Division Simulator Toy (Monte Carlo)

Doctor No

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As I mentioned in the other thread, I've put together a reasonably simple division simulator, and I'm going to post results and perturbations resulting from that here.

Underlying this:
For each scenario, I'll be running 10,000 simulated seasons.
I'm using a Log5 win probability system to determine the probability of winning a game when two teams of varying strengths play (you can Google what this is, but it's sufficient here to note that the Log5 function is the only function shape that is consistent with - for example - a 75% team beating a 100% team never, beating a 50% team 75% of the time, and beating a 0% team always). I then add on a loser point a given percentage of the time (user input).

I can set number of division and non-division games in the model.
 
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Doctor No

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Here's the baseline situation:
  • Five teams (Alphas, Beta, Gammas, Deltas, and Epsilons). Four teams make the playoffs.
  • 20% of games will have a loser point.
  • 8 divisional games
  • 42 non-divisional games.
  • Non-divisional opponents have a uniform strength of 0.5
In the baseline, I set all five teams to have the same strength (0.5), identical to the non-division teams. We would therefore expect each team to make the playoffs 80% of the time.

TeamOSLAvg PtsPct PO
Alphas 0.50 90 80.2%
Betas 0.50 90 79.9%
Gammas 0.50 90 79.9%
Deltas 0.50 90 80.4%
Epsilons 0.50 90 79.7%
[TBODY] [/TBODY]
As you can see, each team made the playoffs essentially 80% of the time.
 
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Doctor No

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Okay, let's make one team (the Alphas) really good, holding all else constant. Let's make the Alphas a 70% team instead of a 50% team (meaning that they'd win 70% of the time against a 50% team).

I'm going to add two columns - the greatest number of points that a team earns in 10,000 simulations, and the fewest number of points that a team earns in 10,000 simulations.

TeamOSLAvg PtsPct POMaxPtsMinPts
Alphas 0.70 120 100.0% 147 87
Betas 0.50 87 74.8% 120 57
Gammas 0.50 87 74.5% 120 49
Deltas 0.50 87 75.7% 119 55
Epsilons 0.50 87 75.1% 118 48
[TBODY] [/TBODY]
This is consistent with the starting assumptions - since every one of their opponents is a 50% team, the Alphas will win 70% of 82 games (114.8 points) and get a loser point in 20% of 30% of 82 games (4.9 points) for an expected points total of 120.

In the 10,000 simulations, the Alphas made the playoffs every single time. If I ran enough simulations, they would fail eventually, but remember that there are four playoff spots, so in order for the Alphas to miss the playoffs, they would need all four divisional opponents to pass them. As you can see, the Alphas were as bad as 87 points in some seasons, and all of the other teams exceeded that amount in an average season, but it never happened for all four teams at once.
 
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Doctor No

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Okay, let's bring the Alphas back to average, but make the Epsilons really bad; say, a 30% team. How often will this team make the playoffs? Remember, they only have to beat out one of their four colleagues.

TeamOSLAvg PtsPct POMaxPtsMinPts
Alphas 0.50 93 99.6% 124 60
Betas 0.50 93 99.6% 122 60
Gammas 0.50 93 99.7% 125 63
Deltas 0.50 93 99.6% 123 62
Epsilons 0.30 61 1.5% 91 30
[TBODY] [/TBODY]

Yes, Virginia, even bad teams will make the playoffs on occasion.
 
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Tweed

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I'm lovin' it!
A request, if it's not already in your plans, nor a pain in the butt... can you do the 5-5-5-6 format for 21 teams, with ties?
 
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Doctor No

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Before we do that, here's a five-team division (four make the playoffs) with teams that vary from great (Alphas at 0.7) to poor (Epsilons at 0.30).

TeamOSLAvg PtsPct POMaxPtsMinPts
Alphas 0.70 122 100.0% 146 90
Betas 0.60 106 100.0% 132 72
Gammas 0.50 90 99.7% 123 57
Deltas 0.40 75 90.6% 105 46
Epsilons 0.30 59 9.6% 89 28
[TBODY] [/TBODY]

So in this example, the Alphas and Betas make the playoffs every single time. The Epsilons sneak in almost 10 percent of the time, usually at the expense of the Deltas but sometimes in place of the Gammas.
 
