Lemieux scoring 5 different ways - what are the odds?

[fastvoteman]

You may know that Lemeiux scored in 5 different ways in a game:

Short handed
Power play
Empty net
Penalty shot
Even strength

It seems like an impossible occurrence! It today's game this would never happen as nobody even scores 5 goals in a game.

I am wondering if anyone can figure out the odds of Lemieux doing this (or any other player) particularly from that era. It would an interesting quest.

Click to read more...

 

[Rebuilt]

This is the one thing Mario pulled off but Gretzky never did.

However, its not sanctioned as an official 'record' .

 

[badtakemachine]

Just for fun, a rough estimate. Of course, this does not take into account players who play in a scoring role, or ice time of any kind. This estimate will represent the odds that any average player could achieve this - star players would of course have (slightly) better odds.

In 1988/89, teams averaged 299.3 total goals for, each. Let's call it 300. Of those goals, 84.3 were on the powerplay, call it 84. 12.2 (so 12) were shorthanded. 8 goals were scored on penalty shots this season, for a total of about 0.4 per team for the season. In 92/93, 136 empty net goals were scored league-wide. It took me longer than 60 seconds to find this stat, so that's as close as we will get to 88/89 for this exercise and we will consider it to be accurate. That means 6.5 empty net goals for per team, which is definitely lower than it is today. Anyway:

300 total goals scored per team

84 power play goals scored per team
0.4 penalty shot goals scored per team
12 shorthanded goals scored per team
6.5 empty net goals scored per team

Adding these up -> 197 even strength goals scored per team

Dividing this by 18 skaters per team per game, and 80 games each:

0.06 power play goals per player per game
0.0003 penalty shot goals per player per game
0.008 short handed goals per player per game
0.005 empty net goals per player per game
0.14 even strength goals per player per game

Thus, the odds of getting all five in the same game:

0.06 x 0.0003 x 0.008 x 0.005 x 0.14 = 0.000000000008, or a 0.0000000008% chance of happening. Converted to a fraction, this is about 1 in 1,250,000,000 for the average Joe. Yeah. Never happening again.

 

[Claypool]

The empty net goal shouldn't have counted since the game ended.

 

[palefire]

Just for fun, a rough estimate. Of course, this does not take into account players who play in a scoring role, or ice time of any kind. This estimate will represent the odds that any average player could achieve this - star players would of course have (slightly) better odds.

In 1988/89, teams averaged 299.3 total goals for, each. Let's call it 300. Of those goals, 84.3 were on the powerplay, call it 84. 12.2 (so 12) were shorthanded. 8 goals were scored on penalty shots this season, for a total of about 0.4 per team for the season. In 92/93, 136 empty net goals were scored league-wide. It took me longer than 60 seconds to find this stat, so that's as close as we will get to 88/89 for this exercise and we will consider it to be accurate. That means 6.5 empty net goals for per team, which is definitely lower than it is today. Anyway:

300 total goals scored per team

84 power play goals scored per team
0.4 penalty shot goals scored per team
12 shorthanded goals scored per team
6.5 empty net goals scored per team

Adding these up -> 197 even strength goals scored per team

Dividing this by 18 skaters per team per game, and 80 games each:

0.06 power play goals per player per game
0.0003 penalty shot goals per player per game
0.008 short handed goals per player per game
0.005 empty net goals per player per game
0.14 even strength goals per player per game

Thus, the odds of getting all five in the same game:

0.06 x 0.0003 x 0.008 x 0.005 x 0.14 = 0.000000000008, or a 0.0000000008% chance of happening. Converted to a fraction, this is about 1 in 1,250,000,000 for the average Joe. Yeah. Never happening again.

This calculation is definitely wrong -- at a minimum you're missing a factor of 120=5*4*3*2*1, representing the number of different orders that the five types of goals could have come in. (The odds of flipping heads is 1/2, the odds of flipping tails is 1/2, the odds of flipping twice and getting one of each isn't 1/2*1/2 -- it's twice that because you could have either HT or TH.)

Let me come at this a different way. Let's stipulate the distribution of goals you worked out: 65.4% of goals are even strength, 28.2% are power play, 4.1% short-handed, 2.2% empty-net, 0.13% penalty shot. *Given* a five-goal game, the likelihood that it involves all five different types of goals is gotten by multiplying those five probabilities together, and multiplying by that factor of 120 that I mentioned. (See footnote...) This works out to roughly 1 in 38000. The likelihood that someone with a six-goal game gets all five different types of goals (plus one more goal) is three times higher, so roughly 1 in 13000. The calculation for a 7-goal game is a bit more complicated, so I'm going to ignore that that happened and lump it in with the 6-goal games.

