Winning 4 in a row after a 2-0 series deficit vs. 3-0 series deficit

[SnowblindNYR]

3 times in NHL history a team has come back from a 3-0 series deficit and that's 3 times the amount it happened in baseball and basketball combined. I have always been fascinated by that stat.

Here's my question, without looking at stats I would think think teams have won 4 in a row way way way more times after being down 2-0. I know the Caps even have a losing record in series where they take a 2-0 series lead. I assume that a decent amount of those were 4 straight losses in a row. So why is it so much harder to win 4 in a row after being down 3-0 than 2-0? Here are a couple of reasons I can think of, with some objections:

1) Psychology. 3-0 comebacks are so rare that it takes away confidence from teams. They might think they can't do it and actually not be able to do it because of their confidence being so low. That said they're still professional athletes. Also 2-0 is a pretty daunting task too. Why such a big gap?

2) The 3-0 team is usually just the better team. But honestly all 3 games could have gone into OT. 3 games is too small of a sample size.

3) If we're comparing a 2-0 team to a 3-0 team, we're in essence comparing a 2-1 team to a 3-0 team (otherwise the 2-0 team would be a 3-0 team) and they have to win 3 in a row. Still is winning 3 in a row that much easier than 4 in a row? Plus they DID have to overcome big odds to win 4 in a row anyway.

Of course, without numbers, maybe the fact is teams don't win 4 in a row after being down 2-0 significantly more than winning 4 in a row after being down 3-0. Would be interested in stats.

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[Mike Martin]

Down 2-0 you can still afford to lose a game, at 3-0 you have to win every game. The best comparison I can think of is those college classes where you can drop your lowest test grade, it takes some of the pressure off going into each test, so that's what being down 2-0 versus 3-0 feels like, the pressure of having to win every game for the rest of the series is just too much stress.

 

[SnowblindNYR]

Down 2-0 you can still afford to lose a game, at 3-0 you have to win every game. The best comparison I can think of is those college classes where you can drop your lowest test grade, it takes some of the pressure off going into each test, so that's what being down 2-0 versus 3-0 feels like, the pressure of having to win every game for the rest of the series is just too much stress.

Well you have the same effect down 3-1. I did once check and teams that win game 4 after being down 3-0 have a similar success rate for coming back than teams that are down 3-1 in any other scenario. I checked each path of getting to 3-1 and compared it to getting there by winning the 4th game. The reason I checked each past is because there are 3 different ways to get to 3-1 without losing the first 3, so you have a much bigger sample size than if you get there by losing the first 3.

 

[Bear of Bad News]

I tried simulating this - similar technique to what I've described in other threads.

Assumptions:
Two teams, team A and team B
On neutral ice, team A wins 60% of games
Each team has a 10-point home ice advantage (so team A wins 70% of games at home, and team B wins 50% of games at home)

Seven-game playoff series
Home games are A-A-B-B-A-B-A

Game outcomes are independent from one another (so no momentum involved)

Number of playoff series simulated: 5 million

Outcomes:

Overall results:
A wins in 4: 12%
A wins in 5: 24%
A wins in 6: 18%
A wins in 7: 20%
B wins in 4: 2%
B wins in 5: 5%
B wins in 6: 11%
B wins in 7: 8%

A wins 74% of series

If A leads the series 2-0 (which happens 49% of the time):
A wins in 4: 25%
A wins in 5: 35%
A wins in 6: 16%
A wins in 7: 14%
B wins in 6: 4%
B wins in 7: 6%
B comes back to win the series 10% of the time
(B wins four straight 4% of the time)

If B leads the series 2-0 (which happens 9% of the time):
B wins in 4: 25%
B wins in 5: 15%
B wins in 6: 21%
B wins in 7: 9%
A wins in 6: 9%
A wins in 7: 21%
A comes back to win the series 30% of the time
(A wins four straight 9% of the time)

If A leads the series 3-0 (which happens 24% of the time):
A wins in 4: 50%
A wins in 5: 35%
A wins in 6: 7%
A wins in 7: 5%
B wins in 7: 2%
B comes back to win the series 2% of the time (necessarily winning four straight games)

If B leads the series 3-0 (which happens 5% of the time):
B wins in 4: 50%
B wins in 5: 15%
B wins in 6: 17%
B wins in 7: 5%
A wins in 7: 12%
A comes back to win the series 12% of the time (necessarily winning four straight games)

When reviewing these results, it's important to remember (1) the assumptions, (2) A is considered to be the better team, and (3) I assumed that momentum is not a real thing in playoff series - and only described as such after the fact.

 

[hatterson]

Part of what Taco also demonstrated is the fact that a 2-0 lead can be achieved by a team only winning on home ice whereas a 3-0 lead requires at least 1 road win.

The home advantage is also a reason why an interesting quirk is displayed.

Team A has a greater chance of winning 4 straight when they're down 3-0 than when they're down 2-0. When they're down 2-0, 3 of the next 4 games are on the road where they have a lesser chance to win. When they're down 3-0, it's an even split.