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Doctor No

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We now add a sixth team, the Zetas, who are about as good as the Epsilons (0.3). With eight divisional games, the number of non-divisional games goes from 50 to 42.

TeamOSLAvg PtsPct POMaxPtsMinPts
Alphas 0.70 124 100.0% 151 91
Betas 0.60 108 100.0% 136 77
Gammas 0.50 93 99.5% 120 62
Deltas 0.40 77 84.0% 107 44
Epsilons 0.30 62 8.5% 94 32
Zetas 0.30 62 8.0% 92 30
[TBODY] [/TBODY]

Four teams still make the playoffs, and the Alphas and Betas have a monopoly on those spots still. Specifically for the Deltas, there's a tougher battle for playoff spot, since there are now two "bad" teams who could have an outlier season where everything comes together.
 
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Doctor No

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Here is roughly the 1985-86 Smythe Division (including ties instead of three-point games):

TeamOSLAvg PtsPct POMaxPtsMinPts
Edmonton 0.745 119 100.0% 141 93
Calgary 0.520 89 100.0% 118 60
Vancouver 0.300 59 74.5% 89 33
Winnipeg 0.300 59 75.5% 89 32
Los Angeles 0.270 54 50.0% 82 31
[TBODY] [/TBODY]
Let's add a league average team to the division, and keep four playoff spots. What happens to the playoff probabilities?

This new team will be in Seattle, since I'm from Seattle.

As the simulation's running, I'll speculate on what *should* happen. The league average team will likely make the playoffs a lot, since they will be better than Vancouver, Winnipeg and Los Angeles (and they only have to be better than two of them to qualify). This also assumes that Edmonton and Calgary make the playoffs every time.

TeamOSLAvg PtsPct POMaxPtsMinPts
Edmonton 0.745 119 100.0% 142 86
Calgary 0.520 89 99.9% 116 59
Vancouver 0.300 59 40.2% 86 32
Winnipeg 0.300 59 40.5% 86 29
Los Angeles 0.270 55 19.5% 87 29
Seattle 0.500 87 99.9% 114 53
[TBODY] [/TBODY]

Interesting. In six of the 10,000 simulations, Calgary fell out of the top four. Given the spread, Edmonton keeps serve, the new Seattle team makes the playoffs almost as much as Calgary (99.85% to 99.94%), Vancouver and Winnipeg fall down and Los Angeles hits the skids.

I'll putter around with this over the next few days, but hopefully this provides evidence that yes, it's harder to make the playoffs in a larger division (holding the number of playoff spots constant).

Yes, the introduction of wild cards would add a wild card to this calculation.
 
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Michael Farkas

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A) This is awesome. Thank you. I'm sure this was the internet's intended purpose. (AINEC)

B) Secondly, I'm curious as to why you come to the conclusion that you do? I'm looking at posts 8 and 9 in the thread.

The top team (and the second-to-top team, for that matter) perform better in the six-team division than the five-team. Which I'm sure has much to do with having more control over points, right? I feel like this is what I was saying, but I guess I'm about to get pointed to something obvious that I'm missing (the internet's secondary purpose)...
 

Tweed

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Here is roughly the 1985-86 Smythe Division (including ties instead of three-point games):

TeamOSLAvg PtsPct POMaxPtsMinPts
Edmonton 0.745 119 100.0% 141 93
Calgary 0.520 89 100.0% 118 60
Vancouver 0.300 59 74.5% 89 33
Winnipeg 0.300 59 75.5% 89 32
Los Angeles 0.270 54 50.0% 82 31
[TBODY] [/TBODY]
Let's add a league average team to the division, and keep four playoff spots. What happens to the playoff probabilities?

This new team will be in Seattle, since I'm from Seattle.

As the simulation's running, I'll speculate on what *should* happen. The league average team will likely make the playoffs a lot, since they will be better than Vancouver, Winnipeg and Los Angeles (and they only have to be better than two of them to qualify). This also assumes that Edmonton and Calgary make the playoffs every time.

