Hockey Abstract Presents. Stat Shot: The Ultimate Guide To Hockey Analytics

Paperback | September 13, 2016

byRob VollmanAs told byTom Awad, Iain Fyffe

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Making advanced stats simple, practical, and fun for hockey fans

Advanced stats give hockey's powerbrokers an edge, and now fans can get in on the action. Stat Shot is a fun and informative guide hockey fans can use to understand and enjoy what analytics says about team building, a player's junior numbers, measuring faceoff success, recording save percentage, the most one-sided trades in history, and everything you ever wanted to know about shot-based metrics. Acting as an invaluable supplement to traditional analysis, Stat Shot can be used to test the validity of conventional wisdom, and to gain insight into what teams are doing behind the scenes - or maybe what they should be doing.

Whether looking for a reference for leading-edge research and hard-to-find statistical data, or for passionate and engaging storytelling, Stat Shot belongs on every serious hockey fan's bookshelf.

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Making advanced stats simple, practical, and fun for hockey fansAdvanced stats give hockey's powerbrokers an edge, and now fans can get in on the action. Stat Shot is a fun and informative guide hockey fans can use to understand and enjoy what analytics says about team building, a player's junior numbers, measuring faceoff success, rec...

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Making advanced stats simple, practical, and fun for hockey fansAdvanced stats give hockey's powerbrokers an edge, and now fans can get in on the action. Stat Shot is a fun and informative guide hockey fans can use to understand and enjoy what analytics says about team building, a player's junior numbers, measuring faceoff success, rec...

Best known for Player Usage Charts and his record-breaking ESPN Insider contributions, Rob Vollman was first published in the fall 2001 issue of the Hockey Research Journal and has since co-authored 10 books in the Hockey Abstract, Hockey Prospectus, and McKeen's magazine series. He writes for NHL.com, and lives in Calgary, Alberta. To...
Format:PaperbackDimensions:352 pages, 9 × 6 × 0.8 inPublished:September 13, 2016Publisher:ECW PressLanguage:English