Now in NHL history there have been 34 5-goal games and 8 6+ goal games, so the number of "all 5 types of goals" games we would have expected would be around 34/38000 + 8/13000 which is roughly 1/660.

So, the likelihood that this has occurred at all in NHL history is around 1 in 660.

Footnote: the calculation here is actually slightly naive, because empty-net goals aren't quite independent occurrences in the way that the other types of goals are. They only happen at the end of the game, and only in a close game. A game in which someone has already scored 4 goals is less likely to be a close game than other games, so the final likelihood is probably a somewhat lower than reported.)

 

[dr robbie]

You may know that Lemeiux scored in 5 different ways in a game:

Short handed
Power play
Empty net
Penalty shot
Even strength

It seems like an impossible occurrence! It today's game this would never happen as nobody even scores 5 goals in a game.

I am wondering if anyone can figure out the odds of Lemieux doing this (or any other player) particularly from that era. It would an interesting quest.

Could definitely happen today. I remember back in 09ish Crosby had a short handed penalty shot that, if he had scored, it would have been all 5 in 4 goals.

 

[jcbio11]

You may know that Lemeiux scored in 5 different ways in a game:

Short handed
Power play
Empty net
Penalty shot
Even strength

It seems like an impossible occurrence! It today's game this would never happen as nobody even scores 5 goals in a game.

I am wondering if anyone can figure out the odds of Lemieux doing this (or any other player) particularly from that era. It would an interesting quest.

Gaborik scored 5 a few years ago. No empty net or penalty shot too, mighty impressive.

 

[badtakemachine]

This calculation is definitely wrong -- at a minimum you're missing a factor of 120=5*4*3*2*1, representing the number of different orders that the five types of goals could have come in.

Valid. Order certainly doesn't matter.

Let me come at this a different way. Let's stipulate the distribution of goals you worked out: 65.4% of goals are even strength, 28.2% are power play, 4.1% short-handed, 2.2% empty-net, 0.13% penalty shot. *Given* a five-goal game, the likelihood that it involves all five different types of goals is gotten by multiplying those five probabilities together, and multiplying by that factor of 120 that I mentioned. (See footnote...) This works out to roughly 1 in 38000.

Okay, I agree that odds of scoring five different ways, given a five goal game, is 1 in 38000.

The likelihood that someone with a six-goal game gets all five different types of goals (plus one more goal) is three times higher, so roughly 1 in 13000. The calculation for a 7-goal game is a bit more complicated, so I'm going to ignore that that happened and lump it in with the 6-goal games.

Now in NHL history there have been 34 5-goal games and 8 6+ goal games, so the number of "all 5 types of goals" games we would have expected would be around 34/38000 + 8/13000 which is roughly 1/660.

So, the likelihood that this has occurred at all in NHL history is around 1 in 660.

Footnote: the calculation here is actually slightly naive, because empty-net goals aren't quite independent occurrences in the way that the other types of goals are. They only happen at the end of the game, and only in a close game. A game in which someone has already scored 4 goals is less likely to be a close game than other games, so the final likelihood is probably a somewhat lower than reported.)

The main difference between our approaches, aside from the importance of order (which I agree should not matter), is how likely it is to score 5 goals in one game. Choosing to look at how often it has happen in NHL history is valid for "how likely is it to happen at any point in NHL history", it is not quite as descriptive for "how likely it is to happen tonight by an average player". Granted, an "average" player is not necessarily "any" player. Of course, you could just divide your result by the number of games played in NHL history to get a reasonable estimate. However, the odds would be much worse for an "average" player, i.e. a player that scored at a rate of 15 goals per season in 88/89 (roughly 1 out of 5 games). Thus, I would employ looking at the compounded probability of (1/5)^5 = 1/3125 (neglecting 6+ goal games as they would hardly make a dent).

At this point, we have the odds of a player scoring 5 goals in one game as 1/3125, and given this is true, another 1/38000 chance that they would be five different ways. This would represent about a 1/120,000,000 chance that an average player could score 5 goals 5 different ways in one game in 88/89. Assuming order matters (which it shouldn't, but I had it in my original calculation as you pointed out), i.e. dividing by the factor of 120, this would then go back to about my original estimate of 1 in 1.4 billion.

 

[FissionFire]

Fedorov had a 5 goal game against Washington where he scored all his teams goals in a 5-4 OT win. This was in the era of ties and 5v5 OT as well. That's far more impressive to me than Lemieux.

 

[wgknestrick]

Fedorov had a 5 goal game against Washington where he scored all his teams goals in a 5-4 OT win. This was in the era of ties and 5v5 OT as well. That's far more impressive to me than Lemieux.

