phew, just had to get that out of my system Join Wrath of Math to get exclusive videos, lecture notes, and more: ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin More math chats: ruclips.net/p/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO
This is a really hot take. The Chiefs have a good of chance of winning as any of the 8 teams remaining. As long as Patrick Mahomes is the quarterback, you always have a very high chance of winning the Super Bowl.
@@gadglichtg4840 Well, I was to do it, I'd first normalize the data... it doesn't matter what the exact PF and PA are, just the ratios. With that the two values add up to 1, so the ratio for PA is equal to 1-PF. So we've reduced our function to one variable. Similarly, you take the results and normalize them by reducing them to the win percentage. So we have a function from one value to another, and lots of data. So we want a regression on that data... like finding the exponent that minimizes the sum of the squares of the errors. Personally, I'd just do it numerically, write a program to crunch the numbers and find the best fit to within a reasonable factor (which given the very discrete nature of "win-loss" records doesn't have to be that focused).
2:11 great reference. I think the falcons should take that advice. Great video I would like to see that Pythagorean expectation used on some other teams like the 07 patriots or the 2017 browns to see examples of it being used in either extreme. Another thing you could do is bring up the point differential of the teams in the AFC who are still around (Texans, ravens, bills) and look at their Pythagorean expectation. Or get the NFC teams (lions, eagles, commanders, rams) and look at them as well to give a better comparison. I know it’s not perfect but it would help visualize it better getting more points
I wonder how the idea of "skipped points" factors into these formulas. For example, if two teams are playing baseball, and the team who plays second is in the lead as of the middle of the 9th inning, then they don't play that inning -- they have already won, and the points that they might have earned in that inning aren't counted in the total, even though the points they allowed (if any) in that inning are counted. Or sometimes, if a football team is in the lead in the last 30 seconds or minute (not sure exactly what the limit is) and they have control of the ball, they might just put the ball down and do nothing, having won the game. They don't need to try to score on the last play. Maybe if they had played, they could have increased their lead, but they didn't.
Love the math but American football has always been a game of inches. They are always on the edge. If not, they lose. It like a famous racecar driver once said, "If you feel you are in control, you're not winning".
Chiefs have outperformed their point differential every year with mahomes (thats 7 seasons in a row). Every single year they made the top 4 (conference championship). The reason all their games are close is because Andy Reid likes to manage their leads so whenever the Chiefs are up 7+, they try to run the clock out instead of scoring more points (because when Andy was aggressive in 2013, they blew a 28 pt lead to the colts in the wild card and lost 45-44). The chiefs have gotten lucky for sure but they're still the favorites. The issue with Pythagorean expectation is that it assumes all points are equal and can be manipulated like that. But some points are garbage time points and others are clutch time points. The metric win probability added is unbiased since for every game the winner has added exactly 50% more Win Probability than the loser. This properly accounts for different points being worth different amounts. Imagine a team could score 50 points in the first quarter then played scrubs the final 3 quarters. The pythagorean formula puts too much weight on the garbage time skewing it incorrectly. Conclusion, the Chiefs went 15-2 but are more like a 13-4 team (similar to the Bills and Ravens), so yes they were slightly lucky but they're not completely fraudulent as Pthag says since it includes a 38-0 loss with the backups playing. Your video makes incorrect conclusions based on hatred of the Chiefs. The Chiefs only having a +59 point differential is a cool statistical oddity, but they are the exception that proves the rule. I'm a huge sports guy and a huge math guy.
Football is fake. It's bread and circus, nothing more. Imagine being so naive to think that millions of dollars are on the line, but the winners of each game are left to random chance...
@@inutamer3658 For the purpose of winning a game, you only need one more point that the opposing team when the game finishes. If your strategy is to get a modest lead and then defend it hard, and you are better at the game than the opposing teams, you would win plenty of games (because you're good at the game) but have a relatively low difference between points allowed and points conceded (because you stop attempting to earn more points when you have that small lead). In the data being gathered for the expectation you'd see games you lost by a huge difference, games you barely lost, and games you barely won, but would see very few games which you won by a great point difference (because you don't try to do this), and this violates some of the assumptions behind the expectation. Aiming to play conservatively maintaining a small lead will make you more vulnerable to bad luck in the final minutes of the game, but bad luck earlier in the game results in you switching back to aggressive play and potentially regaining the lead. I suspect that mathematically the result of different scoring strategies (particularly a flexible one which changes based on the state of the game) is a different optimal exponent in the pythagorean expectation, but I doubt there's enough data out there to generate the more accurate array of exponents for the modern strategies and teams - 2.37 is going to be a best fit averaged out across the coaching styles of all the NFL teams, while you'd get a different result for each if you looked at each coach in isolation (can't say if it would be a large difference, of course).
@@inutamer3658Because there's no difference venteee winning by 30 points or by 100 points, so once you're that far ahead they're not even trying anymore
@davidp.7620 from what I gather that's when they shift to preventing goals? That's accounted for in the equation. I mean I assume you aren't saying they put down their hats and just sit the rest of the game out right
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
phew, just had to get that out of my system
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Isaac Punts shout out is not something I expected in this video
"if you go up 28-3, well its a lock youre not gonna beat that team" *falcons fans are angry*
I probably would enjoy sports more if there was this much math during the games.
that 28-3 joke hurt
im not even from atlanta but it still hurt
This is a really hot take. The Chiefs have a good of chance of winning as any of the 8 teams remaining. As long as Patrick Mahomes is the quarterback, you always have a very high chance of winning the Super Bowl.
