Good Players, Bad TeamsComments for Good Players, Bad Teams at http://hockey.dobbersports.com , comment 1 to 8 out of 8 comments
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http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14607
16% of all goals scored are game-winning goals.
It is a very simple calculation.
I'm not going to check your math.
The answer is not 2%. - Pengwin7Tue, 14 Jun 2011 04:28:41 +0100@ Pengwin7
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14603
I did this pretty quick, so it's possible I missed something, but I'll show the work to check it for you.
For all possible 4, 5, & 6 goal games, I did 2^4 + 2^5 + 2^6 = (16) + (32) + (64) = 112 to get all possible orders in which 4 5 or 6 goals could be scored in a game. That's where I went wrong. There's actually no straightforward formula for problems of this type, as it turns out, but I did find this link helpful: [url]http://ask.metafilter.com/151680/ount-all-the-ways-that-15-objects-can-be-put-into-four-piles-so-that-each-pile-has-a-different-number-of-objects-in-it[/url]
Ties have no GWG so and are only possible with an even number of goals; only 2-2 and 3-3 satisfy these conditions for 4-6 goal games. Therefore, permutations of ties include all 4-integer and 6-integer binary strings with equal numbers of 1's and 0's. You could use the "N choose r" method (for "4 choose 2" and "6 choose 3"), but it's easier to show you by writing the permutations:
(1 = team A scores, 0 = team B scores)
Possible 2-2 ties (2 1's & 2 0's):
0011, 0101, 0110, 1001, 1010, 1100.
Possible 3-3 ties (3 1's & 3 0's):
(000111, 001011, 001101, 001110, 010011, 010110, 011001, 011010, 011100, 100011, 100101, 100110, 101001, 101010, 101100, 110001, 110010, 110100, 111000)
Total = 25 ties possible (my 1st mistake, I had 23 somehow...)
If only tie games have no GWG, and these occur (25/112)% of the time, then it follows that all remaining games must have a GWG (since the total must =100%). Therefore, there are 25/112*100 = 22.32 games without a GWG, and 100% - 22.32 = 77.68% of games that have a GWG.
Let's say that every player (non goalie) has an equal opportunity to score a goal. We know that 77.68% of games have one GWG. There are 4 F lines and 3 D pairs on a team (conservatively). This means that the average F plays 25% of the game and the average D plays 33.33%.
F: 25%/game * 60 min/game = 15 minutes
D: 33.33%/game * 60min/game = 20 minutes
The weighted average of minutes played per game for F & D gives average ice time per PLAYER, not per line (my mistake!):
(6 * 20min/D/game + 12F * 15min/F/game) / 18 players = 16.667min/player/game
If the average player is on the ice for 16.667 min/game, that's the same as 27.78% of the game (16.67 / 60 * 100 = 27.78%). Equivalently, 0.2778 is the probability that the average player is on the ice.
Remember that for each non-tie game only one GWG must occur and that HALF of those GWG are scored by the average team (the other half are scored by the opponent). Therefore, in the 77.68% of games with a GWG, half will see your player's team score the GWG:
77.68% / 2 = 38.84%
Now, we know that probability is 0.2778 that the average player will be on the ice. The probability that he is on the ice AND his team scores a GWG is given by 0.2778 * 0.3884 = 0.1079.
That means: 10.79% of the time, the average player is on the ice when the GWG is scored. He's on the ice with 4 other guys, so his odds of scoring the GWG himself are 1/5 (or a probability of 0.2) of the 10.79%.
P(on-ice [b]&[/b] gwg is scored) = 0.1079
P(on-ice [b]&[/b] gwg [b]&[/b] 1/5 players scored it) = 0.1079 * 0.2 = 0.02158
Equivalently, 2.158% of the time, the average player is on the ice when the GWG is scored [b]&[/b] scored it himself.
If I find a simple solution to problem of the form "distribute N objects into P piles", I'll revise my model. I'm not in the mood to brute force this by hand... - JeffMon, 13 Jun 2011 15:27:29 +0100Math
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14543
Jeff - you walked through too much math. Somewhere you got lost.
I have a spreadsheet of all players stats in the NHL this year.
There were 6721 goals scored in the NHL this year. 1081 GWG.
16% is the magic number.
I'm not sure how you arrived at 2%... but WAY off. ;)
[Actually, I had made a typo myself. There are 4GWG in 5games & 25 total goals. 4/25 = 16%]
Defensemen scored 940 goals. 166 were GWG. 17.7% of defensemen goals were GWG.