I'd also like to point out one thing that may get hidden in the outcomes, all games are given the same probabilities (excluding constant home bias). This means that injuries are ignored, the obvious reason being that you can't predict them in a generic mathematical model like this. But, it can have a very real impact on a series. Losing 3 straight to an Isles team that has Tavares healthy, and then having him get injured changes things significantly, especially if you compare it to a situation where you lose 3 straight and then *your* star player gets injured.

Clearly the team in the first circumstance would have a much higher chance of coming back than the team in the second circumstance, mainly because the underlying relative strength of the team has fundamentally changed.

Just one of the little kinks that comes when applying generic models to specific real world scenarios.

 

[SnowblindNYR]

I tried simulating this - similar technique to what I've described in other threads.

Assumptions:
Two teams, team A and team B
On neutral ice, team A wins 60% of games
Each team has a 10-point home ice advantage (so team A wins 70% of games at home, and team B wins 50% of games at home)

Seven-game playoff series
Home games are A-A-B-B-A-B-A

Game outcomes are independent from one another (so no momentum involved)

Number of playoff series simulated: 5 million

Outcomes:

Overall results:
A wins in 4: 12%
A wins in 5: 24%
A wins in 6: 18%
A wins in 7: 20%
B wins in 4: 2%
B wins in 5: 5%
B wins in 6: 11%
B wins in 7: 8%

A wins 74% of series

If A leads the series 2-0 (which happens 49% of the time):
A wins in 4: 25%
A wins in 5: 35%
A wins in 6: 16%
A wins in 7: 14%
B wins in 6: 4%
B wins in 7: 6%
B comes back to win the series 10% of the time
(B wins four straight 4% of the time)

If B leads the series 2-0 (which happens 9% of the time):
B wins in 4: 25%
B wins in 5: 15%
B wins in 6: 21%
B wins in 7: 9%
A wins in 6: 9%
A wins in 7: 21%
A comes back to win the series 30% of the time
(A wins four straight 9% of the time)

If A leads the series 3-0 (which happens 24% of the time):
A wins in 4: 50%
A wins in 5: 35%
A wins in 6: 7%
A wins in 7: 5%
B wins in 7: 2%
B comes back to win the series 2% of the time (necessarily winning four straight games)

If B leads the series 3-0 (which happens 5% of the time):
B wins in 4: 50%
B wins in 5: 15%
B wins in 6: 17%
B wins in 7: 5%
A wins in 7: 12%
A comes back to win the series 12% of the time (necessarily winning four straight games)

When reviewing these results, it's important to remember (1) the assumptions, (2) A is considered to be the better team, and (3) I assumed that momentum is not a real thing in playoff series - and only described as such after the fact.

The bold is counterintuitive. A has a better chance of winning in 7 if they lose the first 3 than in 6 if they lose their first 2? Is it because of the option for A to win in 7 if they lose their first 2? So then a loss there gets added to the "win in 7" option and thus it's winning the series 21% of the time meanwhile a loss for lose the first 3 gets added to the lose in 4-6 option and they win the series only 12% of the time instead of 21%? I guess that makes sense.

 

[Bear of Bad News]

Under the assumptions I used, the last result is straightforward to explain.

Given that B wins the first three games, for A to win the series, they have to win game four, five, six, and seven:

Game Four (on the road): 50% chance of winning
Game Five (at home): 70% chance of winning
Game Six (on the road): 50% chance of winning
Game Seven (at home): 70% chance of winning

So the probability of this event is 0.5*0.7*0.5*0.7 = 12.25%

Part of this is that I assume that A is the better team. If B finds itself in a similar situation, then the probability is 0.5*0.3*0.5*0.3 = 2.25%.

 

[Bear of Bad News]

As for the disparity between the two bolded numbers...

If B leads the series 2-0, A has a 30% chance of winning the series (9% + 21%).

If B leads the series, 3-0, A has a 12% chance of winning the series.

 

[Mike Martin]

Well you have the same effect down 3-1. I did once check and teams that win game 4 after being down 3-0 have a similar success rate for coming back than teams that are down 3-1 in any other scenario. I checked each path of getting to 3-1 and compared it to getting there by winning the 4th game. The reason I checked each past is because there are 3 different ways to get to 3-1 without losing the first 3, so you have a much bigger sample size than if you get there by losing the first 3.

When a team is down 3-0 they have no evidence that they can beat the other team, down 3-1 at least you have that game you won to look back on to prove it can be done. That must be a major boost of confidence.

 

[SnowblindNYR]

As for the disparity between the two bolded numbers...

If B leads the series 2-0, A has a 30% chance of winning the series (9% + 21%).

If B leads the series, 3-0, A has a 12% chance of winning the series.

Yeah but specifically winning in 6 if you're down 2-0 is less than winning in seven when you're down 3-0, but I guess that's just the weird breakdown of home/away games.

 

[Bear of Bad News]

Yeah but specifically winning in 6 if you're down 2-0 is less than winning in seven when you're down 3-0, but I guess that's just the weird breakdown of home/away games.

That's exactly right - in the example you cite, team A is down 2-0. To win four straight, they need to win three road games and one home game: 0.5*0.5*0.5*0.7 = 8.75% probability.

If they are down 3-0, then to win four straight, they need to win two road games and two home games: 0.5*0.5*0.7*0.7 = 12.25% probability.