We analysed 4,678,387 NBA shots

Check out Grant's Summer of Math Exposition (supported by Jane Street!)
some.3b1b.co/
More details here: 3blue1brown.substack.com/p/so...
Tim Chartier has a great book called "Get in the Game - An Interactive Introduction to Sports Analytics" if you'd like to learn more about their work. press.uchicago.edu/ucp/books/...
Here is their Davidson College page: www.davidson.edu/people/tim-c...
The song "Get Ready for Maths" is written and recorded by Jonny Berlin (based on the original "Get Ready for This" by 2 Unlimited). Listen to it over here: jonnyberliner-sciencesongs.ba... and check out Jonny's site: www.jonnyberliner.com/
And thanks to Nolan Rau, Liz Labows and Bec Hill for rounding out our team of six.
Check out MoMath's Hoop Curves. momath.org/home/hoop-curves/
Huge thanks to my Patreon supporters. They keep me in the game. / standupmaths
CORRECTIONS
- At 04:44 I say "Noel" in the voice over instead of Nolan. Sorry Nolan!
- Yes, in the plots of our shots at 05:13, 05:59 and 14:22 I left the axis labelled as "inches" and it should be "feet".
- At 11:18 I say "eight points" but I mean "point eight points".
- Let me know if you spot anything else!
Diagram of basketball court adapted from this one:
commons.wikimedia.org/wiki/Fi...
Photo of restricted zone during a game from Roy on Flickr.
www.flickr.com/photos/thehutc...
Filming by Alex Genn-Bash
Editing by Nico Turner
Some graphics by Grant Sanderson
Other graphics by Matt's Terrible Python Code™
Written and performed by Matt Parker
Produced by Nicole Jacobus
Music by Howard Carter and Jonny Berliner
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

[@3blue1brown]

Nice video, thanks for inviting me, and thanks for spreading the word on SoME3! I was surprised that an NBA player would have to be 2 feet from the hoop to get the equivalent expected points as a typical three-pointer.

[@mezzanine2670]

It is important to remember though that the players who are scoring 3 pointers are way more homogeneous than those who are scoring 2 pointers. If you would pick a random nba player, let him take a random shot at a maximum of 350 inches and repeat this 4 million times, the hunch would be way smaller around the 3 pointer distance

[@esgee3829]

good question & follow-up posed 18:04

[@johnchessant3012]

hi Grant!!

[@robertbyrne8718]

15:48 Bloody hell grant didn't realise how hench you were, make a workout channel already, that's what we really want

[@tobiasbrewin4355]

You are unreasonably attractive, like wow

[@DeenBoi]

Matt Parker is now officially a baller

[@Gekoloudios]

top comment spotted

[@freescape08]

Ball is life Especially when Matt is focused on a spreadsheet about basketball.

[@erwinjohannarndt4166]

He was always a balder.

[@DeenBoi]

@@erwinjohannarndt4166 i read it as bladder and i was concerned for a bit

[@dtemp132]

He’s a baller, but is he a shot caller?

[@CapnCrazy110]

I feel like part of the reason the slope of the accuracy chart beyond the 3 point arc is so gentle, is because the only ones crazy enough to take the longer and longer shots regularly are the players like Steph who have the skills to back it up, and so the data is skewed/inflated

[@yatzyac]

He also mentions that in recent years, the midrange shot percentage has trended upwards. That's because the only players taking long 2s anymore are guys like Kevin Durant or Kawhi Leonard

[@DrKaii]

I'm pretty amazed tbh that this very simple point wasn't addressed or even mentioned anywhere in the video

[@cptfwiffo]

@@yatzyac It's a constant battle. Defenses nowadays cover the paint and the three point line. Different players have different skillsets. A great outlier is Shaq. Shaq had 60% field goal percentage. That equates to a 40% threepoint percentage for points-per-attempt; quite similar to a great threepoint shooter. But inside scoring leads to balls staying nearer to the basket, which leads to less breaks as the offensive shape has more time to recover to a defensive shape. And it leads to more fouls and free throws, which has additional benefits -- teams had to actively just put bodies on shaq to take the fouls, which lead to a lot of teamfouls, which meant that small fouls on other players were giving 2 shots much quicker. And there was less paint protection, since the paint protectors were already covered in fouls. A Jordan, Durant, CP3 have 55+% midrange, which equats 36+% 3point percentage, which is slightly above the average threepoints taken. These players are as effective at midrange as they are at threepoint range, and they force defenses out of shape, since they loose too many points running them off the three point line, which then opens more open threes or layups. There are layers upon layers in these stats :)