All forwards scored 5781 goals. 915 were GWG. 15.8% of forward goals were GWG.
Top 90 scorers scored 2471 goals. 403 were GWG. 16.3%
David - I said there will be a "slight" boost to top scorers. This is because they are more likely to play late in the game. 0.5% equals "slight" boost.
- Pengwin7Fri, 10 Jun 2011 12:15:16 +0100Playoff factor
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14519
In both my fantasy leagues, we have playoffs during real Stanley Cup playoffs. Thus, an average player from a good team is normally more valuable than a good player from a bad team. Unless you are fighting for a playoff spot, that is. :-)
And, of course, some players might gain or lose "playoffability" due to a real-life trade, which could be quite a surprise (good or bad) on the trade deadline day. :-)
This year, for example, I was keeping Wheeler simply because he was in Boston... only to end up with an unneeded Atlanta player. I am in the final now, and I could really use Wheeler, had he stayed a Bruin! - Pavel NikiforovitchFri, 10 Jun 2011 06:21:51 +0100GWG Model
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14502
Assuming there are 4, 5, or 6 goals per game, there are 112 possible permutations of goal scoring. Of those, only 2-2 & 3-3 ties have no GWG, which makes 23 possible outcomes with no GWG.
Overall, 23/112 games have no GWG, so a GWG occurs with a probability of 1 - 23 / 112 = 0.79. Half of those will go to the correct team, so 39.5% of the time, it will be your player's team that gets the GWG.
If all lines scored equally (i.e. they all scored an equal number of goals per game), then only the ice time they received per game would determine their likelihood of scoring the GWG. The average line gets 16.67 minutes per 60 minute game, the average line thus plays 27.78% of each game (if you count forward lines and defensive pairings).
The probability of your player's line scoring the GWG is therefore approximated by: 0.278 * 0.395 = 0.1098 = 10.98%. One player, of the 5 on the ice, then has 10.98% / 5 = 2.196% chance to score the GWG.
Under conditions of 4-6 goal games and equal play time, 2.2% of the average player's goals should be GWGs. That may seem low, but remember that it's the average; for each player with 4 GWG in a season, I'm sure there are 10 players with none. - JeffThu, 09 Jun 2011 16:21:15 +0100GWG's
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14494
I really hate GWG's as a fantasy stat. I think of it as a fluke category.
I disagree with Pengwin that there is any sort of formula for it or that first liners have a tangible advantage (maybe they have some as a function of total time on ice). I would be that at least 50% of GWG's occur outside the last 5 minutes of regulation or overtime which makes it completely random as to who gets it, not some weird clutch stat.
It is also a team stat, as better teams will win more games. Example Tavares is great but the NYI suck in the short term so he isn't getting a lot of GWG's. - David GoodburnThu, 09 Jun 2011 07:38:17 +0100Nice
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14487
For a short article, this is a very nice little contribution.
These can be some great additions in depth leagues.
One point to make (agree w/Rob below):
Game-winning goals will fluctuate year-to-year, but it should be expected to be a direct function of goals, with a slight boost to a team's 1st line forwards (Why: They are most likely to get ice-time late in a game & OT).
A quick mathematical model:
4/5 games are decided in regulation or standard OT.
A game typically has about 5 goals.
20 goals = 4 GWG.
A player's GWG total should be about 20% of their GOAL total.
Higher = lucky (typically)
Lower = unlucky (typically)
Reasoner was on the lucky-side.
But we shouldn't advise buying a player just for their GWG.
Great little piece though! :) - Pengwin7Thu, 09 Jun 2011 05:35:35 +0100GWG?
http://hockey.dobbersports.com/index.php/eric-maltais/3719-good-players-bad-teams#comment-14455
GWG can be such a crap shoot of a stat. For the most part the more goals you get, the more GWG you get. however,you're always left with the stat anomalies such as Micheal Ryder having 6 GWG (18 G) yet 30+ goal scorers like Skinner & Backes have 2. Even Crosby only had 3 GWG in in 32 G.
Does this mean that Ryder is a clutch player? Personally I don't think so.
To me it just seems that GWG is a stat that involves a bit more fluke/luck than other stats, since a GWG is ultimatley determined by how many goals the losing team gets.
- Rob MyattWed, 08 Jun 2011 07:49:43 +0100