Mathematical Equation As To Why No NBA Team Has Ever Recovered From A 3-0 Deficit

HacheMan · May 8, 2018

Wayne Chang
Finance PHD Student At USC

It’s a matter of probability.

Suppose two teams are equally matched such that each team has a 50% chance of winning any particular game. Coming back from a 3–0 deficit requires winning 4 consecutive games, with a probability of only 6.3% (=.5^4).

This estimate is too high though. We should account for the fact that the other team has already won 3 consecutive games and is thus likely to be a better team. To have a majority chance of winning three in a row requires the other team to have won each game with at least a 80% probability (.8^3=51%). So the losing team only has a 20% chance of winning each game going forward. This means coming back to win 4 in row occurs with a probability of only 0.2% (=.2^4).

I’m clearly simplifying (ignoring the technicalities associated with playing basketball) and the setup isn’t entirely correct (e.g. there’s also the chance that the better team happens to fall behind and thus has a higher likelihood of catching up). But hopefully, this shows the gist of how unlikely it is.

HacheMan · May 8, 2018

I'm curious is any other math gurus find the above reasonably accurate

Greenbacks · May 8, 2018

76ers are going to do it against the Celtics....Just a feeling

festeringZit · May 8, 2018

Greenbacks said:
76ers are going to do it against the Celtics....Just a feeling

Not gonna happen.

PatsFan1283 · May 8, 2018

It's accurate that if you get up 3-0 that you are likely to be the better team and thus the next 4 games don't average out to 50/50 propositions.

But when he assigns the team up 3-0 an 80% probability to win, he's basically just pulling that # out of nowhere. That's a big #, it's -400 every single game. So his .2% is off unless we're talking a Rockets/Jazz type disparity in team ability.

Who says winning 3 in a row means you had 80% probability to win atleast 3 games? It could just be variance that got you to 3-0. His premise is kinda dumb. When he says "the setup isn't entirely correct", he basically means it isn't correct at all.

skins85 · May 8, 2018

Greenbacks said:
76ers are going to do it against the Celtics....Just a feeling

they dont have the coach to do it. the line being what it is for game 5 has all the philly backers thinking it too but it wont happen. boston at home is too much for a young philly team

festeringZit · May 8, 2018

Hache Man said:
Wayne Chang
Finance PHD Student At USC

It’s a matter of probability.

Suppose two teams are equally matched such that each team has a 50% chance of winning any particular game. Coming back from a 3–0 deficit requires winning 4 consecutive games, with a probability of only 6.3% (=.5^4).

This estimate is too high though. We should account for the fact that the other team has already won 3 consecutive games and is thus likely to be a better team. To have a majority chance of winning three in a row requires the other team to have won each game with at least a 80% probability (.8^3=51%). So the losing team only has a 20% chance of winning each game going forward. This means coming back to win 4 in row occurs with a probability of only 0.2% (=.2^4).

I’m clearly simplifying (ignoring the technicalities associated with playing basketball) and the setup isn’t entirely correct (e.g. there’s also the chance that the better team happens to fall behind and thus has a higher likelihood of catching up). But hopefully, this shows the gist of how unlikely it is.

I think his logic is really bad. He says "To have a majority chance of winning three in a row requires the other team to have won each game with at least a 80% probability (.8^3=51%). So the losing team only has a 20% chance of winning each game going forward." The problem with this logic, is that teams that find themselves in an 0-3 hole didn't necessarily get there because they only had a 20% chance of winning each game, as a matter of fact - this almost never happens.

He's assuming that teams that are down 0-3 are there because they had a "majority chance" of being in that position from the get-go. So basically he's saying that the chance of a team coming back from 0-3 is .2% if and only if they
only had a 20% chance of winning the first 3 games, which rarely ever happens in the playoffs (if ever).

festeringZit · May 8, 2018

PatsFan1283 said:
It's accurate that if you get up 3-0 that you are likely to be the better team and thus the next 4 games don't average out to 50/50 propositions.

But when he assigns the team up 3-0 an 80% probability to win, he's basically just pulling that # out of nowhere. That's a big #, it's -400 every single game. So his .2% is off unless we're talking a Rockets/Jazz type disparity in team ability.

Who says winning 3 in a row means you had 80% probability to win atleast 3 games? It could just be variance that got you to 3-0. His premise is kinda dumb. When he says "the setup isn't entirely correct", he basically means it isn't correct at all.

You beat me to it...

