How Can Hockey be Changed for the Better?

Putting aside any argument about whether hockey can be improved or not, I've been thinking about rule changes that could be put in place that at least some people would think improved the game. Some of the proposals below I think would be good for the game and some I don't, but I'm going to lay them out here without imposing my opinion as best as I can and I'd like to know what other people think. Please note: these are not my proposed rule changes, I'm just collecting several here that I've seen elsewhere.

Introduce a Goal Verification Line
This is one that was play-tested in the AHL a few years back. I think it was just as the NHL was getting back on the ice after the lost season, but I don't remember for sure. Basically, a goal verification line is a line drawn exactly one puck-width behind the goal line between the goal posts. The picture below is from the original article I read about this many years ago. I saved the picture because I thought it was interesting, but I have no idea who to credit. I think it was NHL.com.

The idea here is that if the puck is even touching the goal verification line then it is a valid goal. This is supposed to help on those goals that are too close to call even on replays because the goal line itself is blocked from view by equipment, etc.

Cease Allowing a Penalized Player to Return to the Ice After a Goal
The NHL has explicitly stated that many of the rule changes instituted since 2005 are intended to increase scoring (e.g., smaller goalie pads, the introduction of the trapezoid behind the net, and the moving of the blue lines closer to center ice). One thing that would greatly increase scoring would be eliminating the rule that allows a player serving a minor penalty to return to the ice after their team is scored on.

Believe it or not, the rule allowing a penalized player to return to the ice at that point was only instituted in 1956 (http://www.rauzulusstreet.com/hockey/nhlhistory/nhlrules.html). Prior to that time, a minor penalty lasted a full two minutes and the penalized team was a man short for that entire time (http://www.nhl.com/history/060656.html). The rule was modified to allow the penalized team to return to full strength because the Montreal Canadiens had gotten so good on the power play that they would regularly score several times in the two minutes (http://media.nesn.com/2011/03/top-10-most-important-rule-changes-in-nhl-history/5/).

Don't Allow a Shorthanded Team to Ice the Puck
As far as I know, a team  that is shorthanded has always been allowed to ice, or "rag" the puck. In fact, until 1925, play was not stopped regardless of whether the icing team was shorthanded or not (http://www.rauzulusstreet.com/hockey/nhlhistory/nhlrules.html). The idea behind taking that privilege away is once again to increase scoring. I've also heard that there are kids' leagues that don't allow a shorthanded team to ice the puck (this to encourage skill development), so it's not an unheard-of concept.

Institute No-Touch or Hybrid Icing
This one is a hugely hot topic. Many levels of play use a "no-touch" icing rule, meaning that icing is called as soon as the puck crosses the goal line, regardless of whether there is a player on the attacking team there to play the puck first or not. A lot of people have been supporting this idea because of the number of injuries sustained by players when they get knocked down during a fast race for the puck. The resulting crash is often quite awkward and results in the player slamming into the boards at 25 mph or so. Don Cherry has advocated no-touch icing for many years. (If you don't know who Don Cherry is, don't sweat it, but most hockey fans have at least heard of "Grapes".)

The argument against no-touch icing refers to maintaining the purity of the game and the excitement of the race for the puck (which is rare, yes, but exciting nonetheless). Those that argue this side are not ignoring the safety issue. The argument is that the key to preventing the often catastrophic, career-ending injuries is better enforcement of the rules about interference, checking from behind, and boarding. The idea is that if a player knows that he'll be called for a penalty if he so much as touches his opponent in that vulnerable situation then he'll lay off.

In an effort to keep the race for the puck but eliminate the injuries incurred by crashing into the end boards, the concept of "hybrid" icing was developed. Many leagues have adopted this approach, including the NCAA, and it was play-tested in the AHL a few years ago. The exact rules for hybrid icing vary from implementation to implementation, but the basic idea is that there is an invisible line across the ice somewhere far from the end boards (frequently between the face off dots). Icing is called if the usual requirements are met and the first player to cross that invisible line is a defender. It is not called if the first player across that line is an attacker.

Institute Stiffer Penalties for Fighting/Ban Fighting
If no-touch icing is a hot topic then fighting is scorching. On the one hand, you have the people who want to ban fighting, who are pointing out head injuries that occur as a result of fights and that most 'enforcers' are really not skilled players and don't belong in an elite league. On the other hand, you have those who say that fighting is part of the game and that those who want it removed aren't real hockey fans (this is frequently stated using crude insults, which kind of undermines the argument  if you ask me).