TeamOSLAvg PtsPct POMaxPtsMinPts
Edmonton 0.745 119 100.0% 142 86
Calgary 0.520 89 99.9% 116 59
Vancouver 0.300 59 40.2% 86 32
Winnipeg 0.300 59 40.5% 86 29
Los Angeles 0.270 55 19.5% 87 29
Seattle 0.500 87 99.9% 114 53
[TBODY] [/TBODY]
Interesting. In six of the 10,000 simulations, Calgary fell out of the top four. Given the spread, Edmonton keeps serve, the new Seattle team makes the playoffs almost as much as Calgary (99.85% to 99.94%), Vancouver and Winnipeg fall down and Los Angeles hits the skids.

I'll putter around with this over the next few days, but hopefully this provides evidence that yes, it's harder to make the playoffs in a larger division (holding the number of playoff spots constant).

Yes, the introduction of wild cards would add a wild card to this calculation.


Awesome stuff. Totally looking forward to seeing more sims! This stuff not only supports what I was showing, but it's also really interesting to see how much disparity there actually is between 0.300 team and a 0.270, for example. An average difference of only 4 pts on the season, yet the impact is significant (more than double) in terms of likelihood of playoff berth.

I was preparing a counter-point in a Main Board debate (Peak '16 Pens vs 2 Cup Kings vs 3/6 Hawks), and was positioning myself to illustrate that the Kings 3 year output wasn't especially flattering at a 0.610 Winning %, when using it to demonstrate the Hawks "domination", as they beat them in the WCF.

The Poster cited the Pens playing weak opponents, and my stance was the opponents appeared weak, by virtue of the Pens strength.

I looked at the clip the Pens were winning at in '16, and it was 0.750% Post-Johnston. Which is absolutely absurd. I have a feeling the point would have been lost on the guy, to be honest. But what I discovered was that only 5 other teams had played at that level, for a season, in the last 40 years.

77-78 Habs
95-96 Red Wings
05-06 Red Wings
12-13 Pens & Hawks

(Edit note: Only the Habs and Hawks won the SC, which goes to show that anything can happen in the playoffs, and probability isn't completely subjective to domination.)

Not even the mighty Oil managed it in the 80s. I was surprised (especially given how weak that division was, and how many games the Oilers racked up in there).

The Pens really screwed up a glorious oppportunity for everybody to witness one hell of a SCF in 2013. They were on a 14-0 tear heading into TDL, and mucked up their chemistry by adding Iginla and juggling the lines. The smallest things, eh?

Anyway, I plan on tweaking my calculations over in my thread, to reflect division disparities, as well as wild card scenarios... once I get my head completely around a couple (probably straightforward) things.

Thanks for doing all this stuff, Doc!
 
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Canadiens1958

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Truly interesting.

Excellent base for a study into the fairness of scheduling. Specifically an even number of teams will produce a balanced schedule that is fair. An odd number of teams creates an inherently unfair schedule since at least one team starting on opening night will not be playing. Gaining the advantage of rest, scouting and preparation on their first opponent. Granted this advantage is passed along thru the season but there are advantages to being chased as opposed to chasing.
 
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Tweed

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Truly interesting.

Excellent base for a study into the fairness of scheduling. Specifically an even number of teams will produce a balanced schedule that is fair. An odd number of teams creates an inherently unfair schedule since at least one team starting on opening night will not be playing. Gaining the advantage of rest, scouting and preparation on their first opponent. Granted this advantage is passed along thru the season but there are advantages to being chased as opposed to chasing.

I don't mean to derail at all, but if I can diverge for a second... the stuff you are talking about was completely of interest to me this year. The bolded part is the most significant factor, of what you pointed out. I was super-pissed off at the NHL for the schedule they handed the Pens, this season, having played nearly 3 seasons worth of hockey in 2 calendar years. Saddled with the most Back 2 Back games in the league, as well as the most games against Rested Teams, it was absolutely ridiculous.

The advantages gained/lost to scheduling are completely lost on the schedule-makers. I don't have the numbers on hand, but the probability of success on the 2nd of B2B nights, drops significantly... something like an 18% reduction. Goalies SV% goes down significantly too, dropping to somewhere around 0.880'ish I think. Conversely, Sharks and Ducks fans had a major gripe about the Kings getting all their sloppy seconds, when teams make a West Coast swing. For whatever reason, a rested Kings squad always got the visitors AFTER the Sharks/Ducks hosted them the night before.

