shooters.

Forwards On-Ice SH Against Sh% FSh% Sh% Lower Sh% Upper FSh% Lower FSh% Upper
3 3 19.2% 13.7% 16.5% 21.8% 11.4% 16.0%
4 3 22.3% 16.2% 19.5% 25.0% 13.8% 18.7%
3 4 11.5% 8.2% 11.0% 12.0% 7.8% 8.6%
4 4 13.0% 9.3% 12.4% 13.7% 8.7% 9.8%

The table above outlines the overall shooting percentage and Fenwick shooting percentage for both 3 and 4 forward approaches in 5v3 and 5v4 situations. The usual caveats about the accuracy of the NHL’s play-by-play data apply here, but the results do point towards the 4 forward approach providing a statistically-significant advantage, at least in the 5v4 case (unfortunately, given the limited sample size we can’t say anything conclusive about the 5v3 case).

But what about the defensive side of things? The obvious counter-argument to the 4 forwards approach is that it decreases the defensive ability of the unit and puts the team at risk of giving up a short-handed goal. And if we look at the data presented in the table below, we see that that does seem to be true: short-handed teams shoot better when they’re playing 4 forwards rather than 3 (note that once again, the 5v3 numbers aren’t significant).

Forwards On-Ice SH Against Sh% FSh% Sh% Lower Sh% Upper FSh% Lower FSh% Upper
3 3 3.0% 2.6% -2.8% 8.9% -2.8% 8.0%
4 3 17.6% 12.0% -0.5% 35.8% -3.4% 27.4%
3 4 7.5% 5.7% 6.5% 8.5% 4.8% 6.5%
4 4 11.3% 8.7% 9.8% 12.7% 7.4% 9.9%

The question that we have to ask then is whether the offensive benefit provided by using the 4 forward approach outweighs the defensive cost. Ideally, we’d look at the Fenwick For/Against rates for both 4 forward and 3 forward situations but I’m too lazy to write a query to pull that data out but that TOI and Shot/Fenwick data isn’t straightforward to put together. We can, however, put together an estimate of how many additional goals a 4 forward approach is worth to an average team by looking at the average Shots For/Against of a team on the power-play and comparing whether the increase in expected shooting percentage outweighs the decrease in expected save percentage.

Avg Shots Avg Goals
For 394 5.97
Against 70 2.63
Delta  3.34

I put together the table above by taking the average 5v4 Shots For and Against from 2007-2012 from stats.hockeyanalysis.com and comparing the expected shooting/save percentages in 4 forward and 3 forward setups based on the data above. As you can see, the benefit of playing with 4 forwards clearly exceeds the risk: teams that played an all 4F approach would be expected to score an additional 3.3 PP goals over the course of an 82 game season, which works out to roughly half a win. This, of course, also ignores any effect on the shot rate that the 4F approach would have. It’s entirely possible that 4 forwards produce more shots per powerplay minute than the standard approach further increasing the value of this approach. In either case it does seem like one of those cases where the aggressive approach should payoff: regardless of the defensive risk that teams are taken by putting a forward on the point, the offensive benefit appears to outweigh it, and in the long run, teams that take this approach should see a non-negligible bump in their powerplay percentage.

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