Among arguments for keeping the fighting rules just as they are in the NHL, tops is probably "it's part of the game; leave it alone." The next argument usually points out that if pests such as Sean Avery or Matt Cooke don't know that they're going to have to fight the opponents' enforcer then they'll continue to make dirty hits and attempt to injure other players. (Different topic, but Matt Cooke has actually changed his ways. It would be nice if people noticed that.) Finally, the argument is frequently made that hockey is a rough sport and by removing fighting, you remove some of the 'manliness' from it. (Frequently, a reference is made to figure skating at this point.)

Arguments for banning fighting altogether include the injury argument mentioned above as well as opening up the spots currently taken by team enforcers for more skilled players. Fighting is not a part of the game, this side argues, because if it was then the game wouldn't stop whenever a fight broke out and there wouldn't be any penalties. Besides, look at international hockey (such as the Olympics and World Championships); fighting is banned in international hockey and you see some of the best hockey you ever will at that level. This side also points out that dirty plays exist now, so there's no basis for arguing that fighting deters dirty plays. In fact, many fights are started after a good, clean, solid check is made, so the argument can be made that fighting actually discourages good, solid checks, which are undeniably part of the game.

Eliminate the Shootout
The shootout is apparently very popular amongst fans, but there are those who don't like it because they feel that it's not really hockey. Hockey is a team sport, the argument goes, so something so individual as a shootout should not decide a game. Either allow for endless overtimes or accept ties. 

Replace the +/- with the Adjusted +/-
Okay, so I'm probably the only one who has ever put this forward as a 'rule' change, and it's not even technically a rule, just stats. Still, I think it would be cool to see it adopted.

There are many more proposed rule changes out there, some serious, some not-so-serious, but this is probably plenty to get any conversation rolling. Please feel free to share other ideas or to discuss those mentioned above in the comments section. Please note, however, that I do not tolerate name-calling in the comments. Any comments that include ad hominem attacks will be deleted.

The Adjusted Plus-Minus

With the start of hockey season (though no NHL season just yet) upon us, my thoughts have turned towards the sport I love. This post may not be of much interest to those of you who aren't hockey fans (and maybe even to those who are but couldn't care less about stats). You have been warned.

The plus-minus; what it is

The plus-minus (or +/-) is relatively new in the hockey statistics world. It was first employed by the Montreal Canadiens in the 1950s and started being tracked by the NHL in 1968. That's over 40 years, but most fans had never heard of it until the last 15 or so (if ever). These days you hear it mentioned several times in most broadcasts, but what is it?

As with many sports, the most well known hockey statistics (goals and assists) are geared towards measuring a player's offensive ability. The plus-minus is intended to be a measure used for defensemen and defense-minded forwards. The statistic is calculated by taking the number of non-power play goals scored by the player's team (so even strength and shorthanded goals) while he/she is on the ice and subtracting the number of non-power play goals scored by the other team while he/she is on the ice. For example, suppose Roy was on the ice for 3 goals scored by his team, one of which was a power play goal. This gives him +2 (since the power play goal doesn't count).If the other team also scored 3 goals, none of them on the power play, then his plus-minus for the game is +2 - 3 = -1.

Once you get used to it, this is pretty straightforward. The idea is that a better defensive player will have a higher plus-minus since the other team will score less when he is on the ice and the offensive players on the team will likely score more since they can be confident that the defense is being taken care of.

What's wrong with the plus-minus

The plus-minus has a number of issues, but there two that I want to address here:

The first is that the plus-minus does not take into account the amount of time a player spends on the ice. A player that spends 20 minutes playing and earns a +1 is seen as contributing the same as a player who plays just 1 minute and also happens to earn a +1. This is not equitable.

The second (and, in my opinion, bigger) problem is that there is no baseline. Suppose Roy's team in the example above lost that game 14-3. Roy's -1 is actually quite good. On the other hand, if Roy's team won the game 14-3 then Roy's -1 is really bad. This becomes worse as you look at season or (shudder) career plus-minus. Someone who is very bad but plays for a very good team can have a season plus-minus that looks great, while someone who is very good but plays for a very bad team can have a plus-minus that looks horrible. (Take John Tavares, for example. His season plus-minus in 2011-12 was -6. That's on the minus side, so looks bad, but when you take into account that the Islanders were 26th in a league of 30 and that they were outscored by their opponents by 55 goals (251-196), his -6 is actually pretty decent. It's not great, but he's also a very offensively-minded player and it is 5th place on the team among players who played at least half the season.)

