March 31, 2007
Upcoming Playoff Series Summary
Ok, so it's a little early, but I got to make sure my code is working for the playoffs before they start. And it's fun to anticipate the postseason.
And the other 7 series. If you go to the web page you will see all 7 series as if they have already been determined, however there is still a lot of variability in the possible matchups and it wont be until the regular season we will know for sure, but these current matchups are the current best guesses.
I made these last year, they have information many other sites don't share or know. The primary interesting numbers on the right (record, GF, GA) come only from games in which both teams made the playoffs. So games against nonplayoff teams are excluded. It should also be noted that shootout win goals and empty nets are not counted. The F,D,G numbers are just a score out of 10 that I give to different parts of the game: Forwards (F), Defense (D) and Goaltending (G). So Vancouver I gave a perfect 10 to goaltending and consider the defense and offense a bit above average. San Jose has excellent forwards and defense and a bit above average goaltending. The current F,D,G numbers are preliminary estimates and are probably not very good. If someone wants to suggest F,D,G values for a certain playoff team let me know in the comments.
The big % number on the left represents the odds that team wins the series based on my current regulation data and performances throughout the regulation season (primarily goal differential). And the topleft is the current season series record. As the series record changes so do the odds so these will be updated nightly. The San Jose  Vancouver series doesn't seem to be a good one for Vancouver, as the home team (Vancouver) has only a 43% chance of winning based on regular season performance.
NYI and Carolina are Out
This means only Toronto and Montreal are fighting for #8
March 29, 2007
Canucks sign Salo
I'm a big fan of paying <$4M for a defenseman. Unless you really know what your getting (Pronger, Lidstrom), your better off getting 2 decent defenseman than one you hope will be amazing (and will likely be injured). There are plenty of examples of overpaid players, but some of the more recent signings are quite embarrassing (Chara, Jovanovski). In fact I would argue that 5 of the 9 defenseman who get more than $5 million per season are significantly overpaid. I was concerned that Salo would test the market and there would be a number of teams who would offer $4.5M+ for him, however it appears Salo would rather stay in Vancouver than anything else.
Happy day for a Vancouver fan.
March 28, 2007
East Playoff Race
March 24, 2007
The cost of Safeway’s Score & Win contest.
I’ve often wondered what the odds of winning the Score & Win contest's $1,000,000 grand prize. Every game you see the ad and know that there is almost no chance of actually winning it (especially with the Canucks who can’t even score 5 goals combined). I can’t imagine what it’s like to know you’re the one who has a chance at a million though. Presumably they’ve got some accountant type calculating the odds and making sure they are able to pay award with the advertising if such an unlikely even occurs. So I’m just going to provide you with the accountant’s math so you all know the chances of winning the big prize.
First I looked at 20022003 to 20052006 data to get this list:
Probability of scoring exactly 1 goal given you scored at least 1 goal
= 0.89279 = P(G=1G>0)
Probability of scoring exactly 2 goals given you scored at least 1 goal
= 0.09583 = P(G=2G>0)
Probability of scoring exactly 3 goals given you scored at least 1 goal
= 0.01043 = P(G=3G>0)
Probability of scoring exactly 4 goals given you scored at least 1 goal
= 0.000953 = P(G=4G>0)
Using the assumption that goal scoring is Poisson, which is proved to be reasonable by Ryder, implies P(G=X) = exp(k)*k^x/(x!).
P(G=1G>0) = P(G=1)/P(G>0)
P(G=2G>0) = P(G=2)/P(G>0)
P(G=1G>0)/P(G=2G>0) = P(G=1)/P(G=2)
P(G=1)/P(G=2) = [exp(k)*k^1/(1!)]/[exp(k)*k^2/(2!)] = 0.89279/0.09583 = 9.3
Solve for k: [with computer]
k = 0.215
You can do the same for 2>3 and get K = 0.32 and 3>4 gets K = 0.274
Since I consider 1>2 to be the most accurate I went with 0.215
The probability of an average player getting 5 goals is:
exp(0.215)*0.215^5/(5!) = 0.000003
The probability that a given player doesn’t score 5 is 99.99969%, so the probability that none of the 18 possible scorers gets 5 is:
(0.9999969)^18 = 99.994%
Or the probability that a player does score 5 in a game is: 0.00005577
Since the prize is an annuity distributed over 20 years it’s only worth about $680,000 when it is won (@ 4% discounting).