Anyway, sorry for showing my Black and Yellow fandom, and subjecting you guys to my whines... but I just wanted to mention that, haha.

I've been advocating for fair-scheduling for decades now... specifically where B2B games, as well as afternoon games, are concerned.
 
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Canadiens1958

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I don't mean to derail at all, but if I can diverge for a second... the stuff you are talking about was completely of interest to me this year. The bolded part is the most significant factor, of what you pointed out. I was super-pissed off at the NHL for the schedule they handed the Pens, this season, having played nearly 3 seasons worth of hockey in 2 calendar years. Saddled with the most Back 2 Back games in the league, as well as the most games against Rested Teams, it was absolutely ridiculous.

The advantages gained/lost to scheduling are completely lost on the schedule-makers. I don't have the numbers on hand, but the probability of success on the 2nd of B2B nights, drops significantly... something like an 18% reduction. Goalies SV% goes down significantly too, dropping to somewhere around 0.880'ish I think. Conversely, Sharks and Ducks fans had a major gripe about the Kings getting all their sloppy seconds, when teams make a West Coast swing. For whatever reason, a rested Kings squad always got the visitors AFTER the Sharks/Ducks hosted them the night before.

Anyway, sorry for showing my Black and Yellow fandom, and subjecting you guys to my whines... but I just wanted to mention that, haha.

I've been advocating for fair-scheduling for decades now... specifically where B2B games, as well as afternoon games, are concerned.

Bolded. What you refer to as sloppy seconds is known as the "Sitting at home waiting effect". Off night while the next night's visitor plays in the vicinity.Common in the following areas. New York,NJ, Philly. To a degree Florida. Montreal, Ottawa, Toronto. Calgary, Edmonton, Vancouver.Plus California as you stated.

The 3rd game in 4 nights is especially tough on the visiting team, especially visiting teams time zones removed.
 
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Tweed

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Bolded. What you refer to as sloppy seconds is known as the "Sitting at home waiting effect". Off night while the next night's visitor plays in the vicinity.Common in the following areas. New York,NJ, Philly. To a degree Florida. Montreal, Ottawa, Toronto. Calgary, Edmonton, Vancouver.Plus California as you stated.

The 3rd game in 4 nights is especially tough on the visiting team, especially visiting teams time zones removed.

Interesting elaboration. Thanks!

Yeah, I definitely feel for PST teams, when they come east. They are essentially playing from 10pm to half-past-midnight their time. That's gotta be brutal on players, who are creatures of habit and routine.
 

Canadiens1958

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Interesting elaboration. Thanks!

Yeah, I definitely feel for PST teams, when they come east. They are essentially playing from 10pm to half-past-midnight their time. That's gotta be brutal on players, who are creatures of habit and routine.

Other way around. EST teams going in PST are playing from 10PM to after midnight. PST teams coming to the EST zone are playing early. A 1 or 2 PM start is like 10 - 11 AM PST.
 
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Tweed

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Other way around. EST teams going in PST are playing from 10PM to after midnight. PST teams coming to the EST zone are playing early. A 1 or 2 PM start is like 10 - 11 AM PST.

Yeah, haha, I derped there. Both ways it's pretty rough. Thanks for catching that.
 
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AfroThunder396

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Truly interesting.

Excellent base for a study into the fairness of scheduling. Specifically an even number of teams will produce a balanced schedule that is fair. An odd number of teams creates an inherently unfair schedule since at least one team starting on opening night will not be playing. Gaining the advantage of rest, scouting and preparation on their first opponent. Granted this advantage is passed along thru the season but there are advantages to being chased as opposed to chasing.
I think this is pretty much the sole reason NJ made the playoffs and Florida didn't this year. Even with Florida's torrid pace to end the season (.724 after Feb 14th), they just couldn't gain ground because the Devils played well enough to maintain separation (.634). At those rates Florida only closes the gap by ~5 points over the course of 25 games an at that point NJ had an 8 point lead.
 

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