Come shed a tear

[Snowman]

Originally Posted by raulus

Just out of curiosity, what does the math say about the difference between a 5-game and a 7-game series in terms of the probability of a major underdog knocking off a favorite? Just for fun, let’s say a hypothetical team with 89 wins was facing another hypothetical team with 111.

There are a few ways to estimate the probability that team A will beat team B for any given game. Bill James uses a logistic rating model that he dubbed the 'Log5 method'. It's basically the same thing as the Bradley-Terry model or the Elo rating system in chess. That formula looks like this:

Let P(A) = team A's true win%
Let P(B) = team B's true win%
Let P(A,B) = the probability of team A beating team B for any given game (yes, this ignores the variance incurred through specific pitching matchups and would need to be adjusted for home field advantage, but it is still a useful estimate over the course of a series)

Then,
P(A,B) = [P(A) - P(A)*P(B)] / [(P(A) + P(B) - 2*P(A)*P(B)]

In this example, the Dodgers win% = 0.685, and the Padres win% = 0.549. So, plugging those values in for the Dodgers vs Padres, we get:

P(A,B) = 0.641

In order to estimate the probability for a 5-game or 7-game series, we can use binomial expansion. The formula looks like this, where p is the win% of team A and q is the win% for team B (or 1-p) for any given game:

win%_7game = p^4 + (p^3)*(q)*choose(4,3)*p + (p^3)*(q^2)*choose(5,3)*p + (p^3)*(q^3)*choose(6,3)*p

win%_5game = p^3 + (p^2)*(q)*choose(3,2)*p + (p^2)*(q^2)*choose(4,2)*p

So, in our example here with the Dodgers having an expected win% of 0.641 vs the Padres, the likelihood of the Dodgers winning a series against the Padres could be estimated as:

Dodgers 5-game win% = 75.0%
Dodgers 7-game win% = 78.5%

I didn't look this up for the series, but it's probably a good estimate for what the Vegas line might have been for the Dodgers to win the series against the Padres before any games were played.

Also worth noting is that this is a pretty wide win% gap for baseball. The Dodgers were an historically elite team this year. Most series odds are going to be a lot closer than that. Baseball playoffs nearly is a game of flipping coins for the most part. Luck plays a much larger role in the MLB than it does in the NBA and NFL.

Originally Posted by brianp-beme

How about NFL playoff where you lose once and you are gone? And flipping coins is a ritualized part of every football game.

Brian

That actually doesn't matter nearly as much as you'd think because in the NFL, the better team beats the weaker team far more often than in baseball for any given game. If you look at the win% for the best team in the NFL, it's usually pretty close to 90% for any given season, whereas in the MLB, it's typically only around 60%. In the NBA, it's closer to 80%.

The best teams win the championship far more often in the NBA and the NFL than they do in the MLB. It's just the way it is. There's a LOT of luck in baseball, and it takes a very long time for that to even out.

[raulus]

Originally Posted by Snowman

So, in our example here with the Dodgers having an expected win% of 0.641 vs the Padres, the likelihood of the Dodgers winning a series against the Padres could be estimated as:

Dodgers 5-game win% = 75.0%
Dodgers 7-game win% = 78.5%

So a 3.5% difference in win probability between a 5-game series and a 7-game series?

Doesn't seem like it's enough to get too fussy about the Dodgers losing a short series. But I suppose if you were banking on that 3.5% to be the difference between victory and defeat, then your fussiness level might rise.

[Snowman]

Originally Posted by raulus

So a 3.5% difference in win probability between a 5-game series and a 7-game series?

Doesn't seem like it's enough to get too fussy about the Dodgers losing a short series. But I suppose if you were banking on that 3.5% to be the difference between victory and defeat, then your fussiness level might rise.

Ya, it's not a huge gap. The delta between 5 & 7 game series is not uniformly distributed though, meaning it's not always going to be 3.5%. It depends on the delta between team strengths.

For the Yankees vs Guardians series, the calculation works out to the Yankees winning a 7-game series 59.6% of the time and a 5-game series 58.3%, so it's even more narrow when the teams are closer in strength.

Honestly, the whole idea of having playoffs is kinda silly to begin with if looking at it from the perspective of wanting the best team to win. The way they did it back in Mantle's day was obviously best for that. You just played 162 games to see who the best teams are. Now you know. Just have one 7-game series between the Dodgers and the Astros, and call it good. But where's the fun in that (and the money)? Hence... playoffs.

[Snowman]

Originally Posted by Peter_Spaeth

Maybe over 162 games that pays off. In a shot series no thank you. If Max Scherzer is in total command after 4 innings, every computer on earth could tell me to pull him in in favor of the no name middle reliever, and I would absolutely ignore that. A computer can't see command.

Originally Posted by G1911

I have no doubt that, on average, after 6 innings putting in a fresh pitcher is more likely to help your team win over the course of a season with a large sample size.

I have serious doubts that, after 6 innings, pulling a star pitcher who is still doing well and putting in a rando will help your team win over the course of a season with a large sample size.

On a game by game basis, it is a stupid thing to do without factoring in the specifics of that day and how the pitchers 'feel' as teams keep finding in the playoffs.

