This summer the Thinking Basketball podcast has been doing a series on the top 25 players[1] of the 21st century. I’ve been following the person behind the podcast for a while, Ben Taylor, and I think he has extremely good epistemics.
Taylor makes a lot of lists like these and he always is very nervous and hesitant. It’s really hard to say that Chris Paul is definitively better than James Harden. And people get mad at you when you do rank Paul higher. So Taylor really, really emphasizes ranges. For Paul and Harden specifically, he says that Paul has a range of 6-17 and Harden has a range of 13-25. So yeah, given these ranges it’s very possible that Harden is in fact the better player.
Here’s what his list looks like with ranges in brackets:
LeBron James [1-3]
Shaquille O’Neal [1-6]
Steph Curry [1-8]
Kevin Garnett [2-9]
Nikola Jokic [2-9]
Tim Duncan [2-10]
Dwyane Wade [4-11]
Kobe Bryant [6-15]
Giannis Antetokounmpo [6-15]
Kevin Durant [7-15]
Kawhi Leonard [7-16]
Chris Paul [6-17]
Steve Nash [8-19]
Dirk Nowitzki [7-19]
Shai Gilgeous-Alexander [7-20]
Tracy McGrady [10-24]
Anthony Davis [12-23]
Luka Doncic [12-24]
James Harden [13-25]
Joel Embiid [11-23]
Manu Ginobili [17-24]
Draymond Green [18-26]
Dwight Howard [17-28]
Jayson Tatum [20-28]
Russell Westbrook [20-32]
I think these ranges can be said to be confidence intervals. Taylor never explicitly used that phrase or said whether it’s an 80% confidence interval or 90% confidence interval or whatever, but yeah, I think that’s what these ranges are.
These confidence intervals made me think back to this idea ladder from What’s Our Problem?.
The author of the book, Tim Urban, distinguishes what you think from how you think, and lays out each of these dimensions in that diagram. For the horizontal axis, we can use politics as an example where liberal is to the left and conservative is to the right. For the vertical axis of how you think, high is good (like a scientist) and low is bad (like a zealot).
Of course, these two dimensions don’t tell the whole story. We’re compressing things down and losing information when we plot a point on this 2D graph. But as the saying goes, all models are wrong, some are useful.
Anyway, I think it’d be cool to add a third dimension: confidence. Maybe you think James Harden is the 19th best player of the 21st century, and you arrived at that belief by taking the high rung approach of thinking like a scientist, but how confident are you in that belief? Are you 90% sure that he’s like the 18th to 20th best player, or is your 90% confidence interval much wider?
Maybe we can describe this third dimension in terms of width. Someone who is “wide left” leans to the left but has a wide confidence interval. I don’t love conceptualizing this with width though because there aren’t enough adjectives. How do you describe medium width? Medium wide? I dunno.
When briefly describing your beliefs you need to reduce things down to few dimensions and be concise, so I think we need to be careful about “what we add”. But still, I’m a huge fan of talking about how confident you are in what you believe. I think it’s pretty underutilized and wish people included their confidence when describing their beliefs more frequently. And that said, my confidence in that belief is probably medium-low.
On your example: confidence intervals on ranking seem like quite a strange beast; it seems like you would get it by something like interval arithmetic on your confidence intervals for a scalar rating.
This summer the Thinking Basketball podcast has been doing a series on the top 25 players[1] of the 21st century. I’ve been following the person behind the podcast for a while, Ben Taylor, and I think he has extremely good epistemics.
Taylor makes a lot of lists like these and he always is very nervous and hesitant. It’s really hard to say that Chris Paul is definitively better than James Harden. And people get mad at you when you do rank Paul higher. So Taylor really, really emphasizes ranges. For Paul and Harden specifically, he says that Paul has a range of 6-17 and Harden has a range of 13-25. So yeah, given these ranges it’s very possible that Harden is in fact the better player.
Here’s what his list looks like with ranges in brackets:
LeBron James [1-3]
Shaquille O’Neal [1-6]
Steph Curry [1-8]
Kevin Garnett [2-9]
Nikola Jokic [2-9]
Tim Duncan [2-10]
Dwyane Wade [4-11]
Kobe Bryant [6-15]
Giannis Antetokounmpo [6-15]
Kevin Durant [7-15]
Kawhi Leonard [7-16]
Chris Paul [6-17]
Steve Nash [8-19]
Dirk Nowitzki [7-19]
Shai Gilgeous-Alexander [7-20]
Tracy McGrady [10-24]
Anthony Davis [12-23]
Luka Doncic [12-24]
James Harden [13-25]
Joel Embiid [11-23]
Manu Ginobili [17-24]
Draymond Green [18-26]
Dwight Howard [17-28]
Jayson Tatum [20-28]
Russell Westbrook [20-32]
I think these ranges can be said to be confidence intervals. Taylor never explicitly used that phrase or said whether it’s an 80% confidence interval or 90% confidence interval or whatever, but yeah, I think that’s what these ranges are.
These confidence intervals made me think back to this idea ladder from What’s Our Problem?.
The author of the book, Tim Urban, distinguishes what you think from how you think, and lays out each of these dimensions in that diagram. For the horizontal axis, we can use politics as an example where liberal is to the left and conservative is to the right. For the vertical axis of how you think, high is good (like a scientist) and low is bad (like a zealot).
Of course, these two dimensions don’t tell the whole story. We’re compressing things down and losing information when we plot a point on this 2D graph. But as the saying goes, all models are wrong, some are useful.
Anyway, I think it’d be cool to add a third dimension: confidence. Maybe you think James Harden is the 19th best player of the 21st century, and you arrived at that belief by taking the high rung approach of thinking like a scientist, but how confident are you in that belief? Are you 90% sure that he’s like the 18th to 20th best player, or is your 90% confidence interval much wider?
Maybe we can describe this third dimension in terms of width. Someone who is “wide left” leans to the left but has a wide confidence interval. I don’t love conceptualizing this with width though because there aren’t enough adjectives. How do you describe medium width? Medium wide? I dunno.
When briefly describing your beliefs you need to reduce things down to few dimensions and be concise, so I think we need to be careful about “what we add”. But still, I’m a huge fan of talking about how confident you are in what you believe. I think it’s pretty underutilized and wish people included their confidence when describing their beliefs more frequently. And that said, my confidence in that belief is probably medium-low.
Well, single season peaks.
On your example: confidence intervals on ranking seem like quite a strange beast; it seems like you would get it by something like interval arithmetic on your confidence intervals for a scalar rating.