In deeper fantasy leagues many find themselves facing a difficult choice of who to select in later rounds. Typically I would look to a third line player on a strong team like Detroit or Vancouver to provide some offense and maybe boost my plus/minus. Lately however, I have been trying to buck that trend and look outside the box when it comes to the depth of my roster.

There are some gems out there from the NHL's bottom third that can be acquired at the end of a draft or simply plucked off waivers early in the year. Here are a few that come to mind:

**Matt D'Agostini - STL**

D'Agostini quietly had a solid year for the Blues. He played in every game potting 21 goals and 46 points. He finished third on the team with six power play goals and first with five game winners. He was also a plus-8 on a weak St. Louis squad. The kicker is he ranked just 20th on the team in ice-time, averaging just under 15 minutes a game.

**Bryan Little - ATL**

There weren't a ton of bright spots for the Thrashers last season but Little was one of them. He led the team in plus/minus at plus 11 and finished with a respectable 48 points. Little also had two shorthanded goals and two three game point streaks, one four game point streak, and a five game point streak.

**R.J. Umberger - CLB**

Umberger is a great score for head to head weekly leagues. His 57 points last year were second on the Blue Jackets and he finished first on the team in ice-time among forwards. He also led the team in power play goals with eight and shorthanded goals with three. Not to mention he rattled off a ten game point streak and had a four game stretch in February where he notched eight points.

**Marty Reasone****r - FLA**

Four of his 14 goals were game winners and that was good for first on the Cats. He also played in every game and was a plus player. A UFA July 1st, Reasoner may find himself on a contender next season and if so, his numbers should improve even more.

**Frans Nielsen - NYI**

Nielsen can really boost your PK categories. He sniped seven goals shorthanded which accounted for more than half his entire season total of 13. His 44 points are nothing to sneeze at and his plus-13 ranking led the team.

**Luke Schenn - TOR**

Stay with me on this one, if you are in a league with some obscure categories he can be valuable. Schenn was the only player in the league last season with over 250 hits and 150 blocks. Despite the toll that can take on one's body he proved his durability by playing in every game. His point totals have also increased every year he has been in league from 14 to 17 to 22.

*This was an article contributed through our Black Aces project. If you are interested in having a column published on DobberHockey, post one in the Black Aces section of the forum. If we like it and we need some content (it happens, from time to time), then we'll use it!*

#### Jeff said:

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: http://ask.metafilter.com/1516...ects-in-it

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

**&**gwg is scored) = 0.1079

P(on-ice

**&**gwg

**&**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

**&**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...

#### Pengwin7 said:

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.

#### Pavel Nikiforovitch said:

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!

#### Jeff said:

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.

#### David Goodburn said:

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.

#### Pengwin7 said:

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!

#### Rob Myatt said:

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.

It is a very simple calculation.

I'm not going to check your math.

The answer is not 2%.