[Xenoamorphous]

> Recently, teams have realized three-pointers have higher point value despite their lower scoring percentage.

This was such an eye-opener for me. A high-stakes sport like basketball/the NBA went on for decades without realising the simple math that three pointers are more valuable than two-pointers if you just do the basic math. How many areas in our lives are yet to be optimised with really basic math?

[BoxFour]

Disclaimer: I have only extremely limited exposure to this topic (I worked in sports analytics, attached to a team, quite awhile ago), so take it all as heavy speculation:

1) It seems like there’s a natural resistance to change driven by loss aversion; you see a similar pattern in the NFL with decisions like punting vs. going for it on fourth down. Even if the expected value is positive, the failures are given far more weight than the successes.

2) In general, there's a lot of skepticism toward analytics until they reach a tipping point where they’re impossible to ignore, at which point they take over completely and introduce shifts like the ones shown here.

Moneyball, for example, has plenty of anecdotes about front office staff and coaches dismissing analytics in favor of “gut instincts”—and that was in 2002! In baseball, a sport which adopted advanced analytics far faster than others (obviously in no small part due to teams like that As roster).

Even today, plenty of NBA personalities push back against analytics—Reggie Miller, for example, has been pretty vocal about his distaste for them. He's obviously increasingly alone in that opinion, but it can be really hard to break old habits.

[dleink]

Baseball lent itself to advanced analytics even before player tracking became a thing, since the sport consists of a series of discrete one-on-one matchups with limited possible outcomes.

[ysavir]

I'm guessing that it's more complicated than that. Possibly when the specifications for a basketball court were laid out, the 3-point line was intentionally drawn where it would be a risky shot. And the coaching/playing culture developed with that mindset.

But since then people have gotten at least a little bit taller. We developed more ways in which to train and grow our physical strength. Training got more intense, improving results. And more subtle changes along those lines, which are micro-changes that accrue over time, and often hard to notice.

It can take a while for someone, anyone, to realize that all the various changes have made what was intended to be a risky maneuver into a viable play. It seems obvious in retrospect, but until someone points it out, it's one of those avenues of thought requires you to shake off what you've known your whole life before you can accept it.

Could also be that none of that was relevant, but it's worth considering and keeping in mind.

[brandall10]

"But since then people have gotten at least a little bit taller. We developed more ways in which to train and grow our physical strength."

The person who shifted this mindset is one of the smallest players in the the NBA though, would be considered small by the standards of any era of the game. And in fact, the game has shifted to smaller players in general in recent years. It's more of a skill/agility thing.

I do believe technology has played a part though. Being able to 3d scan a player's motion and find mechanics adjustments has proven to be quite powerful.

[Y_Y]

Ok, so we learn a function mapping position on the court to point value. Clearly a step function was too simple. Might want to fix the values during the games though to make it a bit easier on the fans.

[rossdavidh]

One possibility is that there are more players who can make 3-point shots at a high enough percentage to make this true. Also, it depends on how good the defense is vs. 2-point shots; if that gets tighter, then the 3-point shot becomes more valuable.

Which also suggests how things may continue to evolve; the best defense vs. 3-point shots probably compromises your defense vs. 2-point shots, and eventually some team will "realize" that they can do better with _fewer_ 3-point shots.

Further complication comes from rebounds; the player taking the 3-point shot is less likely to be able to get the rebound if he misses, relative to a player trying to dunk it. So, the math is not trivial, and it depends on what the other team is expecting/guarding against, which might make it a non-linear system (i.e. constantly evolving over time).

There was a time when chess theory said that there was one perfect, optimal opening, and anything else was a mistake. It was sort of true, until everyone took it as a given, and then doing another opening meant your opponent wasn't as likely to be prepared for it.

[prawn]

A tall player who can't make threes, is more limited in the modern NBA and more limiting for roster construction. As a result, a lot more practice would be allocated to shooting from range. Look at someone like Brook Lopez (7-foot centre) who attempted 31 threes total in his first 8 seasons. Then started attempting 250-500 threes/season after that (peaked at 512 attempts).