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ISBN - 10:177041309X

ISBN - 13:9781770413092

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WHAT'S THE BEST WAY TO BUILD A TEAM? By ROB VOLLMANWithout question, the most ambitious topic to tackle with statistical hockey analysis is how to build a team. Not only is team management an extremely challenging subject, but many of its key concepts aren't exactly easy to explain in a meaningful and entertaining way. On the other hand, what's the point of a book like this if it shies away from this type of question?The analysis here is entirely focused on the post-2005 salary cap era, when the dynamics of how teams are built completely changed. For example, the Chicago Blackhawks brilliantly assembled a dominant collection of talent on their way to the 2010 Stanley Cup, but the salary cap forced them to part ways with superstars like Antti Niemi, Andrew Ladd, Dustin Byfuglien, and Brian Campbell, not to mention useful secondary players like Kris Versteeg, Troy Brouwer, and Tomas Kopecky. Somehow Chicago was able to successfully manage its roster and remain competitive by replacing those players with rookies and other bargains, winning yet again in both 2013 and 2015, only to find themselves in exactly the same position they had been in five years earlier. At season's end, Chicago had eight forwards, four defencemen, and two goaltenders under contract for a combined 65 million, leaving the team with just over $6 million to fill six to nine remaining roster spots. Once again, some excellent players had to go and were replaced by rookies and bargain-priced depth players.The Blackhawks are an ideal case study for a guide to building a team in the salary cap era, which could actually be a topic for an entire book. The NHL is a dynamic market of very different players at various points in their careers, with ever-changing market inefficiencies and a collective bargaining agreement (CBA) chock full of both rules and exceptions. There are entry-level contracts, several different types of restricted and unrestricted free agents, and many different types of bonuses as well as trade deadlines, waivers, front-loaded contracts, buyouts, and special rules for players both young and old. How can we sort all this out? The primary concept is to create a team-building model upon which all of these rules can be added. Its primary goal is to maximize the expected value of a team while staying within the team's total cap space and abiding by all the numerous rules and regulations of the most recent CBA. For this model, the central requirement is a method of projecting a player's expected value over the life of his contract relative to his expected cost in cap space. Among other factors, this method will have to weigh each player's offensive and defensive contributions, to allow a comparison between players of different types and positions, to consider the scarcity of each type of player, to project each player's future by including some kind of age curve to make the distinction between up-and-coming players and declining veterans, and to account for a wide variety of additional factors, such as a player's acquisition cost and situations where the opinions of the scouts significantly disagree with the numbers. That may sound like an overwhelming project, and more than a little dry, but it actually makes perfect sense when everything is broken down into bite-sized pieces. It also sheds some fascinating light on our favourite teams and players on a case-by-case basis.Before we begin, it's critical to note that what's being presented in the following pages isn't the only team-building model, nor is it the perfect one, but it will fully represent what every model needs to look like. If newer and better methods come along for any of its components in the future, such as a better way to measure player talent or a superior projection system, then these methods can be easily substituted for what is included here. Above all, think of everything that is presented in this chapter as more of a way of thinking about the problem, as opposed to being a definitive solution in and of itself. TABLE IMAGEAs a bonus, the completed model will produce a list of general rules and guidelines that apply in the here and now, like how much cap space should be invested in goaltending, and some tricks to getting the most out of free agency. Some of these rules and guidelines will be timeless, whereas others are a result of market inefficiencies that exist only at the present moment but may no longer be valid in the future. That's why the process by which these guidelines are discovered will be of far more interest than the conclusions themselves. After all, Chicago didn't become dominant by following trends that others uncovered years ago; they dominated by discovering and exploiting new opportunities.These discoveries will be referred to as guidelines, instead of strict rules, because we aren't dealing with fantasy hockey teams that are being built from scratch and in a static universe. A front office already has a set of players and contracts from which to start, along with instructions from ownership and requests from the coaching staff. Furthermore, the desired players won't always be available in trade, through free agency, or in the team's farm system, leaving teams to make the best decisions possible with their available resources. That's why no team could ever achieve the perfect model, even if such a thing exists. The most successful team-building process is a dynamic one, with organizations following a set of gradually changing guidelines to forever improve their team one step at a time.Before unveiling the model and exploring the resulting rules and guidelines, let's first take a close look at the salary cap and some of the specific details that are most relevant to what we intend to build.The Salary CapCreating a team-building model would be easier if the salary cap were just a single, predictable sum of money under which the total combined salaries of all the players had to remain-but that would just be too easy.In practice, the NHL's salary cap has many rules, and each rule has many exceptions, most of which change with each new CBA. A player's age, the number of games in which he has played, and the number of seasons during which he has played at least a certain threshold of games are all factors that need to be carefully monitored and considered. To be honest, I'm convinced some of the new conditions were added just so the greater complexity would justify more jobs and higher salaries for the league's lawyers and agents. That's why it's essential for each team to have an expert in cap-related matters on staff, who manages the model at all times. There are a lot of intricate rules and regulations that can be land mines for the unaware, as well as potential market inefficiencies that can be exploited by those who know the finer details. While I'm sure that a comprehensive account of the salary cap and all of its rules would be a real page-turner, it is thankfully far outside the scope of this book. There are, however, a few significant details with which we need to be familiar before we can build the model. Starting at the beginning, the NHL salary cap was introduced during the 2005 lockout. Well, reintroduced, actually-there was an NHL salary cap in the pre-Original Six days. Today's cap is known as a hard cap because there is no allowance for going over. A team that has run out of cap space doesn't pay a penalty; it would simply have to play its remaining games with fewer players, as the Calgary Flames did late in the 2008-09 season.6The NHL's hard cap varies from year to year and quite unpredictably. It is calculated as a percentage of the NHL's revenues from the previous season, with a current minimum of $64.3 million. Initially, 54% of all hockey-related revenues went to the players, which increased to 57% in the 2013 agreement.NHL SALARY CAP, 2005-06 TO 2015-16SeasonSALARY CAPChange2005-06$39,000,000New2006-07$44,000,000+12.8%2007-08$50,300,000+14.3%2008-09$56,700,000 +12.7%2009-10$56,800,000 +0.1%2010-11$59,400,000 +4.6%2011-12$64,300,000 +7.6%2012-13$70,200,000 +9.2%2013-14$64,300,000 ?8.4%2014-15 $69,000,000 +7.3%2015-16$71,400,000 +3.5%The salary cap for the 2015-16 season is $71.4 million, which is almost twice what it was when it was first introduced, for the 2005-06 season. That quickly rising salary cap is like a life raft for poor general managers. Deals that really don't make sense today could make sense down the line, as the deal's total percentage of a team's overall cap space decreases over time. Once that cap ceiling starts to stabilize, the teams with the most effective