It's not really a question anymore though. We have the data to be able to answer that now. Every arm eventually tires out. And a tired arm from even an elite pitcher is still outperformed by a fresh arm from a good reliever. And you can't really know when that elite SP's arm is going to tire out. It typically happens very quickly. They're throwing fire until all of a sudden they're getting shelled. And the SP can't tell you either. They always think they're fine. Egos get involved too. So you go to the data. You look at things like xFIP rates and WHIP rates and K/BB rate curves by pitch count and some of the more advanced sabermetrics for each guy over the course of a season, and you pull him when that curve shows he's most likely about to drop.

Originally Posted by Peter_Spaeth

If the NFL season was 162 games, would the best team still win 90 percent, or is there something going on here with sample size?

Yes, they'd still win 90%. Or rather there's an underlying "true" team win% that each team converges to over the course of a season. It happens very quickly in football and basketball, and it takes a very long time in baseball. Fivethirtyeight.com did study on this a few years back where they calculated the amount of information gain about team strength across various sports. They used a methodology developed by Tom Tango that examines variance of outcomes. The Cliff Notes are that a 17-game NFL season provides as much information about team strength as would 104 MLB games, and as much information as 19 NBA games.

https://fivethirtyeight.com/features...e-nfl-and-nba/

[Fred]

Well Yankee haters, gotta wait another day to either celebrate or say "damn Yankees". Gotta feel sorry for those that drove from Jersey to see the game. Could have had a nice T206 HOFer for the tolls, parking and other money spent. Now they gotta do it again on Tuesday.

[Peter_Spaeth]

Originally Posted by Snowman

It's not really a question anymore though. We have the data to be able to answer that now. Every arm eventually tires out. And a tired arm from even an elite pitcher is still outperformed by a fresh arm from a good reliever. And you can't really know when that elite SP's arm is going to tire out. It typically happens very quickly. They're throwing fire until all of a sudden they're getting shelled. And the SP can't tell you either. They always think they're fine. Egos get involved too. So you go to the data. You look at things like xFIP rates and WHIP rates and K/BB rate curves by pitch count and some of the more advanced sabermetrics for each guy over the course of a season, and you pull him when that curve shows he's most likely about to drop.

But for decades and decades, elite pitchers went the distance, and until very recently went 7, if they were pitching well, and countless low ERA seasons throughout MLB history support that they didn't lose that much effectiveness? How do you reconcile that with the notion that even elite pitchers should be yanked after 4 routinely?

[campyfan39]

Roberts is an idiot. I have no doubt with a full season last year he would have found a way to make the Dodgers lose.

I love Kershaw and Chris Taylor and JT and a few other players and that is why I pull for them.

Hated to see Jansen, Seagar and Joc go last year but my second favorite player in the league was Freeman and the Dodgers got him so I was all in again...... Not sure about going forward. Staying up late and buying mlb package to watch Roberts screw it up again has really burnt me.

[robertsmithnocure]

Originally Posted by campyfan39

Roberts is an idiot. I have no doubt with a full season last year he would have found a way to make the Dodgers lose.

Don’t you mean 2020? The Braves won it all last year.

[Peter_Spaeth]

Originally Posted by Snowman

There are a few ways to estimate the probability that team A will beat team B for any given game. Bill James uses a logistic rating model that he dubbed the 'Log5 method'. It's basically the same thing as the Bradley-Terry model or the Elo rating system in chess. That formula looks like this:

Let P(A) = team A's true win%
Let P(B) = team B's true win%
Let P(A,B) = the probability of team A beating team B for any given game (yes, this ignores the variance incurred through specific pitching matchups and would need to be adjusted for home field advantage, but it is still a useful estimate over the course of a series)

Then,
P(A,B) = [P(A) - P(A)*P(B)] / [(P(A) + P(B) - 2*P(A)*P(B)]

In this example, the Dodgers win% = 0.685, and the Padres win% = 0.549. So, plugging those values in for the Dodgers vs Padres, we get:

P(A,B) = 0.641

In order to estimate the probability for a 5-game or 7-game series, we can use binomial expansion. The formula looks like this, where p is the win% of team A and q is the win% for team B (or 1-p) for any given game:

win%_7game = p^4 + (p^3)*(q)*choose(4,3)*p + (p^3)*(q^2)*choose(5,3)*p + (p^3)*(q^3)*choose(6,3)*p

win%_5game = p^3 + (p^2)*(q)*choose(3,2)*p + (p^2)*(q^2)*choose(4,2)*p

So, in our example here with the Dodgers having an expected win% of 0.641 vs the Padres, the likelihood of the Dodgers winning a series against the Padres could be estimated as:

Dodgers 5-game win% = 75.0%
Dodgers 7-game win% = 78.5%

I didn't look this up for the series, but it's probably a good estimate for what the Vegas line might have been for the Dodgers to win the series against the Padres before any games were played.

Also worth noting is that this is a pretty wide win% gap for baseball. The Dodgers were an historically elite team this year. Most series odds are going to be a lot closer than that. Baseball playoffs nearly is a game of flipping coins for the most part. Luck plays a much larger role in the MLB than it does in the NBA and NFL.




That actually doesn't matter nearly as much as you'd think because in the NFL, the better team beats the weaker team far more often than in baseball for any given game. If you look at the win% for the best team in the NFL, it's usually pretty close to 90% for any given season, whereas in the MLB, it's typically only around 60%. In the NBA, it's closer to 80%.

The best teams win the championship far more often in the NBA and the NFL than they do in the MLB. It's just the way it is. There's a LOT of luck in baseball, and it takes a very long time for that to even out.

If the NFL season was 162 games, would the best team still win 90 percent, or is there something going on here with sample size?