Fun little dice game you can use in social situations. It’s called ‘Mexico’. You have two six-sided dice, and your score is based on the actual digits facing up rather than the addition. The highest score, a 21 or a ‘Mexico’ comes when a two and a one show up on the table. Next up are doubles—66, 55, 44, 33, 22, 11—and then the single rolls, 65 all the way in descending order down to 31, the lowest possible roll. The idea of the game is to not have the lowest roll in a round.

It’s an interesting probability problem. I didn’t get around to calculating all the odds for all situations, but you get to either pass on the dice or take another roll, up to three rolls, if you’re the first roller in the round. If you take multiple rolls, so do all your opponents. If you end up with a fairly high score you have a good chance of not being the lowest once everybody else has shot during the round, but I found it interesting what scores most people were keeping. A player would pass on the dice almost instantaneously if a ’6′ showed on one dice while they were a little more reluctant if they saw double-3s or double-2s or double-1s, despite those latter rolls being a higher score.

In most dice games, where you add the dice together, the higher rolls are the ones with lots of black dice. Every kid grew up playing Risk and Monopoly and Backgammon where generally, the more numbers the better. ‘Mexico’ flips that around, and if the player is aware of ‘anchoring bias’, they’re less likely to be satisfied even with rolls of 54 or 53, which look like large numbers but are some of the worst in the game.

Every party has the awkward kid over-thinking everything during drinking games, right? Or was that just Kamloops circa 2006-2012?

Either way, I found it interesting which rolls people were keeping as opposed to passing on. Snake eyes, an awful roll if you’re playing Risk, is the 8th best roll in ‘Mexico’ out of 36 possible dice combinations. Years of cultural indoctrination had players during this particular evening still thinking that the one and the one together were a poor roll, as opposed to the 61 or the 54, which just look like higher numbers.

I chalked it up somewhat to the phenomenon that causes most prices to end in a 9. Danny Gray wrote about it extensively last summer:

Anchoring is when people base their evaluation of an item or decision making process on one piece of information. They “anchor” all subsequent analysis to the first piece of evidence they encounter. Any piece of information can act as an anchor. Generally speaking anchoring is a consumer bias, it has the ability to significantly impact the amount people are will to pay for an item.

The lesson we can learn from anchoring is that one piece of information has the ability to define all subsequent analysis of a player. Our first impressions are incredibly powerful and hard to eradicate. Once we have established the value of a player, as a result of either draft position or salary, it is incredibly difficult to alter that perception. Most people are unaware they have anchored themselves to one particular stat or another. We must be aware of our brain’s natural tendency to create anchors and to try and combat it by ensuring our opinions are based on as many relevant factors as possible.

One of the quietest signings this offseason was the New York Rangers’ grabbing of Benoit Pouliot, the former 4th overall pick, and a very solid checking line winger that scores an awful lot considering his role. He’s never been a 20-goal scorer and probably never will be, and I guess some general managers can’t get past the fact that his production doesn’t match his talent level. I figure there’s a certain point in player’s lives where we ought to accept them for what they are rather than what they could be, and I wonder how much more easily Gilbert Brule could have found an NHL job if hockey people were able to accept that he’s pretty much a less physical Boyd Gordon in that he’s probably an effective third liner, but Gordon didn’t score as much in junior. It’s easier to accept that he’s more suited to the role, being a veteran and a checking centre in Dave Tippett’s system for two seasons.

People never fail to point out that hockey’s analytics systems aren’t developed enough to show the marginal difference between two players on different teams, especially if they’re playing different roles with different calibre of teammates. That’s always tough to do considering hockey is a team game of twelve moving human beings (except when Hal Gill is on the ice) and game situations dictate certain strategies are better suited to defending leads or pressing when trailing. The major thing to take away is that the good teams generally have good players. Small, tall, skinny, fat, medium, skates fast, skates slow, it doesn’t really matter if the player just has a good ability to help his team score goals and prevent the same. I think the Rangers signing Pouliot on the first day of unrestricted free agency was overshadowed by the movement of some of the big players that day. He’s an interesting fit for Alain Vigneault, who loved playing the heck out of possession wingers in Vancouver, and it was odd to see Tampa Bay let him go to unrestricted free agency based on the fact he’s never really been a ‘poor’ scorer for his role and doesn’t make a whole lot.

He’s a supporting cast player that provides value to a club. A team realistically has 13 supporting cast roster positions, behind the first line, the first pairing defence, and starting goaltender. I think that depth is crucial, that having three good centremen is preferable to having two, and having three lines that can score is preferable to having two. The reliance of Joel Quenneville on his line of David Bolland, Viktor Stalberg and Michael Frolik was pretty new. A lot of coaches would opt for the more physical Jamal Mayers on the fourth line, since we’ve anchored our belief that the fourth line is for the occasional face-puncher. It’s always fun to see when bottom six forwards have success on good teams when they weren’t tough enough for teams still looking to rebuild. “Spot the former Edmonton Oiler” was a good game during last year’s postseason.