models will truly have the greatest advantage over the teams who frequently overpay. Individually, there is also a player limit of 20% of the team's overall cap, or $14.28 million for the 2015-16 season. At the time of writing, the highest individual cap hit is $10.5 million for Chicago's Patrick Kane and Jonathan Toews. Remember that it's the cap hit that must remain below $14.28 million, not the salary. A player's cap hit is calculated as his average salary over the length of his current contract, so adding some lower-paying seasons at the end of the deal can reduce the annual cap hit. Kane and Toews are actually being paid $13.8 million in the 2015-16 season, for instance, but only $6.9 million in their final two seasons, which is the legal minimum of 50% of the highest-paid year. This is known as a front-loaded deal, and it's a perfectly common, legal, and legitimate way to reduce a player's annual cap hit-even if he retires prior to playing out those final, low-paying seasons. But watch out-the retired player's cap hit will continue to count if the contract went into effect after he turned 35. This is just one of the many points written in fine print (to create more jobs). Even without this clause, a veteran who plays out one of the lower-priced seasons may be frustrated if his subsequent contract doesn't include some extra compensation for that. This was the case with Daniel Alfredsson, a career-long Senator who spent his final season with Detroit after being displeased when he wasn't sufficiently rewarded for playing out a $1 million season with Ottawa in 2012-13.As for term, there's also a maximum contract length of seven seasons, with an additional year allowed if the player is re-signing with the same team. Once again, there are some special job-creating exceptions. Players who sign their first NHL contracts, which are called entry-level contracts (ELCs), are limited to three-year deals or less, depending on their age. Furthermore, these players have their salaries capped at $925,000 plus an additional signing bonus capped at 10% of their initial salary. Even with additional performance bonuses, which can reach $2 million, ELCs are obviously the most affordable types of contracts and should be timed carefully to maximize a player's value.These, and all other types of bonuses, do count against the cap. However, teams are allowed to go over their salary cap on performance-related bonuses, which may or may not occur, and carry them over into the next year. The down side of this practice is that it could leave a team with less cap space with which to work the following season. This was exactly the case for the Boston Bruins, who had $4.2 million of their 2014-15 cap space used up by a bonus earned by Jarome Iginla the previous season, a player who had since moved on to the Colorado Avalanche. Oh, and the Bruins missed the playoffs by two points that year. Doh!There is also a cap floor, incidentally, which can be safely ignored in any model designed to produce champions. It's the individual league minimum that's more relevant to the model, because that's the cost of a replacement-level player. Even if a player isn't worth it, every NHLer must be paid this league minimum, which will increase far less gradually after the 2016-17 season.INDIVIDUAL LEAGUE MINIMUM SALARY, 2005-06 TO 2021-22SEASONLEAGUE MINSEASONLEAGUE MIN2005-06$450,0002014-15 $550,0002006-07$450,0002015-16 $575,0002007-08$475,0002016-17$575,0002008-09$475,0002017-18$650,0002009-10$500,0002018-19$650,0002010-11$500,0002019-20$700,0002011-12$525,0002020-21$700,0002012-13$525,0002021-22$750,0002013-14$550,000What does this mean for the model? Since a team dresses 20 players for each game, 18 skaters and two goalies, even a team of replacement-level players will use up $11.5 million of the team's total cap hit (in 2015-16 and 2016-17). Teams are allowed three additional players on their active roster, pushing the total up to just over $13.2 million. That means that our model is all about how a team should invest its remaining $58.2 million in cap space, or roughly $2.53 million per player. Signing too many players for a greater sum of money could expose teams to some risky situations and send them in search of cap relief.Cap ReliefWhat can teams do with a bad contract? Beyond the previously discussed front-loaded deals, here are a few ways teams can achieve a little bit of cap relief. 1. SEND A PLAYER TO THE MINORSHistorically, useful but high-priced players were sent to the minor leagues, more specifically the American Hockey League (AHL), in order to avoid the player's cap hit. New York's Wade Redden was one prominent example in 2010, along with Sheldon Souray, Jeff Finger, and Mike Commodore in the following seasons. As of the 2013 CBA, this no longer works for any player who is on a one-way contract (one that pays him the same salary regardless of where he plays), which is the case with most NHL regulars. In this case, the cap relief is limited to a maximum of $375,000 over and above the league minimum salary. That's not much cap relief at all, but it does explain why those making around $950,000 are more likely to be sent to the AHL by cap-strapped teams, since a higher-paid player doesn't offer any further cap relief. And, as before, there is an exception for players who were 35 or older at the time their contract took effect, who provide no cap relief at all, regardless of where (or if) they play. For added risk, NHL players sent to the minors, either to reduce the team's cap hit or because they aren't contributing, must clear waivers. That process allows every other NHL team the option of assuming that player's contract in return for an almost trivial monetary compensation for those rights. Prior to the new 2013 CBA, players also had to clear waivers upon their re-entry to the NHL, at which point they could be claimed by other teams for half the annual cap hit. While the discontinuation of that particular clause might have killed some of those lawyer jobs, there is still a rather complicated set of regulations that exempt players under age 25 from having to clear waivers at all, based on when they played their first season and their number of career games played. Though all of the exact details aren't necessary to build our model, teams must keep a keen eye on every player's status, especially as they approach one of those cut-offs. For example, one key threshold for rookies is 11 NHL games, at which point a player is defined as having played his first NHL season for this and several other rules. That's why you'll find that many first-time NHLers are limited to only 10 games in their first season. 2. LONG-TERM INJURED RESERVEIf a player is expected to miss at least 10 games over at least 24 days, he is eligible to be placed on long-term injured reserve (LTIR). While that player's cap hit still counts, the combined cap hits of any replacement players don't count toward the team's cap, except for any portion that is over and above the injured player's own cap hit. These injury replacements are also exempt from the waiver-clearing process described earlier.Remember that only long-term injuries can provide any kind of cap relief. Therefore, it is improper to consider a player's cap hit on a per-game basis, since there is no relief for shorter and more occasional injuries, and certainly none for healthy scratches.Since the cap relief applies only to replacement players, some teams trying to reach the cap floor seek out such players on purpose, like Marc Savard for the Florida Panthers or Chris Pronger for the Arizona Coyotes. On the flip side, some teams don't care about the underlying salaries and just want the cap relief, which leads to bizarre trades like Toronto acquiring the injured Nathan Horton from the Columbus Blue Jackets, to free up the cap space, in exchange for the otherwise useful but overpaid David Clarkson. This may give us fans a chuckle, but I wonder how it must feel to be the guy actually traded for someone who isn't playing anymore . . . It's probably a little bit like high school felt for me.3. RETAINING CAP SPACE IN TRADEIt isn't always easy to find a trading partner willing to take on a bad contract, with those aforementioned exceptions, which is why there is the option to retain a portion of a player's cap hit when making a deal. As of the 2013 CBA, teams can retain up to half of a player's cap hit when trading him, to a maximum of three contracts per team and totalling no more than 15% of the team's cap space. Entering the 2015-16 season, for example, the Toronto Maple Leafs are retaining portions of Carl Gunnarsson's and Phil Kessel's salaries, leaving space for one more, while Carolina is similarly retaining