Not even close to impressive. Not a single person here other than you remembers that game or feat.

 

[Doctor No]

Not even close to impressive. Not a single person here other than you remembers that game or feat.

It's very bold of you to speak for the entire forum, but I happen to remember that game, and that feat.

Not even close to impressive?

 

[geofff]

This calculation is definitely wrong -- at a minimum you're missing a factor of 120=5*4*3*2*1, representing the number of different orders that the five types of goals could have come in. (The odds of flipping heads is 1/2, the odds of flipping tails is 1/2, the odds of flipping twice and getting one of each isn't 1/2*1/2 -- it's twice that because you could have either HT or TH.)

I think you are incorrect here, though im still trying to wrap my head around it a bit.

The factor of (5*4*3*2*1) only applies if you are doing the same thing over and over. The reason it applies for the coin example with 1 H and 1 T is you could be wrong on the first flip, but it doesn't matter because you satisfied the other requirement so you can make up for it on the second flip. (HT or TH)

With the hockey scenario, If you fail to score an even strength goal, it doesn't mean that you did score a goal in another fashion.

So with the goal scoring calculation you have to be correct in each fashion. If you fail to score the first one, you can't make up for it. Using the coin example, it's more like saying you need a H both times. so 0.5*0.5 =0.25.

lets look at a simpler, but related example and say a player has a 50% chance of scoring a PP goal in a game and a 50% chance of scoring a SH goal. What are the chances he does both in the same game? 0.5*0.5 = 0.25

The 4 scenarios would be:
PP GOAL- SH GOAL <---- only 1 of 4 fit our requirement.
NO PP G - SH GOAL
PP GOAL - NO SH G
NO PP G - NO SH G

 

[geofff]

Thus, the odds of getting all five in the same game:

0.06 x 0.0003 x 0.008 x 0.005 x 0.14 = 0.000000000008, or a 0.0000000008% chance of happening. Converted to a fraction, this is about 1 in 1,250,000,000 for the average Joe. Yeah. Never happening again.

Though that is the chance of a certain player doing it in a single game. there are (18*30)*80= 43,200 different attempts in a season (18 players, 30 teams, 80 games)

So the chance of it happening in a season is 1 in about 28,936.

Good estimate, but a couple notes on this calculation:
1. This does assume every player has an equal chance of scoring, when in reality the top players will be scoring most of the goals making it more likely the feat will happen. (in real life the goals aren't distributed evenly, much more go to the best forwards)

2. Also it doesn't take into account players scoring multiple times in the same fashion in the same game. Example a player may score 40 goals in 80 games, but he only scored in 30 different games. Taking this into account would make the feat less likely to happen.

So one assumption takes away a bigger chance of the feat happening, and the other takes away a lesser chance of it happening. Call it even I guess, though i think point 1 would have a bigger effect.

 

[badtakemachine]

1. This does assume every player has an equal chance of scoring, when in reality the top players will be scoring most of the goals making it more likely the feat will happen. (in real life the goals aren't distributed evenly, much more go to the best forwards)

Correct - for the sake of simplicity, I considered all skaters to be equal, regardless of their role on the team. The most notable factor here would be considering a forward to have an equal chance to score as a defenseman, which of course we know is not a valid assumption.

2. Also it doesn't take into account players scoring multiple times in the same fashion in the same game. Example a player may score 40 goals in 80 games, but he only scored in 30 different games. Taking this into account would make the feat less likely to happen.

True, my guesstimate would include all 6+ goal games provided 5 of them were scored different ways, but I chose not to bother with that part of the calculation because that term would be another order of magnitude smaller than the already tiny chance of scoring 5.

So one assumption takes away a bigger chance of the feat happening, and the other takes away a lesser chance of it happening. Call it even I guess, though i think point 1 would have a bigger effect.

Definitely agree. If nothing else, I think we can all agree on the fact that forwards are much more likely to achieve this than defensemen. A possible modification to this calculation would be looking at the share of goals that forwards get, and adjusting the goal per game rate accordingly. It of course would still result in very low odds, but it would make it a bit more likely.

 

[Thenameless]

Fedorov had a 5 goal game against Washington where he scored all his teams goals in a 5-4 OT win. This was in the era of ties and 5v5 OT as well. That's far more impressive to me than Lemieux.

No.

More people in hockey history, say a thousand years from now, will have scored five goals in a game. What Lemieux did takes such an exceptional set of circumstances, that it may not happen again.