Multiply the costs by the odds of winning in a given game:
$680,000*0.00005577 = $38/game
Works out to one 5 goal game every 78 seasons. [Does anyone have a list of 5goal games?]
There are about 2 million possible shoppers (exaggeration) and Safeway has a 30% market share, so there are about 600,000 entrants (assuming they all shop equally often). Making the final value to the individual viewer:
$0.00006/game or 0.006 cents/game.
March 23, 2007
Who is the most valuable player?
When I look for the best players I ask one basic question. What percent of the team’s offence was this player on the ice for? A great player will be on the ice for almost every goal, a horrible player will be on the ice for every goal against. In reality a star forward will see around 50% of a team’s offense (240GF*(1 IGF^{1}/2 GF)*(3 Goals or Assists/4 IGF^{1}) = 90 Points. Do they contribute to that 1 goal out of four in which they don’t get a goal or an assist I would say most certainly they do, is it maybe as large a contribution as the assists? Maybe, maybe not it would depend on the player. In contrast these star players are often on the ice for very few goals against. Now to make things “fair” I’ve excluded goals against when short handed as some star players play short handed and others don’t (their percentage of goals against would be much larger if you play short handed). The difference between the two gives some sort of value of a given player. If for example a player is on the ice for 75% of the goals for and 80% of the goals against, I wouldn’t consider that player as amazing as the one on the ice for 50% of goals for and 40% of goals against. So the difference between the two values equals a sort of “star power” ranking.
The basic equation is quite simple I look at how many goals the player scored on the power play, penalty kill and at even strength and divide by how many goals the team scored in those same situations. For goals against I look at how many goals the player has against at even strength and when their on the power play and compare that to how the team did as well. This can be expressed in an equation as:
GF% = (GF.pp + GF.sh + GF.ev)/ (TGF.pp + TGF.sh + TGF.ev)
GA% = (GA.pp + GA.ev)/ (TGA.pp + TGA.ev)
GF = Goals for, TGF = Team goals for
GA = Goals against, TGA = Team goals against
pp = power play, sh = shorthanded, ev = even strength.
GF.pp = Goals for on the power play
GA.pp = Goals against while on the power play
Score = GF%GA%
TGF and TGA can either be used as the total number of goals over the course of the season or only calculated using games in which the given player has played in. For example, Forsberg has played 40 games I could use
This statistic has the opposite problem to the plus minus statistic in the fact that it will make players on bad teams (teams without depth) look better then they maybe are and players on good teams (teams with depth) look average as when the player is off the ice the team is still producing goals. Therefore, this should be a good balance to a plus minus statistic. This effect does not prevent top players from getting to the top, be they on a bad team or a good team. This statistic, like almost all hockey statistics, suffers from line quality factors, which should be kept in mind. Since I’m looking at total goals for on the power play and even strength I excluded players without power play time, to be specific: power play time/even strength time > 13%. For most players this works out to about 2 minutes of power play time per game.
Last season Joe Thornton won the Hart Trophy and rightly so, with a +25% difference between percentage of offence and percent of defense Joe Thornton ranked number one in his ice time category (Nagy was #1 over all, 1.1 points/game on a bad team). Smyth last season scored +10% and +20% this season (+25% so far in NYI). Bergeron was 5% in 20052006 and 20062007, and sitting at amazing 30% (in 13 games). So anyone dying to look at these huge tables in person, here they are:
Should
1. IGF = individual goals for, IGA = individual goals against (plus or minus statistics including power play and penalty kills)
2. A comparable number of points for defenseman to compare to forwards (1.7*Points)
3. Point ranking out of all forwards.
March 21, 2007
Goal Differential
Epct = gf*gf/(gf*gf + ga*ga)
also known as the Pythagorean expectation.