salary for Winnipeg's Jay Harrison and New Jersey's Tuomo Ruutu.Retaining salary can make it easier for a team to clear up most of a bad contract's cap space and can sometimes come with other advantages. The Arizona Coyotes, for example, received an excellent collection of prospects and picks at the 2015 trade deadline, when they agreed to retain half of Keith Yandle's salary upon trading him to the cap-strapped New York Rangers. To an extent, that makes cap space essentially an asset that can be exchanged like any other.4. BUYING OUT THE CONTRACTThe most common way that a player's cap hit can be reduced is by buying out his contract, thereby making him an unrestricted free agent. In this case, the team will continue to carry a cap hit that is two-thirds of the player's total multi-year deal, but it will be spread out over twice as many seasons. If the player is 26 or younger, it is further reduced to only one-third of the original deal's total cap hit.Using the Toronto Maple Leafs as the example once again, they agreed to carry a combined cap hit of $5.33 million over four seasons, for an average of $1.33 million per season, when they bought out the final two years of Tim Gleason's contract, which was scheduled to carry an annual cap hit of $4 million. Gleason's buyout made sense only if the Leafs felt that they could get a better player with the remaining $2.67 million of cap space, in order to justify dealing with $1.33 million of so-called dead money for four seasons. Given that Gleason ultimately signed for $1.2 million in Carolina, it stands to reason that the team was indeed better off with the extra cap space than with Gleason's services. And yes, I have noticed that I've used Toronto as an example of bad contracts as frequently as I have used Chicago for good ones-but it's unintentional, I assure you.5. RETIREMENTSFinally, retirements end a player's cap hit, but with one notable exception. If the player turned 35 prior to when his contract began, then his cap hit will continue to apply for the entire original duration of the deal. This so-called Mogilny rule means that the cap hit of the older veterans will count whether that player is active or not. If such a player retires or leaves for the KHL, buying him out is the only way to free up (a portion of) that cap space. Such contracts should therefore be considered very carefully.Summing it all up, teams can achieve a certain degree of cap relief using some combination of front-loaded contracts and these five methods, but it can result in a lot of so-called dead money down the road. High cap hits at the end of a front-loaded contract, buyouts, retained salaries, and the previously mentioned carried-over bonuses could result in a team having a lot less cap space with which to work. Dead money should be carefully monitored, and it's a key variable in a team's salary cap model.The Hockey Abstract Team-Building ModelThe first rule of hockey analytics is that winning is what matters, and the second rule is that goals scored and allowed are the only factors that affect winning. If that sounds familiar, then you have probably heard of Alan Ryder, who crafted 10 such rules back in 2008.7 This means that there is no single best way to build a team. Whether a team is built around scoring goals or preventing them, whether it's based on a few franchise players or a well-balanced lineup, or whether it is linked to elite goaltending or generational scorers, goals are goals. There are, however, easier and safer ways to build that team.Managing a team's roster in the salary cap era is somewhat like managing a financial portfolio. Although it's a simplistic and insensitive way of visualizing the task, the players can be thought of as stocks, and the goal is to manage the performance of these limited resources. That's why the model requires a way to measure a player's value in a very specific way. It must be expressed relative to a replacement-level player, in terms of cap space, and it must be projected over the entire duration of a player's deal. This requires using the player's history, comparable players, and some kind of age curve to calculate each individual's expected value.Projecting Expected Player ValueThe central component of a team-building model is a statistic that will measure a player's value, in terms of cap space, and project it up to eight seasons in the future. On the whole, that is no easy task, but it becomes far less daunting when that entire process is broken down into single, manageable steps.There are a lot of ways of going about this, some of which may prove simpler or more useful than mine. That's why I'll be generously referencing and summarizing the work of others, to provide those additional perspectives and detail. I'll also walk through how you can complete each of these tasks for yourself, in case you have your own ideas about how to fine-tune the approach or wish to update the model in the future, as circumstances change. In essence, this will be like a cooking recipe, except that the step-by-step instructions will include the purpose of each task and what happens if you increase or decrease each ingredient or select a substitute. Let's begin.1. CAPTURING PLAYER VALUE IN A SINGLE METRICThe first ingredient is a way to measure the performance of every player with a single number. Years ago in the NHL, and still today in other hockey leagues, the only way to accomplish this objective was with some combination of points and plus/minus, but we have come a long way since then. Hockey may not have progressed quite as far as baseball in being able to measure all of a player's different types of contributions in a single metric, but there are several modern options available from which to choose, including, in chronological order:Points allocations (PA), the first of its kind, introduced in 2002 by my co-author Iain Fyffe.8Goals versus threshold (GVT), introduced in 2003 by my other co-author, Tom Awad. (Apparently this was my unwritten prerequisite for being a contributor to this book.)9Player contributions (PC), also introduced in 2003, by Alan Ryder.10DeltaSOT, the first shot-based and context-adjusted option, which Tom introduced in 2010.11Point shares (PS), introduced by Hockey Reference's founder, Justin Kubatko, in 2011 and inspired by DeltaSOT, PA, GVT, and PC.12Total hockey rating (THoR), the second shot-based metric, introduced by Mike Schuckers and James Curro in 2013.13dCorsi, the most recent of the shot-based metrics, introduced by Steve Burtch in 2014.14Wins above replacement (WAR), which is a GVT-like statistic calculated completely differently, introduced by Andrew Thomas and Sam Ventura in 2015.15If none of these are to a team's liking, there is always the option of developing a new catch-all statistic, a process that was explained in the inaugural edition of Hockey Abstract, along with the details of all but the most recent metrics listed here.16 In fact, I know of a few front offices that have already gone this route, in some cases many years ago.In this book we'll use GVT because of its longer and more established history, its use elsewhere in this and previous books, and the accessibility of the data, but, mostly, because I'm pretty sure I'd get an earful from Tom if I went with one of the others.While a goal-oriented, results-based statistic like GVT will serve nicely for forwards and goalies, I'm not as comfortable using it to measure the effectiveness of defencemen. Over the years we have learned from several analysts, most recently from Domenic Galamini, that defencemen have very little influence over their team's on-ice shooting and save percentages, and therefore over their team's on-ice scoring.17 Quite frankly, it's a little unfair to measure their value around goal-based factors that are beyond their control. That's why possession-based statistics are far more appropriate for defencemen than the goal-based GVT, especially those that are adjusted for contextual factors like a defender's linemates, opponents, manpower situation, the zones in which he's used, and so on. To avoid another earful, I've chosen one of Tom's other statistics as a substitute, deltaSOT, which he has kindly modified for our purposes in a fashion compliant with the additional points that follow. The beauty of this team-building model is that it can be constructed to use any of the other options instead (assuming Tom doesn't have your phone number) or even a superior catch-all statistic that is developed in the future. Each option has its own strengths and weaknesses, but the only key requirements are that the chosen metric measures all of a player's contributions in a single number and that it can be calculated relative to a player's cap