How do they decide the exponent? I mean specifically. Does it get adjusted?
There's decades of data... use that to find the exponent that best fits the data.
Wondering too
@@gadglichtg4840 Well, I was to do it, I'd first normalize the data... it doesn't matter what the exact PF and PA are, just the ratios. With that the two values add up to 1, so the ratio for PA is equal to 1-PF. So we've reduced our function to one variable. Similarly, you take the results and normalize them by reducing them to the win percentage. So we have a function from one value to another, and lots of data. So we want a regression on that data... like finding the exponent that minimizes the sum of the squares of the errors. Personally, I'd just do it numerically, write a program to crunch the numbers and find the best fit to within a reasonable factor (which given the very discrete nature of "win-loss" records doesn't have to be that focused).
2:11 great reference. I think the falcons should take that advice. Great video I would like to see that Pythagorean expectation used on some other teams like the 07 patriots or the 2017 browns to see examples of it being used in either extreme. Another thing you could do is bring up the point differential of the teams in the AFC who are still around (Texans, ravens, bills) and look at their Pythagorean expectation. Or get the NFC teams (lions, eagles, commanders, rams) and look at them as well to give a better comparison. I know it’s not perfect but it would help visualize it better getting more points
Love from new zealand! ❤ 🇳🇿
I wonder how the idea of "skipped points" factors into these formulas. For example, if two teams are playing baseball, and the team who plays second is in the lead as of the middle of the 9th inning, then they don't play that inning -- they have already won, and the points that they might have earned in that inning aren't counted in the total, even though the points they allowed (if any) in that inning are counted.
Or sometimes, if a football team is in the lead in the last 30 seconds or minute (not sure exactly what the limit is) and they have control of the ball, they might just put the ball down and do nothing, having won the game. They don't need to try to score on the last play. Maybe if they had played, they could have increased their lead, but they didn't.
What a magnificent dive
Surely the Devil Rays were more likely to... flounder.
They won’t be doomed if they used something more natural.
instead of the devil magic they have been using?
Can't believe I'm saying two videos in a row *clears throat*
Of COURSE it had to be 37
When a mathematician gets bored. Please get back to the good stuff!
Love the math but American football has always been a game of inches. They are always on the edge. If not, they lose. It like a famous racecar driver once said, "If you feel you are in control, you're not winning".
True, it's part of why it's such a great sport!
Chiefs have outperformed their point differential every year with mahomes (thats 7 seasons in a row).
Every single year they made the top 4 (conference championship).
The reason all their games are close is because Andy Reid likes to manage their leads so whenever the Chiefs are up 7+, they try to run the clock out instead of scoring more points (because when Andy was aggressive in 2013, they blew a 28 pt lead to the colts in the wild card and lost 45-44).
The chiefs have gotten lucky for sure but they're still the favorites.
The issue with Pythagorean expectation is that it assumes all points are equal and can be manipulated like that.
But some points are garbage time points and others are clutch time points.
The metric win probability added is unbiased since for every game the winner has added exactly 50% more Win Probability than the loser. This properly accounts for different points being worth different amounts.
Imagine a team could score 50 points in the first quarter then played scrubs the final 3 quarters. The pythagorean formula puts too much weight on the garbage time skewing it incorrectly.
Conclusion, the Chiefs went 15-2 but are more like a 13-4 team (similar to the Bills and Ravens), so yes they were slightly lucky but they're not completely fraudulent as Pthag says since it includes a 38-0 loss with the backups playing.
Your video makes incorrect conclusions based on hatred of the Chiefs. The Chiefs only having a +59 point differential is a cool statistical oddity, but they are the exception that proves the rule.
I'm a huge sports guy and a huge math guy.
I don't know much about sports. Why are all points not to be treated equally?
Football is fake. It's bread and circus, nothing more. Imagine being so naive to think that millions of dollars are on the line, but the winners of each game are left to random chance...
@@inutamer3658 For the purpose of winning a game, you only need one more point that the opposing team when the game finishes. If your strategy is to get a modest lead and then defend it hard, and you are better at the game than the opposing teams, you would win plenty of games (because you're good at the game) but have a relatively low difference between points allowed and points conceded (because you stop attempting to earn more points when you have that small lead). In the data being gathered for the expectation you'd see games you lost by a huge difference, games you barely lost, and games you barely won, but would see very few games which you won by a great point difference (because you don't try to do this), and this violates some of the assumptions behind the expectation.
Aiming to play conservatively maintaining a small lead will make you more vulnerable to bad luck in the final minutes of the game, but bad luck earlier in the game results in you switching back to aggressive play and potentially regaining the lead.
I suspect that mathematically the result of different scoring strategies (particularly a flexible one which changes based on the state of the game) is a different optimal exponent in the pythagorean expectation, but I doubt there's enough data out there to generate the more accurate array of exponents for the modern strategies and teams - 2.37 is going to be a best fit averaged out across the coaching styles of all the NFL teams, while you'd get a different result for each if you looked at each coach in isolation (can't say if it would be a large difference, of course).
@@inutamer3658Because there's no difference venteee winning by 30 points or by 100 points, so once you're that far ahead they're not even trying anymore
@davidp.7620 from what I gather that's when they shift to preventing goals? That's accounted for in the equation. I mean I assume you aren't saying they put down their hats and just sit the rest of the game out right
i appreciate the mathematical insides but still u mention the chief without the referees :)))😂
NERD!
Under 8 hunderex views! 4hrs ago!
7
Oh wow I didn't know sports could be made interesting
Cringe