March 18, 2007
First and Second assists
Most people would agree that a first assist is not the same as a second assist and many hockey statistics people have tried to explain how some assists are worth more than others (first worth more than seconds), with little actual analysis I might add. I’ve often wondered about the differences in them, but found it difficult to show one is worth more than the other. Founder of new hockey statistical analysis: Alan Ryder says: “It seems reasonable to conclude that, on balance, there is more value generated in a first assist than in a previous touch of the puck. The Forechecker says: “the general agreement is that 1st assists are generally ‘worth more’ than 2nd assists”.
About a year ago I did a regression on player’s salaries testing many variables, such as player contribution and many of the standard variables: goals, assists (first and second). In general hockey statistics people believe some assists are worth more than others (first worth more than seconds). However, the regression showed the second assists cost GM’s more. That is to say a GM was more likely to spend more on a guy with more second assists than a guy with more first assists. The difference was not statistically significant, but it was interesting none the less and suggested that people’s intuition, that second assists being worth first assists, may not be valid. What matters more than the ratio of first vs. second assists, but rather a players ability to get an assist on a goal (be involved), but even that can be flawed as some player’s roles don’t encourage assists (net presence)
Even if we knew the absolute value of a first assist versus a second assist there would still be the perennial error lingering around that messes with the results. If you assume for the moment that a forward gets a first assist on 33% of goals and a second assist of 23% of and the player sees around 100 goals, then that player should have 56 assists plus or minus 10 (46, 66) and this would be perfectly within the random expectation. Now assuming they have 56 assists, the should get about 33 first assists and 23 second assists (33% and 23% of 100 respectively), with an error of 7, so anything from 26 to 40 first assists and 16 to 30 second assists, this implies the expected random variation in the ratio of 26/56 to 40/56 to or 46% to 71%, this can be seen here. For a player with half as many plusses as
Its interesting looking at how well different players did compared to the expected performance based on how many plusses the player gets in different situations (power play, penalty kill, even strength). I’m not sure how many people are familiar with the graphs below, but these are standard residual vs. fits graphs. They plot the expected value (number of assists you would expect given a certain number of plusses) against the errors (residual or difference from the actual number of assists). In these graphs the residuals are normalized so the typical range for 95% of the data is presented as the green area (2, 2) and the rest of the residuals (error>2) is left as white.
In the first assist graph you will see a lot of play makers in the top half (residual > 2). I’m not sure what to make of all the names though, so I’ll let anyone else try and figure it out.
It’s the second assist graph that I find most intriguing. The most dominating players in this category include: Sakic,
Conclussion
What I’m trying to get across is that second assists and first assists are certainly different, but they don’t necessarily have different values. Certainly some second assists are the result of luck, but all players get some assists as part of luck, but often that pass was as important as the final pass.
March 16, 2007
Playoff Races Update
New York Islanders
Looked home and cooled for a week until they lost DiPietro. 6 home games and 4/6 away games against weaker teams (Tampa, Florida, Philadelphia), if they don't make it they wont deserve it. Two games against the Rangers will be the big impact games.
Toronto
I'll continue to maintain that 3 teams from the North East division will make it in the playoffs (although my numbers show this only happens about 68% of the time). Toronto will battle for this spot with Montreal and they have two games against each other including one on April 7.
New York Rangers
New York has one of the more challenging schedules for their remaining games with 5 games vs. other playoff race teams in their last 7 games. They need to gain ground (against Boston and Philadelphia) in the next two weeks in order to stand a chance.