hit.2. ESTABLISHING REPLACEMENT LEVELWhen a player leaves an organization, for whatever reason, the team doesn't play a man short-the departing player is immediately replaced with someone else. Similarly, a newly acquired player will push his weakest new teammate out of the lineup. That's why a player's value shouldn't be measured relative to zero or the league average but to the difference between him and the next-best available hockey player at his position. That's a concept generally referred to as replacement level.Calculating a player's value relative to a replacement-level player is the most common way for a catch-all metric to take scarcity into account. That means even a theoretical player of constant abilities would have an overall value that fluctuates from year to year with the availability of alternatives. For example, there are a lot of great defencemen available some seasons, while there have also been years where many of them were hurt, retired, left for the KHL, or struggled through vicious slumps. A blueliner's value would definitely go up in those latter cases.So how is replacement level determined? In its simplest form, it is a bar that is established at whatever level the best applicable non-NHL player is performing. For example, it could be considered the 61st-best goalie, the 181st-best defenceman, the 361st-best forward excluding prospects, or, depending on the context, the 31st-best starting goalie or the 121st-best top-four defenceman. These can be determined using team depth charts, cap hits, assigned ice time, or one of the aforementioned statistics in a raw form.In practice, it's not nearly that simple to calculate the league's true replacement level. If a starting goalie is lost, most of his starts go to the backup, not the AHLer who gets called up. Likewise, a top-pairing defenceman plays about 25 minutes a game, many of which get divided among his teammates in his absence, leaving only about 15 minutes to trickle down to his replacement. That drops even lower for forwards, as a newly promoted fourth-line option would be lucky to get to play more than nine minutes a game. In short, comparing a player directly to a replacement-level option is actually overstating the problem in most situations.Not only is replacement level contextual, it is also dynamic. As a population of a certain type of player gets richer, that replacement level goes up, since the number of opportunities remains fixed. Likewise, replacement level goes down when significant numbers in that group get hurt, retire, or otherwise leave the available pool because teams still need the same number of players every year. And yes, replacement level would most certainly drop during the next NHL expansion, when the number of openings increases. How do you think Teemu Selanne and Alexander Mogilny each scored 76 goals in 1992-93? This variable nature of replacement level is why it's important to recalculate every season, in order to keep the overall team-building model up to date.In the case of this particular model, Tom has defined replacement level for GVT and deltaSOT as being about 75% of the league average, taking all factors into account. That is by no means a universal consensus, as Alan Ryder's player contributions, for example, adopts the concept of a marginal player based on 58% of the league average.18 GVT presents a player's value not in absolute terms and not relative to the league average but in terms of how well the team would perform in his absence. That is a key concept and exactly what the VT stands for in GVT (i.e., versus a threshold). For example, Sidney Crosby's 20.4 GVT in 2014-15 measures his value relative to how the Penguins may have done without him. Without Crosby, players like Evgeni Malkin, David Perron, and Chris Kunitz would have been leaned on more heavily, while Blake Comeau and Nick Spaling would have moved up the depth chart, and someone like Jayson Megna or Andrew Ebbett would have secured a regular fourth-line NHL job alongside Craig Adams. However coach Mike Johnston chose to manage his absence, the end result would be that Pittsburgh's goal differential would decrease by 20.4 goals that year-presumably mostly in lost scoring, in this specific case.Does 20.4 goals seem realistic, even as an upper bound? As a sober second thought (not that I've been drinking), consider the results Gabriel Desjardins discovered when he looked at all the NHL teams between 2002-03 and 2007-08 that went without one of their top players for a significant length of time. A season-long absence of this mixed group of top-line forwards yielded a net effect of roughly nine goals.19 That's not atypical of a top-line forward's GVT and not out of line with the 20-goal value of a franchise player like Crosby.While there is yet to be a consensus on the precise level of a replacement player, including the methods by which it should be determined and/or calculated, we can estimate that it is somewhere between 58% and 75% of the league average in today's NHL. Although individual team circumstances may vary, we're using the upper bound of that range in our model-and one that is recalculated each season.3. PROJECTING THE FUTUREThus far, we have studied metrics that measure how effective a player was in the past, not how good he is today nor how well he's expected to perform in the future. Therefore, this model needs a way of converting that historical information into an estimate of a player's expected performance this season and over the remaining years in his entire contract.The basic blueprint for predicting a player's upcoming season from his past is the Marcel method, introduced by prominent baseball and hockey analyst Tom Tango back in 2005. It's a three-step process thatstarts with a weighted average of a player's three most recent seasons;regresses that player's performance toward the league mean, based on games played (we'll explain why and how in a moment); andapplies an age adjustment to account for developing rookies and declining veterans.With regard to the first step, Tango proposes a weighting of 5-4-3, while I prefer a 4-2-1 approach that assumes that every season's data has twice the predictive power as the season previous. In this case, that means multiplying a player's 2014-15 GVT by four, adding his 2013-14 GVT multiplied by two, and finally adding his 2012-13 GVT (scaled to an 82-game schedule) straight up before dividing the entire sum by seven. While closer to it, this end result is not an accurate reflection of a player's actual present-day skill, because an observed performance is partly the result of the player's underlying true talent and partly a result of random variation. That is, when Crosby scored 84 points in 77 games in 2014-15, it was mostly because of his own incredible talent but also because of random chance. After all, he could have just as easily finished with as few as 70 points or as many as 100 or more.Raw statistics can be perfectly suitable for explaining the past, but whenever the past is going to be used to predict the future, historical data should be adjusted to remove the effect of random variation, leaving only the reproducible skill component. To do otherwise is to waste your time.So how much random variation is there in a particular player statistic? That all depends on how repeatable the player's performances have been. Traditionally, that's estimated by dividing the available data in two and seeing how well the two halves correlate.If the two halves have no correlation whatsoever, then it's a completely random event, and we should simply expect the league average in the future.If the two halves correlate very little, then we should assume that future production will be far closer to the league average than to the observed results.If the two halves have a strong correlation, then we should assume that the future performance will be closer to the observed results than to the league average.If the two halves correlate perfectly, then we can assume that random variation plays no role at all, and we can use the observed results as a basis for a projection, with no regression whatsoever.Bear in mind that this isn't a hockey concept, but one of basic statistics that applies equally to everyone and everything. You can go outside and measure yourself taking long jumps, for example, and figure out how much random variation is involved by comparing your odd-numbered jumps to your even-numbered jumps. You can even figure out at what point skill has more influence on your results than random chance. Or, I suppose, you can do something more productive with your life than we have and go take in a show or take your special someone out dancing. To each their own.Getting back on the topic