To make matters worse, stats pages and commentators compare plus-minus values between players on different teams as if that means anything. Is Chris Kunitz's +16 (5th among the Pittsburgh Penguins for players playing at least half the games in 2011-12) really better than John Tavares' -6? That's debatable since the Penguins outscored their opponents by 65 goals (273-218).

To make the plus-minus more comparable between teams, we need a baseline to work from. That's where my proposal for the adjusted plus-minus comes in.

Proposed solution: adjusted plus-minus

The goal behind the adjusted plus-minus is to create a statistic with a known baseline which is therefore comparable for players on different teams. The formula is below, but the idea is simple: adjust everyone's plus-minus so that a player that is neutral (in the sense of not directly affecting which team has more goals in the end) will have an adjusted plus-minus of 0. A positive adjusted plus-minus will show that the player is contributing to the team's success and a negative adjusted plus-minus will show that the player is not (or may, in fact, be contributing to the team's failure). The formula takes into account the player's time on the ice (TOI) as well as the overall performance of his team, thus addressing the two issues described above.

First, some notation:

EVTOI = the player's time on the ice when the teams are even strength. This includes 5 on 5, 4 on 4, 3 on 3, as well as times when one team has pulled the goalie in order to gain a one skater advantage. If either team is on a penalty kill then that time is not counted in the ESTOI.

EVTOT = the team's total time playing at even strength. (Obviously, this is the same for both teams in a single game, but not over the course of many games against differing opponents.)

TPM = the player's team's plus-minus. This is a total of all even strength and shorthanded goals scored by the players team minus all even strength and shorthanded goals scored by the opponent. In short, compute the traditional plus-minus for the entire team as if it was one person.

PPM = the player's traditional plus-minus.

Okay, here's the formula:

Adjusted plus-minus = PPM - (TPM * ^EVTOI/_EVTOT)

The logic is as follows:

^EVTOI/_EVTOT gives you the fraction of the team's even strength time during which the player was playing. Shorthanded goals for or against wind up acting as a bonus or penalty for the player, but power play goals either way do not affect them, so that time is not included in the ratio. In this way, the time that the player spends on the ice is taken into account in the statistic.

Multiplying ^EVTOI/_EVTOT by TPM gives you the player's "expected" plus-minus. This is the plus-minus that would be earned by a player who is neutral in the sense described above. This is very likely to be a fractional amount; I've been rounding to two decimal places in my personal calculations, but any number of places could be chosen.

Subtracting the expected plus-minus from the actual plus-minus gives a statistic with a baseline of zero. A neutral player would be "even" (an adjusted plus-minus of 0), no matter how good or bad his/her team was.

Example with full statistics available:
Let's get some more information about Roy's game. The actual score for the game was 9-4, Roy's team lost, scoring once on the power play and giving up two power play goals against. The team's total plus-minus, then is TPM = 3 - 7 = -4. (3 because they scored 3 non-power play goals and 7 because they gave up 7 non-power play goals).

During the game, Roy played a total of 17:30 of ice time: 0:45 on the penalty kill, 1:15 on the power play, and the rest at even strength. That makes Roy's EVTOI = 15:30 (17:30 - 0:45 - 1:15).

During the 60:00 game, the team spent 4:30 shorthanded and 5:15 on the power play. Thus the teams even strength time is EVTOT = 50:15 and Roy's ^EVTOI/_EVTOT = ^15:30/_50:15 = 0.31 (approximately).

Multiply that by the TPM and you get 0.31 * -4 = -1.24. This is Roy's expected plus-minus. His adjusted plus-minus, therefore is -1 - (-1.24) = +0.24. Roy was actually a little bit of a help to his team in this game, in spite of the -1 rating.

How to adjust for rec league:
Of course, most of us don't have that detailed TOI data to refer to. In my rec league, I've simplified the calculation to simply take the approximate fraction of the game I play based on the number of people playing my position. If I'm one of three centers, for example, then I make the fraction 1/3. If I'm one of 5 defensemen, I make it 2/5 (two defensemen on the ice at any time divided by 5 total). Other than that, I compute it just as described above.  

Update 9/24/2012: As an example of what a difference it can make, I offer my own stats from the SCHL for summer 2012. That was a rough session for my team; we went winless and were completely blown out multiple times. My plus-minus for the summer was -21. My adjusted plus-minus was -0.70. I was still on the minus side, which doesn't please me, but at least it shows that I wasn't a complete drag on the team, which a -21 might seem to imply at first.

Please feel free to ask any questions and/or offer any critiques of this proposed statistic. I've been using it for myself for years, but I'd like to know what other people think.