Developing players who are elite prospects are also now less likely to be pigeon-holed during development into: you're tall as a 12 year old, so just focus on drills for centres. So yes, there would absolutely be growth in the number of capable shooters.

On your point about realisation, teams already optimise to favour threes and high-percentage twos. They try to stretch defence to each extreme, but you need to excel and threaten at both things at any given point because teams will adjust constantly during the game.

[necovek]

While most of what you say correlates, there are other gotchas: moving around a 3pt line leaves a lot more space for defenders to cover, and the real innovation is introducing multiple staggered blocks to open up a 3pt shooter (as a development of pick-and-pop). And moving around an even farther imaginary line at like 40ft from basket and making ~35% of those shots.

So it really is impossible to cover a more than 33% shooter all around the court, and that equates to a better than 50% 2pt shooter.

[atmosx]

No, because hand-checking was allowed back then. Smaller guards like Mark Price for example, would go off in some games but stronger, bigger defenders would ultimate shut them down because they could feel and follow their movements with their hands. Now, if you so much as think too much of a player, they call a foul - supposedly to help the offense and make the game more entertaining. The result? A watered-down product where any team can win on any given night, but no one cares because defense is nonexistent during the regular season.

The only basketball that really matters happens in the playoffs; the rest is irrelevant and says nothing about the true power rankings.

[teej]

This is classic innovators dilemma.

Coaches and owners are not rewarded for innovation. Fans strongly discourage taking bets that could fail.

And then there’s preparing for the strategy change. Training, practice, and coaching time is extremely limited. How much do you re-allocate to this new approach? You don’t just tell players to take more 3s, it’s more complicated than that.

So in traditional innovators dilemma fashion, it’s much easier to follow when you see that the new way works. It’s easier to convince everyone (fans, coaches, players, owners) to get on board when you can point to Steph Curry doing it right.

[raincole]

It's such an arrogant comment.

"Really basic math"? Do you think NBA coaches reached this conclusion like this:

1. A player can throw X 2-points in a game.

2. Or he can throw Y 3-points in a game.

3. 3Y > 2X, so we should just throw 3-points all the time.

It's absolutely not what happened. And the reason teams didn't discovery the current strategy decades earlier was absolutely not that they couldn't do basic math.

[Xenoamorphous]

In the 2008-2009 season, the year before Curry’s debut, the 3p percentage was 36% vs 2p percentage of 48%. If you took 100 shots of each you’d have 108 points vs 96 so yeah I consider that quite simple.

And call me naive maybe but not arrogant, I’ve never been called that in my life so it’s quite surprising to be called arrogant in HN where I know the average person is smarter than me.

[brutalhonesty]

It really is basic math though.

A 3 point shot with 36% chance to go in (league average) = 1.08 points per attempt.

A mid-range 2 point shot with 45% chance to go in = .9 points per attempt.

The math is very basic.

[tomjakubowski]

When you elect to take more three pointers you necessarily have to resort to shooting more difficult ones, which lowers the expected return on each one. In the real world it's not so simple.

Similar reason why star players often have lower FG% than one might think: they are the ones tasked with trying _something_ when the shot clock winds down and there's no clear play. Not all shots are chosen equally.

[Xenoamorphous]

> When you elect to take more three pointers you necessarily have to resort to shooting more difficult ones, which lowers the expected return on each one

But then 2 pointers become easier. You can’t defend tightly both the perimeter and the paint at the same time. Sounds like a win-win. Again, nobody seemingly noticed.

[relaxing]

Do you watch NBA games?

[HDThoreaun]

He is right. The highest volume shooting teams play 5 out which leads to easy layups as well.

[Dylan16807]

> When you elect to take more three pointers you necessarily have to resort to shooting more difficult ones, which lowers the expected return on each one.

Well yeah, the idea is not to go all 3-pointer, it's that the borderline decisions need to adjust a few notches in favor of attempting 3-pointers, until the returns are balanced out.

> Not all shots are chosen equally.

I agree, that is a proper issue to figure out.

[grandempire]

This assumes the game is static and the question is selecting A or B, but all the variables are intertwined.