of this model, I calculated the correlation for GVT's three-year weighted average. Between the 2005-06 and 2008-09 seasons, there were 647 forwards who played in those four consecutive seasons. The correlation between a weighted average of their GVT through their first three seasons and that fourth season was a solid 0.65 (on a scale of 0 to 1), meaning that the observed performances involved mostly skill. There is a still a noticeable element of random variation, which can be addressed by regressing everyone's data toward the league average by one minus the square root of the correlation, which gives us 19%.20 Again, that is not a hockey concept but a long-standing formula in the world of statistics that was established by Sir Francis Galton well over a century ago and without any knowledge of what "hockey" even is. These types of concepts can make a lot more sense with an example. Let's use Chicago's Jonathan Toews, who posted a GVT of 18.9 in 2014-15, 19.1 in 2013-14, and 15.7 in 2012-13 (pro-rated to an 82-game season). Multiplying 18.9 by four, multiplying 19.1 by two, and taking 15.7 straight up and dividing the total by seven results in an estimate of 18.5. To remove the potential impact of random variation, we add 81% of his 18.5 to 19% of a league-average GVT of 4.9 to yield a GVT of 15.9. That's the number we would use in the model as an estimate of his current-day performance.One final technicality is to take the sample size of games played into account. Consider a simple statistic, like points per game and the lockout-shortened 2012-13 season. Toronto's Joffrey Lupul scored 18 points in 16 games, or 1.13 points per game. Obviously that result was a combination of both skill and luck, especially compared to Alex Ovechkin, who scored at roughly the same rate that year over a sample three times that size. This data was far more reliable in predicting the future for Ovechkin, who scored 1.01 points per game the following season, than for Lupul, who managed 0.64. Simply put, the data should be regressed toward the league average to a greater extent based on how limited the sample size is.Finally, bear in mind that I've presented only the simplest possible form of statistical regression. Different and/or more sophisticated approaches can be adopted instead, especially ones that don't make the same assumption that NHL players fit a normal distribution curve. The key concept is that historical data should not be taken at strict face value when used to project the future. Random variation must first be quantified and removed using statistical regression, and it's really not as daunting a task as you may have feared.4. ADJUSTING FOR AGEPlayer performance isn't static. Younger players will develop, older players will decline, and the model can take that into account by incorporating an age curve. For example, on July 9, 2014, Chicago re-signed its two superstars, Jonathan Toews and Patrick Kane, to identical eight-year extensions that carry annual cap hits of $10.5 million. While these are doubtlessly worthwhile contracts in 2015-16, for players at age 27, will they remain so in the 2022-23 season, with players at age 34? If not, will that late decline be bad enough that it cancels out today's early benefits? While that's essentially unpredictable on an individual basis, age curves can be used to figure out when and by how much players will decline, on average. Building age curves is a little bit trickier than it may appear to be at first glance. Indeed, my first pass through this section was long enough to be a full chapter in its own right. Even the venerable hockey statistician Alan Ryder, who I was fortunate enough to have review my work, had to take a break halfway through to get some air and walk his dog.Given the dry complexity of the topic, I had to find a way to make this section a little bit snappier and decided to simply leverage what my baseball colleagues had discovered years ago. After all, statistical baseball analysts have about a 20-year head start on us, during which time they have explored how athletes age in considerable detail. Consequently, they have found solutions for a number of problems, such as survivorship bias, selection bias, and annual changes in league scoring levels, all of which can also be applied to age curves in hockey.Let's back it up and briefly start from scratch. At first glance, the obvious way to build an age curve is to simply calculate the league average for the target statistic, grouped by age. That's how Steve Burtch initially built an age curve for goalies, basing it on the average league save percentage for each age.21 However, he quickly noticed that goaltending statistics didn't appear to drop with age. Why? Because any goalies who dropped below replacement level were demoted to the AHL or retired, so his calculation only ever included the great goalies who continued to play well enough to keep their jobs. Indeed, about a third of the goalies in his age-35 bucket were current or future Hall of Famers, far more than we'd expect from the age-25 group.Survivorship bias, as this is known, can sneak into an age curve in any number of ways. For example, Eric Tulsky ran into it when studying the effect of age on power-play scoring rates.22 Since virtually any decent offensive player will get the opportunity to work with the man advantage at age 25 but only the truly gifted will continue to enjoy such assignments in their twilight seasons, power-play scoring rates will appear to increase for players well into the 30s, as the mediocre players drop off and only incomparable talents like Jaromir Jagr and Teemu Selanne remain, or "survive."One way around survivorship bias is to find a way to actually include the non-survivors in the calculation, much as Gabriel Desjardins once did by including a player's (translated) AHL and IHL statistics in a study of how a player's scoring rate changes from ages 21 through 29.23But I can sense you reaching for the dog's leash, so let me jump to the more elegant solution from baseball, the delta method, which involves creating matching pairs of adjacent seasons. Tango describes this process of building an age curve as calculating the average season-to-season difference (delta) in the chosen statistic for all players who competed in at least a certain numbers of games and grouping them by age.24For example, Toews scored 0.89 points per game at age 25 and 0.81 points per game at age 26, for a difference of ?0.08 points per game. That's called a matched pair. By taking the average of all matched pairs for players going from age 25 to 26, we can get an indication of the average increase or decrease in a player's scoring rate at that age. Of course, scoring can also be measured on a per-minute basis or in terms of percentages or even in absolute terms, but you get the idea.The whole principle is to isolate age as the only variable in the equation, so that any change in scoring can be attributed solely to that one factor. Although a player's statistics can change from one season to the next for any number of reasons, these factors should cancel out over a large enough sample size, leaving age as the only remaining variable. For example, some players will score more because they had better linemates, but a roughly equal number will suffer a downgrade in playing conditions, and it should all average out. We will therefore be left with the assumption that any changes in that group's average statistics were due to their one remaining variable: age. That adjustment can then be applied to the scoring totals of any of today's 25-year-olds to predict how he'll do in the upcoming season. There is still one particularly notable issue with this assumption that I simply can't skip over, and it's caused by puck luck. As we have already covered, any observed performance, such as Toews scoring 0.89 points per game, is actually a combination of both the player's own skill and some random variation, and that random variation won't completely cancel out. Since observed performance has an obvious impact on opportunity, that means that both skill and luck will determine whether or not a player gets the opportunity to play the following season, and therefore the opportunity to form another matched pair. That will result in an uneven distribution of puck luck in the first half of a matched pair, especially as the sets grow older. At the risk of getting your dog some exercise, let me explain this a little further. Ideally, we need our collection of matched pairs to include roughly equal numbers of players who had hot and cold seasons, so that their luck will cancel each other out, just like all the other factors, and leave age as the only variable. But, in