Carolina
If Carolina makes they playoffs they'll prevent Toronto or Montreal from making the playoffs. You could call it a three way battle here (Carolina vs. Toronto vs. Montreal) for the 8^{th} spot. With only one game vs. other playoff race candidates their schedule favors their success, however they need to win about 7 games out of 10 to make it, which would be a challenge, considering they've gone 1213 (OT: 24) since January 1.
Gut feeling: New York Islanders in 7^{th} with Toronto in 8^{th}.
March 13, 2007
March Frequency Stadings Update

PTS  expected points using this method.
SW  average score switching  high numbers likely indicate difficulty maintaining a lead (bad defense/goaltending)
TL  Percentage the team takes lead.
OL  Percentage the opposition takes lead.
LW  Percentage the lead results in win. (otherwise it is tied again).
CB  Percentage of come backs  # of times team reties game. (otherwise opposition wins).
Goalie wins (2007) II

 Wot  regulation + overtime wins.
 Lot  regulation + overtime losses.
 Wso  regulation + overtime + shoot out wins.
 Lr  regulation losses.
 ot% = Wot/(Wot + Lot)
 r% = Wso/(Wso + Lr)
March 11, 2007
Goalie wins (2007)

 W  regulation wins
 Wot  regulation wins + OTW + SOW [NHL wins]
 Wpct  regulation wins/(regulation wins + regulation losses)
March 7, 2007
Avery diving
The first such incident will result in a warning letter being sent to the player, the second such incident will result in a $1,000 fine, the third such incident will result in a $2,000 fine and the fourth such incident will result in a onegame suspension.Avery has been called for his fourth dive. Of course since his 3^{rd} resulted in no action the worst that can occur here is a $2000 fine.
March 4, 2007
OT Percentage
Player Value
Before getting into the specific value of Smyth a word on long term contracts. Many people may be familiar with the Payday lottery or "million dollars a year for 25 years lottery", essentially what these lotteries do allow for a large initial dollar value ($25 million), but cost the lottery corporations significantly less by putting off a lot of the payments into the future. For example, at 6% the million dollars over 25 years is only worth about $12.8 million (this is what the it costs the lottery corp today). For the same reasons the a contract for Dipietro's over 15 years is only worth about $2.9M/year (when you look at it that way it looks like a steal). A 5 year contract for Smyth at $5.4M is really only worth $4.5M. The number can change for example if Smyth's contract is top or bottom heavy. Just because a very large contract is signed doesn't mean it's worth that much. Since the costs of these contracts are known explicitly it's easy to get a long term investment with good returns to cover them. Another good present example is Doan for 5 years works out to about $3.8M, most wouldn't have a problem paying Doan that much. In the end a "real $5.4M" contract would require $6.4M per year, I could easily see Smyth sign for $30M+ over 5 years...
There's been quite a bit of discussion about every aspect of Ryan Smyth. One of the primary questions has been was $5.4M enough [or $4.5M in present value], or was Smyth greedy. First of all player value varies from team to team. Carter for example this summer could've signed in Detroit or Vancouver for around $1.8M, but choose to sign on a team that needed [wanted] him more for $2.5M. RiversQ wrote a long post about comparable players, but the post mentions both Sullivan and Arnott who actually play together, meaning one doing well implies the other will do well. Of the players listed Sullivan is probably the most comparable in my mind, but he for whatever reason choose not to sign for market value. That being said he will get a lot more in 2009. Sullivan also is not the best player on the Nashville team, making his role significantly different to Smyth's.
However, Smyth's value may not be measured completely in terms of points. The nature of his game is both defensive and offense, but much of his offensive contributions can be considered invisible. In fact while Smyth may have ranked 58th in overall scoring in 20052006 he ranked in the top 20 in terms of goals while on the ice per game [1.5] (pp/pk/ev), he was above the likes of: Forsberg, Briere, Brind'amour, Sakic, Strum (anyway you get the drift). This year on a team that was reasonably poor he is ranked 32nd [1.3], since scoring is down slightly this year the drop has occurred for many top players. The players around him in the rankings include Zetterberg, Kunitz, Langkow, Afinogenov. Either way Smyth is on the ice for half of Edmonton's goals, what is that worth? Of course this doesn't get into the question of defensive ability.