Black Dog Pat is one of the more thoughtful writers on the net. He killed it on Saturday with a post asking why it’s just hockey that seems to ask for unreasonable things from its top tier players:

Its not a strong suit in modern society so to expect it in sport may be asking a little much. People generally defer to authority, its in our general nature. People defer to the government, trusting that they are doing right by us. People trust the corporations who steal from us and the unions that steal from us and the media who have their own agenda. As Dave Nonis has blundered time and again this summer his supporters’ most common refrain is ‘he knows what he is doing, there are only thirty GMs and he is one and what do you know anyhow’.

This ignores the fact that holding a position does not necessarily mean you are good at that position. Mike Milbury. Doug MacLean. John Ferguson Jr. Steve Tambellini. They all say hello.

The best general in World War I, bar none, was a real estate agent from Victoria, Arthur Currie.

I’m not saying I could do the job of a GM, I couldn’t, but the idea that a GM is infallible because he is a GM is so obviously ridiculous its not even worth addressing, similar to the idea that one cannot criticize a GM’s move because one isn’t a GM. That logic leads to this – you could not criticize a band unless you were professional musician, a book unless you were a published author, a business unless you were a businessman and so on.

Pat pointed out that most of the ex-players that appear on panels were usually of the replacement-level variety or backup goaltenders. I’d prefer to not appeal to authority when it comes to NHL experience and success to determine where I get my analysis from. If you’re an ex-player, you’re probably better off breaking down certain systems for us plebes than making sweeping statements about the effort levels of certain players despite not being anywhere near the dressing room when it’s closed off to reporters. Some are quite good at the former, and some are notorious offenders for the latter.

The examples the Pat uses in his post are of current players. A lot of Oilers fans don’t like Ales Hemsky because he doesn’t go to the net and he’s hurt a lot. Not tough enough. A lot of Bruins fans turned on Zdeno Chara’s minus-6 performance in the last three games of the Stanley Cup. Not good enough when it’s all on the line. A lot of Leafs fans want to see the team get rid of Dion Phaneuf and Phil Kessel for reasons beyond “the team is likely to be God-awful next season and you may as well get something for upcoming unrestricted free agents if you aren’t going to sign them to extensions right this second”.

Here in Vancouver, I can remember listening to call-in radio a lot and people would continually complain about Henrik and Daniel Sedin during their first four seasons. To hear them tell it, the Canucks had no secondary scoring between 2002 and 2004, despite the team finishing 1st, 2nd and 7th in goal-scoring by team during those seasons, and Daniel and Henrik’s identical 117 points putting them at 124th among forwards at that time. Consider that there are 90 first line players in the NHL… if you’re looking for second line production, the Sedins did quite well.

But a lot of sports talk radio guys are old white guys that peaked in intellectual curiosity during the 1980s when the two best offensive players the NHL has ever seen were tearing up the league and goaltending innovations had yet to catch up to forwards. Between 1981 and 1992, there were 125 100-point players, while between 1993 and 2004, there were just 52, and just three of those came between 2002 and 2004. I think a lot of criticism directed at the Sedins was just unreasonable expectations based on their draft position at the time and it took them a couple of extra years to develop into elite scorers.

The thing I admire about Brian Burke as a general manager is that he doesn’t hamper teams in the long-term even though he knows that those types of moves could prolong his jobs. He never compromised his principles to sign a big albatross contract to Brad Richards in Toronto, maxing his offer at six years while New York offered nine, and he was under a lot of pressure to trade the Sedins in 2004 and never pulled the trigger, eventually getting fired despite building what was an incredible team to watch. I don’t have a lot of primary sourcing to support this, but I generally remember it as Burke sacrificing his job in Vancouver to keep the Sedins here. Henrik would go on to become the best player in team history and what would probably be a Hall of Fame career if he didn’t play like a wimpy Swede (that was the only forward to not miss a single game between lockouts).

Anchoring is the key here. People place wild dreams on skilled players taken high in the draft and it they aren’t producing early and often. Even non-productive players can have some value on the third and fourth lines, and when teams tend to not put a lot of thought into who they dress in those situations, they’re ultimately putting far too much of the burden on the top talent. I think Phil Kessel is an excellent hockey player and one of the best wingers in the game, but no single player is going to turn any franchise around and lead a team to the playoffs singlehandedly. Lord knows that the Chicago Blackhawks didn’t get to the Finals thanks to the scoring of Patrick Kane and Jonathan Toews, and can you imagine the criticism directed at them if they weren’t backed up by Marian Hossa, Bryan Bickell, Patrick Sharp & Co. for three rounds?

Having star talent is great, and about half the teams in the league have a great lottery talent or two on their roster. There are so many good hockey players in the world, and I think the best teams are the ones that have more than Coke machines on the bottom six and can use its lineup effectively. Anchoring remains a problem for many GMs and fans though, those that can’t separate expectations based on junior production, nor those that can separate expectations for point scoring relative to how players in the same situation are being used.

Hockey is unfortunately a lot like Risk. A good strategy can lose if the rolls aren’t there since there’s so much variance and luck involved in the playoffs and still a lot of variance and luck over an 82-game season. There’s no way to do it perfectly, but you get helped out if you’re aware of the old biases that handcuff other managers into building a roster in a less economical fashion.