reality, many unlucky players don't get the opportunity to play the following season, especially the older veterans. Similarly, borderline NHLers who had a lucky season will get the opportunity to keep playing. The net effect is that there are a lot more lucky seasons in the first half of the matched pairs than the second. That will pull down the average season-to-season change at that age. This is a type of bias known as selective sampling.Let's illustrate this with an example. Ville Leino scored 15 points in 58 games for Buffalo in 2013-14. A portion of his disappointing season was due to a dose of bad luck that saw his team score on just 3.9% of its shots while he was on the ice at even strength. Since those poor results prevented him from landing an NHL job the next season, he disappeared from our list of matched pairs. With league-average luck, Leino may have scored 30 points in 2014-15, which would slightly boost the age curve. The impact doesn't always have to be so dramatic that it knocks a player out of the lineup entirely; an unlucky season usually takes on the more subtle form of pushing a player down the depth chart.Until statisticians have the power to instruct coaches on whom they should play, the solution is to identify and remove the impact of random variation from a player's statistics prior to forming the matched pair, leaving only the skill component. This is known as regressing toward the mean, as explained in the previous section.One last adjustment to be mindful of when building age curves is the year-to-year fluctuations in overall league scoring levels. Even a single season can have a big impact on a number of statistics, especially in the wake of a league expansion or a major rule change. Consider annual fluctuations in save percentage, for example. Returning to Burtch's work on goalie aging curves, he accounted for the variable nature of goaltending statistics by basing his age curve on "the average change in save percentage by standard deviations from the seasonal mean for each age group."25 In other words, rather than look at how a goalie's save percentage changed from year to year, Burtch calculated the difference between a goalie's save percentage and the league average and how that changed for each goalie at each age. This allowed him to base his study on a far larger volume of data going all the way to when save percentage was first officially recorded back in 1984, despite the significant fluctuations that occurred throughout the 1980s and 1990s.Now there are a lot of age curves out there-too many, in the eyes of Alan Ryder and his dog-and I have summarized many in this section. Those of you who have already read these many pages on age curves probably can't imagine that there's actually still more ground to cover. Suffice it to say, all age curves that I covered follow the same basic pattern. Most players hit their peak by age 24 or 25 then decline gradually until age 30, at which point their performance can begin to tumble more noticeably, with the risk of absolute collapse by age 34 or 35. All team-building models should take that into account. Now why didn't I just write that up front?5. INCORPORATING INDIVIDUAL CAP HITSConverting the chosen metric(s) into dollars isn't nearly as difficult as it sounds, because hockey's 3-1-1 rule states that every three goals scored or prevented results in one point in the standings (and costs $1 million in cap space, but we'll revisit that momentarily). That means that any metric that is recorded in terms of goals, wins, or points can be converted to cap space quite easily. In fact, that's exactly the basis for the cap-adjusted version of GVT I unveiled way back in 2009, dubbed goals versus salary (GVS).26 Since GVT is measured in goals a player scores or prevents relative to a replacement-level player, like an AHL call-up, a player's GVS can be calculated using the following simple formula:GVS = GVT ? (cap hit ? league minimum) × 3Essentially, to calculate a player's break-even GVT, subtract the cost of a replacement-level player (the league minimum) from his cap hit and then multiply that total by three goals per million dollars. Then a player's GVS is that individual's actual GVT minus this break-even point.Notice that this calculation allows for a negative result, which introduces the key concept of a negative value player, something Sean McIndoe wrote about last season.27 Essentially, he uses the term to describe a player that may (or may not) be an otherwise useful and productive member of the lineup but who has a cap hit that is so steep that his overall value to the team is less than his cap-based peer group. This reality will be reflected by a negative GVS, which isn't to suggest that he is a bad player but merely that his contributions came at a higher cost per goal.While hockey's 3-1-1 rule is a handy way of estimating value on the fly, the team-building model should never include fixed numbers like that. The variables should be recorded with more precision and recalculated every season. Even today, the rising cap space and league minimums have actually made that handy rule a significant overestimate.How can we objectively figure out the cost per win for ourselves, independent of metrics like GVT? One method, popularized by Gabriel Desjardins in 2011, is to take the total amount of money that is spent on all players over and above the league-mandated minimum and then divide that by the number of points in the standings that all those players earned.28 The key point here is that a team composed exclusively of replacement-level players would not finish with zero points. After all, even the lowly 2013-14 Buffalo Sabres, who were arguably the worst non-expansion team in several decades, still managed 52 points. Since the league average is 91 points, that means that each team's $60 million in cap space above and beyond what it would take to pay a 23-man roster at the league minimum has to secure about 40 points. That brings the estimates closer to $1.5 million per point-and rising. Unfortunately, hockey's 6-2-3 rule doesn't have quite the same ring to it.Applying this kind of approach to every season since the cap was introduced back in 2005, it appears that the cost per point has already doubled. Why? Because the cap ceiling has been rising far faster than the cost of a roster full of replacement-level players. The following table includes every variable in the calculation, including the league salary cap, the league minimum, what it would cost to build a 23-man roster at that league minimum, the amount of cap space left over, and the cost of each additional point in the standings (which is achieved by dividing by 40 points).THE COST FOR A POINT IN THE STANDINGS, 2005-06 TO 2015-16SEASONSALARY CAPLEAGUE MIN23-MAN ROSTERCAP SPACE LEFTCOST/POINT2005-06$39,000,000$450,000$10,350,000$28,650,000$716,2502006-07$44,000,000$450,000$10,350,000$33,650,000$841,2502007-08$50,300,000$475,000$10,925,000$39,325,000$983,1252008-09$56,700,000$475,000$10,925,000$45,775,000$1,144,3752009-10$56,800,000$500,000$11,500,000$45,300,000$1,132,5002010-11$59,400,000$500,000$11,500,000$47,900,000$1,197,5002011-12$64,300,000$525,000$12,075,000$52,225,000$1,305,6252012-13$70,200,000$525,000$12,075,000$58,125,000$1,453,1252013-14$64,300,000$550,000$12,650,000$51,650,000$1,291,2502014-15 $69,000,000$550,000$12,650,000$56,350,000$1,408,7502015-16$71,400,000$575,000$13,225,000$58,175,000$1,454,375The cost for a point has gone up in nine of the 11 years of the CBA's existence. It may finally be levelling off, especially since the upcoming rise in the league minimum means that a roster of 23 replacement-level players will cost $14,950,000 in 2016-17 and $17,250,000 in 2021-22. Of course, such a team would be in violation of the league's cap floor, but it remains a valid theoretical construct for the purposes of these calculations.Now that the final digit in hockey's 3-1-1 rule has been explained (and invalidated), let's tackle where the first number comes from. The simplest estimate is to divide all goals by all (regulation time) points. This may vary from season to season, but it's roughly 6,720 goals divided by 2,460 points, which equals 2.73 goals per point.A more visual explanation of why we believe it takes three extra goals to earn one additional point in the standings comes from Eric Tulsky, in one of his very first contributions to the world of hockey analytics.29 He simply built a graph with every NHL team's goal differential on one axis and their points in the standings on the other axis, and he observed that every three goals resulted in approximately one extra point. I've included an updated version of that chart here so we can see that for ourselves.