The real question Edmonton should be asking of any comparable player is who would you choose instead. Would Koivu sign in Edmonton for under $5.5M? If you were to look at comparable players and ask yourself would you trade them straight up no questions asked: Naslund, Havlat, Hossa, Fedorov, Gagne, Gomez, Gaborik, Savard, etc. Who would you rather have as your best player?
An easier question might be to ask: of the forward RFAs where would you rank Smyth in terms of skill? A graph showing the ranking of different salary levels shows that in order to be worth >$5M you have to be a top 25 player (with last year's dollars). At a point per game, typically ranks you around the 20th position and 0.9 points per game around 40th, it appears the team agrees that he is a top 25 forward with their offer, but of course a one year contract is different from a 5 year contract.
One can also look at Smyth in terms of PP/PK/EV. I'm not sure of all the options in the NHL but Smyth would certainly be up there with guys I would want on the powerplay. This year, due to: coaching, players and who know what, Edmonton stopped shooting the puck at the net and this hurt their scoring on the powerplay. Who knows how many more assists/goals Smyth would've had if Edmonton had taken 100 more shots at the net on the powerplay. Smyth leads the team, pretty significantly, although I rate Hemsky about as good as Smyth on the powerplay. In terms of Penalty killing, Smyth may not have the best GA/hr rate, but that's due to the players he was stuck playing with on the penalty kill, by my measures he was the best penalty killer on the team. Just ask the Islanders, where he is averaging 4 minutes per game. Even strength Smyth demonstrates where he really differentiates himself from his team mates and other compatibles in my mind. He's a part of a rare group of forwards who is responsible for >1 goal differential per game at even strength [Vanek, Crosby, Heatley, Datsyuk, Alfredsson, Briere, Selanne, Kunitz, Kariya, Pominville, Erat, Roy, Havlat, Legwand, Mcdonald, Zetterberg, Camalleri]. Some are there because of luck, other skill. In my book the contributions made by Smyth this year peg him at $5.4M, which ranks him #24 in terms of "expected salary".
In terms of Hockey Analytics "Player Contribution" system Smyth scored a decent 51 in 2003, 62 in 2004 and I rated him a 72 in 2006, he's probably a 80+ this season. Each 20 points in the player contribution = 1 win and 1 win is worth about $1M.
A lot of people look at Smyth's numbers and don't consider just how bad a team the Oilers were this year. Ranked 25th in terms of EV GD/hr, 23rd power play, 12th in terms of penalty kill. Goaltending has been good considering how bad the defense was all year.
The problem is with a player like Smyth there are very few alternatives that are truly "available" in July, Smyth would have loved to play in Edmonton and would've signed there. However, goal differential is goal differential and if Edmonton can find a number of good cheap pieces they might be able to finish this complicated puzzle this summer. In general there are fewer elite players than there are teams. The beauty of a player like Smyth [an elite player] is you know his value, you know what you're getting. The problem with the $3M guys is that they've only done well in "perfect" situations or gotten lucky for a year or two [Carter]. You never know if you're getting a goal scorer or a liability.
Some people mention that he can still sign in Edmonton. The problem with trading a player as a rental is that their value generally doesn't go down when they play in the playoffs (unless you're Cloutier), if you lose in the first round your value is flat (no change or small negative change), after that it's all up, up up. So if Edmonton wants to sign Smyth after he loses this year in the conference finals good luck, he'll be expected to sign for $6.5M all of the sudden.
How much will Smyth sign for depends on who he signs with and the terms of the agreement, dollars aren't everything and dollars are never the entire story. I suspect he'll get in the neighborhood of $6M especially after NYI beats New Jersey in the opening round [long shot guess].
Good luck to Edmonton next year, you'll need it.