1. Short-handed goals aren't easy to come by, as usually defensively-minded players are on the ice.
2. Penalty shots aren't easy to come by. And when they do come, most shooters miss. I believe Lemieux was 7-for-7 on his first seven attempts. He was deadly on breakaways; the best ever.
3. After one player scoring so many goals, the game still has to be close enough to offer an empty net chance (probably means good player on a bad team like Lemieux during this Penguins era) - and again, this same player has to cash in with at most about a 1-minute+ opportunity to complete the feat. This, after scoring the first four goals under fairly unique circumstances.

 

[fastvoteman]

How many 4 goals games are there where the player has needed one more to compete the 'cycle'? I bet there are not even many of these. Likely having to score 2 out of 3 on empty nets, penalty shot and short handed makes it real tough.

As for Lemiuex's 'record', it is simply amazing and one of the greatest feats of all-time. I wonder if anyone was paying attention during the game to the fact that he needed the empty net goal and if a big deal was made of the feat.

 

[Ogopogo*]

This is the one thing Mario pulled off but Gretzky never did.

However, its not sanctioned as an official 'record' .

Because it doesn't mean anything. It is just some goofy coincidence like a team winning a game 3-2 with a goal scored in the first minute of each period or rain all week - sunshine for my soccer game - then back to rain for three more days.

It's nothing. Is it really better than a guy scoring 5 times with two short-handed goals? What makes it better than any 5 goal game? Nothing. In fact, it is less impressive than a 5 goal game without an empty-netter.

This "oddity" is up there with the career record for most goals in Saturday matinee games by a left-handed defenseman with a mustache born in January. Who cares?

Will a player with four goals in "four different ways" say "Hey coach, there's 16 minutes left - sit me on the bench until they pull the goalie so I can go for the record..." F'ing absurd.

 

[Jason66]

This is the one thing Mario pulled off but Gretzky never did.

However, its not sanctioned as an official 'record' .

To name just a few other things Mario bettered Wayne in. Mario is the only player to score 40+ goals at even strength in a season twice, he has the most 8 points games in history and he holds the record for most short handed goals in a season.

 

[Jason66]

Because it doesn't mean anything. It is just some goofy coincidence like a team winning a game 3-2 with a goal scored in the first minute of each period or rain all week - sunshine for my soccer game - then back to rain for three more days.

It's nothing. Is it really better than a guy scoring 5 times with two short-handed goals? What makes it better than any 5 goal game? Nothing. In fact, it is less impressive than a 5 goal game without an empty-netter.

This "oddity" is up there with the career record for most goals in Saturday matinee games by a left-handed defenseman with a mustache born in January. Who cares?

Will a player with four goals in "four different ways" say "Hey coach, there's 16 minutes left - sit me on the bench until they pull the goalie so I can go for the record..." F'ing absurd.

Your whacked. It was an amazing feat.

 

[Jason66]

Fedorov had a 5 goal game against Washington where he scored all his teams goals in a 5-4 OT win. This was in the era of ties and 5v5 OT as well. That's far more impressive to me than Lemieux.

Lemieux was in on close to 60% of his team's goals one season. That's impressive, it's also an NHL record. Scoring 5 different ways in a game is also very impressive. Two feats the NHL will never see again.

 

[Jason66]

How many 4 goals games are there where the player has needed one more to compete the 'cycle'? I bet there are not even many of these. Likely having to score 2 out of 3 on empty nets, penalty shot and short handed makes it real tough.

As for Lemiuex's 'record', it is simply amazing and one of the greatest feats of all-time. I wonder if anyone was paying attention during the game to the fact that he needed the empty net goal and if a big deal was made of the feat.

The broadcasters were unaware of the potential feat at the time.

 

[abo9]

Lemieux was in on close to 60% of his team's goals one season. That's impressive, it's also an NHL record. Scoring 5 different ways in a game is also very impressive. Two feats the NHL will never see again.

Maybe if a team is historically bad with a Ovechkin-type player on them?

 

[Hockey Outsider]

To name just a few other things Mario bettered Wayne in. Mario is the only player to score 40+ goals at even strength in a season twice, he has the most 8 points games in history and he holds the record for most short handed goals in a season.

Gretzky and Bossy both had five seasons of 40+ ES goals, while Brett Hull had three.

 

[bobbyking]

It's not that impressive as its rare. Like someone said federov scoring all 5 in one game Is significantly more impressive

 

[mrhockey193195]

I've always wondered - what happens if someone does this, but the empty net goal is shorthanded? Or on the powerplay? What it it's shorthanded but the player didn't score a shorthanded goal prior?

I don't like the empty net goal as a 5th "way" to score, since it isn't mutually exclusive from the ES/PP/SH ones.