[@awandererfromys1680]

My thoughts as well. I think it's less of a factor in the NBA but even with my 182 cm I was still a relatively small player compared to the rest. I was useless around the bucket. I trained a lot on three-pointers because that's where I could get my shots in. Once you have the wrist strength to cover the distance accuracy can go up pretty fast.

[@88porpoise]

There are a lot more ways you can dive into the data. This was a fairly short and high level video so it can't get into lots of the details. But I guarantee you, the analytics guys advising these teams absolutely consider that stuff. And for individual teams and players there will be specific variations, but in general I am confident that for almost every player the data still says to avoid the midrange shots when there is an option. And in the end, these sorts of analytics pretty commonly lead to such a polarization. Much like baseball is hyper focussed on the three true outcomes, basketball has turned into get in close or drop a three.

[@goldenredstone04]

Grant highjacking the video at the end by asking intelligent questions.

[@LeoStaley]

Sounds like the questions he was asking were going over the dudes head, and some headcoach needs to pay grant 5 million dollars to analyze probability vs statistics in these analyses

[@drenz1523]

high jacking? 🤨

[@willball12]

He asked most of the questions I wanted to ask - to compare with health research which I'm more familiar with, there's a classic 'case-mix' issue in which players try for 3s.

[@Huntracony]

And getting replies that sort of resemble answers if you squint and tilt your head a bit.

[@samba272]

@@LeoStaley I think he got the question, the specific scenarios just never came up so he couldn't give an example of those phenomena

[@MeesterG]

As a primary school teacher, this is a huge help to answer the kids as to why math is important even though they only like sports :D Thanks Matt!

[@ananas_anna]

Real answer is that it’s a 99.999% chance that they won’t be playing sports for a living.

[@augustgreig9420]

You might want to watch Money ball too. Baseball is far ahead of every other sport in terms of statistics as strategy.

[@MeesterG]

@@dienvidbriedis1184 playing with friends is different than trying to reach the top and earning money with a sport

[@Ca7iburn]

@@dienvidbriedis1184 Disagree. I can do all the nerd number crunching and still have fun throwing a ball. I would not say me liking (or disliking what ever the case may be), mathematics influences my enjoyment or lack of enjoyment regarding the throwing of a ball. Also the understanding that something is important does not mean that I personally will go further in studies in that field, but at the very least I would not try to influence others that might want to. I had student, who only decided they don't like something, because their parents don't understand or acknowledge the importance. Not to mention peers.

[@RobertoCarlos-tn1iq]

what you should teach the kids is that their health through physical sport and education is more important than any math course you can teach them.

[@aervanath]

Things I learned: 1) Sport math is fun. 2) Grant has some GUNS. Damn.

[@zachrowe6271]

He should name is channel "3plates1bar"

[@TJGibson0]

Matt literally gave Grant a Parker Jersey

[@AndreiTache]

Haha, that took me a second to get, very clever

[@zoonvanmichiel9045]

Even better, a Parker squared Jersey

[@maddy3852]

I believe that means Grant's legal last name is now Parker

[@1st2nd2]

​@zoonvanmichiel9045 its the Parker Square of jerseys!😂

[@vigilantcosmicpenguin8721]

@@maddy3852 Matt's friends count as honorary blood relatives.

[@mirzad674]

I love 3b1b's casual appearance in the beginning of the video. Anyone else would take a good chunk of time from the video to properly introduce another youtuber but Matt's just like "Hey Grant, wanna do some plots" lol

[@animarain]

I can't wait for the uncut video on the second channel where Matt performs 4.678.387 shots. It's going to be a blast!

[@Bismuth9]

I sort of wished Jon Bois would be a part of this as well!

[@DanielHarveyDyer]

Yeah I was thinking this is Chart Party but with more b-roll of math KZbinrs playing basketball.

[@repmel]

All the findings in this video are quite similar to those in Bois’ own video on the three point line.