PatsFan1283 · May 8, 2018

Fwiw it isn't that rare to be 80% the first 3 games of a series. The best teams against the worst teams in rd 1 will be about that. Be like 85% for gm 1-2 and then like 70% for gm 3. I.e Rockets/Wolves, Warriors (if they had Curry) vs SA.

And that's where a lot of sweeps happen. But that's really the only setup it would be accurate for.

MattyMatt · May 8, 2018

PatsFan1283 said:
It's accurate that if you get up 3-0 that you are likely to be the better team and thus the next 4 games don't average out to 50/50 propositions.

But when he assigns the team up 3-0 an 80% probability to win, he's basically just pulling that # out of nowhere. That's a big #, it's -400 every single game. So his .2% is off unless we're talking a Rockets/Jazz type disparity in team ability.

Who says winning 3 in a row means you had 80% probability to win atleast 3 games? It could just be variance that got you to 3-0. His premise is kinda dumb. When he says "the setup isn't entirely correct", he basically means it isn't correct at all.

True that...

919 · May 8, 2018

Knicks forced a game 7 against the Royals in the 1951 finals
Nuggets forced a game 7 against the Jazz in the 1994 WC semis
Blazers forced a game 7 against the Mavs in the 2003 WC 1st round

niltes · May 8, 2018

his analysis is very simplistic. their are severe home/road biases in hoop,
matchups that can't be handled as easily, and a host of other factors.
his math just isn't insightful here. that being said, it will be done. even
as a celtic fan, I can see that the 76's are at least as talented as boston
at the present time. if philly gains some confidence, they could win this
series despite being outcoached.

DrunkenHorseplayer · May 8, 2018

There exists much less variance in basketball compared to hockey or baseball, as evidenced by the fact that it's not uncommon for a basketball team to win 3/4 of their games whereas in the other two sports it's unheard of. When a basketball team goes up 3-0, it's all but guaranteed that it's because they're a significantly superior team; in the other sports, it's possible that there's an element of luck in building that lead.

Willie99 · May 8, 2018

I really don't think it's about math at all, it's about talent

Upsets are truly rare in an NBA best of 7, and the better teams are the ones with the 3-0 series leads

NBAcapper08 · May 8, 2018

Willie99 said:
I really don't think it's about math at all, it's about talent

Upsets are truly rare in an NBA best of 7, and the better teams are the ones with the 3-0 series leads

except this series, where the sixers are clearly better

Willie99 · May 8, 2018

haha, not a chance, what they are is clearly over-matched

while the C's will be fine tuning after the season, the 76er's will be changing their makeup

maybe they can merge with Toronto a create one balanced team that can compete come May

festeringZit · May 8, 2018

NBAcapper08 said:
except this series, where the sixers are clearly better

Huh?

Sixers are not clearly better. And pretty soon they'll be watching the Celtics in the playoffs on their TV.

NBAcapper08 · May 8, 2018

festeringZit said:
Huh?

Sixers are not clearly better. And pretty soon they'll be watching the Celtics in the playoffs on their TV.

ill be cheering for the celtics as if they were my favorite team if they advance past the sixers. but in the mean time they are all fags!

road2perdition · May 8, 2018

NBAcapper08 said:
except this series, where the sixers are clearly better

I hope this was a joke? Sixers beat a lot of bad teams during that streak towards the end of the season. This team isn't as good as people think. Overhyped.

JackStraw77 · May 9, 2018

919 said:
Knicks forced a game 7 against the Royals in the 1951 finals
Nuggets forced a game 7 against the Jazz in the 1994 WC semis
Blazers forced a game 7 against the Mavs in the 2003 WC 1st round

This is what I didn't know. Out of 129 3-0 leads it's only reached game 7 3 times. This shows you how rare a 3-0 team ever gets in jeopardy of losing the series. You know what irritates me is when people bring up the NHL where a few 3-0 leads have been blown noting that the Flyers won several years ago being down 0-3. Hockey is so much different than the NBA where for the most part home ice doesn't matter. You see upsets all the time in the NHL where fluke goals are scored. It doesn't mean the better team won. It also doesn't take much to unnerve a goaltender. A couple of pucks get through and his confidence is gone for the entire series. NBA players can get into shooting slumps but for the most part if they miss a couple of jump shots they shake it off either the same game or the next. Most goaltenders can do that but even the best get rattled in one period and now they can't stop anything. Same goes for lesser goaltender. He makes some key stops and suddenly turns into a Hall of Famer for the rest of the series.

Mathematical Equation As To Why No NBA Team Has Ever Recovered From A 3-0 Deficit

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