Table of Contents

Foreword

Introduction

What's the Best Way to Build a Team?

What Do a Player's Junior Numbers Tell Us?

Who Is the Best Faceoff Specialist?

Who Is the Best Shot-Blocker?

Who Is the Best Hitter?

Who Is the Best Puck Stopper?

Everything You Ever Wanted to Know About Shot-Based Metrics (But Were Afraid to Ask)

What Was the Most One-Sided Trade of All Time?

Questions and Answers

Conclusion

Glossary

About the Authors

Editorial Reviews

"Stat Shot demystifies advanced stats, giving beginners an easy-to-follow introduction, while providing deeper understanding for the hardcore stat geek." - The Hockey News"This book is a must read for fans looking to dive into the world of hockey analytics as it provides a great historical overview of the work that has been done and challenges fans to think contextually when evaluating statistics." - Winging it in Motown"Whether you're a hardcore believer in advanced statistics in the realm of ice hockey, or are merely curious and open-minded, Stat Shot will provide illumination about some area of the game that you never really considered, or maybe even challenge some of your preconceived beliefs." - Flames Nation"Analytics are here to stay in hockey and so is Rob Vollman, who gives us all something to think about with his original thinking in Stat Shot." - Bob McKenzie, TSN Hockey Insiders"With Stat Shot, Vollman has found a way to take readers into deep water in hockey analytics in an easy and at times humorous way. Considering where analysis of the game is heading, this is a must-read for those who want to join the conversation and dig deeper into what's really happening inside the game." - Jeff Marek, Sportsnet"Rob Vollman is one of the pioneers in the hockey analytic community. His vision and perspective on hockey has created many convincing discussions in the evaluation of today's teams and players. Rob's work is highly respected throughout the hockey world." - Jim Nill, GM Dallas Stars"Rob Vollman is one of the leading voices in hockey analytics, and I've learned a lot from him." - Jamie McLennan, TSN"Vollman's work is both groundbreaking and practical-he makes sense of hockey analytics for everyone." - Kelly Hrudey, Hockey Night in Canada and Rogers Sportsnet"Nobody does a better job of breaking down complicated analytics for a mass audience than Rob Vollman. This isn't just a must-read for hockey fans, it should have a place on the shelves of every NHL front office." - Craig Custance, ESPN.com and NHL Insider"Stat Shot does what many say is an impossible task; it makes the world of hockey analytics not just accessible, but fun. It's like math delivered with a wink and a smile." - Damien Cox,  journalist/broadcaster"If you see it in a bookstore, and pick it up, you might find yourself entertained and informed." - Sports Book Review Centre