How does the percentage change when the other team knows you will go for 3? How much more effective is the three when you are able to have the threat of other scoring? A layup is 80-90% isn’t it worth it to try to create one?

[Xenoamorphous]

Precisely. Shooting lots of threes with good/decent efficiency also made two pointers more likely as more players would be defending the perimeter. Again, seemingly nobody thought of this for decades.

[grandempire]

It’s not insightful to say your team is more effective when you have the real threat of scoring 3s. That’s not a new idea.

Comparing probability of shot A vs shot B is just not a sufficient model. Its not simple math to model basketball.

[Xenoamorphous]

Then why the first time someone tried it then it worked and it stuck for 15 years or so? Last season there were 35 3p attemtps per game on average vs 18 in the year before Curry’s debut, almost 2x.

It it really impossible to think that it was a huge oversight?

[chatmasta]

It was not always 36% and in fact for a while it had lower EV than two pointers.

(Also, any league average for three pointers will suffer from obvious selection bias.)

[jitl]

Claim the math is very basic is reminding me of the different conclusions people have drawn from this image: https://en.m.wikipedia.org/wiki/Survivorship_bias#/media/Fil...

[Xenoamorphous]

So in the 2008-2009 season, the one before Curry’s debut, the average number of 3 pointer attempts per game from a team was 18. Last season it was 35, so pretty much 2x.

If it was so intricate why nobody tried it before? And why after someone tried it it seemingly stuck? Is it really that far fetched that it was actually pretty simple and nobody noticed for many years?

Even if you consider the adjustement to the defense, you’d be making two pointers easier as you can’t defend tightly both the perimeter and the paint at the same time.

[relaxing]

It was absolutely tried before. The 08 Magic shot threes at a similar % and volume to the 2015 Warriors, yet they got rolled in the playoffs every time.

[necovek]

But it isn't just simple math.

Yes, 33% for 3pts equals a 50% 2pt shot, so beat that, and you've got yourself a pretty good scorer. But hitting 33% is not trivial unless you make a lot of other adjustments: multiple blocks for the shooters and not just a simple pick-and-roll or pick-and-pop, staggered blocks for a shooter switching from one sideline to the next. This has actually led to less specialization, as every player on the court needs to shoot 3s and defend faster or bigger players as switches became unavoidable.

And with all that, it only led to a "dynasty" when one player who could create his own shot and shoot from nearly anywhere at 35+% (Curry), paired with another ~40% career 3pt shooter and defensive specialist (Thompson) and completed with a power forward who could defend anyone and coordinate the attack too (Green). Even so, they did need another future hall-of-famer in Durant to win two of their last 3 rings.

That same team still has 2 of those core people in them, but they are unable to replicate anywhere near the success.

So if anyone can do this, why doesn't everyone do it?

[zzo38computer]

This math makes sense, but it might not not always be so simple.

For example, maybe these probabilities might not always be the same as this in all circumstances. Also, how much risk you might take also might depend on the current score and remaining time (e.g. maybe you are likely to win even with only one more point than your current score, or maybe it depends how much time it takes to make a specific shot (I don't actually know enough about basketball to know if this is relevant)), and on how your opponent can defend against it at a specific situation (and if their defense would allow them to score instead; I don't actually know how much that is relevant either), maybe. There are probably other considerations as well.

(I do not actually know all of the rules or strategy of basketball, so if I am wrong, you can mention what mistake I made.)

[1970-01-01]

OK so eFGs are basic math. Are we ignoring them??

https://www.basketball-reference.com/leagues/NBA_stats_per_g...

https://www.basketballforcoaches.com/effective-field-goal-pe...

[tracerbulletx]

Right because it was x * 2P% * 2 < Y * 3P% * 3

[unyttigfjelltol]

4th down attempts in American football come to mind. Twenty years ago they were rare; mathematically they should be common.[1] Coaches have shifted with the math but not quite as dramatically as it suggests.

[1] https://malteranalytics.github.io/nfl-4th-down/

[tclancy]

It’s a bit of a dodge. In the 80s and 90s, there were a handful of players making 40% of threes and most shooters were closer to 30% so the math didn’t used to be the same.