[@rickpgriffin]

That's immediately who I thought of when I saw this video, I wondered if he had any input since he already did a statistical analysis. John Bois is the sportswriter for people who don't usually care about sports

[@stephenbeck7222]

Or any of dozens of articles on 538 in the last 10 years. The spray chart that Grant produced was a lot less readable than numerous similar charts that have been created.

[@ChipoJ]

I also wanted a shoutout to that 89 ft Video.

[@privacyvalued4134]

4:00 A heatmap would have been a better representation. You would visually get color variation of the hotspots as they move around over time. Trying to visualize it in 3D in a weird bar chart format makes it a lot more difficult to actually tell what is going on.

[@joshuadorsam4619]

I agree

[@landsgevaer]

Indeed also my thought. 3D plots where 2D are clearer (bar charts, pie plots, etc.) is the M$-Excel approach though, and Matt is all about spreadsheets, so it befits him.

[@maxflentge2158]

Yup!

[@chriswebster24]

It was actually fine the way he did it, though. Don't take this the wrong way or anything,, but, to be totally honest with you, you just aren't very bright.

[@rainbowevil]

@@chriswebster24 as a person who works in data visualisation professionally, you are wrong. 3D bars across a 3D space is a pretty terrible way to visualise things, even when able to rotate things during the presentation (that does improve it, but not as much as just using a heat map). Heat maps can be coloured in such a way to be visually obvious even for completely colourblind people, though often this is not done sadly.

[@YourMJK]

Let me get this straight… Grant is smart, handsome, has an awesome voice AND IS RIPPED??

[@berryzhang7263]

Grant’s beauty is not relatable content /ref

[@metacob]

I'm sure he did very well in academia... everyone knows, people there are always looking for Grants

[@Eizengoldt]

He just like me man

[@bentlergerjamin2783]

@@metacob Take your two drums and your cymbal and get out.

[@metacob]

@@bentlergerjamin2783 Does that cymbalize a rim shot?

[@Raye938]

Your accuracy graph is "distance in inches" instead of what I'm assuming is supposed to be feet. It's got me dying over here imagining you and Grant missing 80% of your shots from 20 inches away.

[@lo1bo2]

I had to scroll down quite a ways to find someone else who caught that error.

[@meneldal]

You wouldn't make an error like this in metric.

[@clusteronemsi]

Same thought here

[@MaxLennon]

@@meneldal ah yes, no one would ever write cm instead of m

[@erinasnow]

The inches and feet part got me very confused, I don't have that instinctual knowledge of how many inch some feet are. Metric is easier to switch between units

[@BurnsRubber]

A 3-point shooting percentage of 26.7% is statistically as efficient as 40% in the mid-range due the 3/2 factor increase in points scored.

[@mattc3581]

Though maybe more efficient long term. mid range you automatically turn over the ball when scoring, 40% of the time, 3 pointers only 26.7% of the time, so you have a greater chance of retaining possession after a three point shot, and if they're worth the same points per shot then that makes the three pointer better?

[@BurnsRubber]

@@mattc3581 True. But missed three point shots lead to long rebounds that often result in transition points for the opponent. There’s a saying that missed corner three result in a layup on the other end. Where as missed midrange shots can create follow-up dunks or layups for the offense team. Someone probably had done a statistical analysis on these factors.

[@hppern3971]

​@@mattc3581 missed shots are also more likely to result in transition opportunities for the other team, and transition offense is consistently more efficient than half-court offense

[@mattc3581]

@@hppern3971 Sure, I don't have any idea of the actual stats, my point was just that hitting 40% of 2 pt shots and 26.7% of 3 point shots is not going to be exactly the same from a game perspective as what comes after impacts the score as well.

[@frederikbrandt424]

@@mattc3581 You also need to take variance into account. If you shoot strictly 3 pointers you’ll have more games where you score very few points since the percentages are lower.

[@Rubrickety]

Let’s all take a moment to appreciate Grant’s sick burn on Matt at 18:10

[@josephnation9063]

Oh hey this is my area of specialty! My official job title is "Lead Nerd", but basically I work doing statistical modeling (among other things) for an agency that represents a few players in the NBA. This particular problem is one that's well-known in our canon. The best way to represent it, IMO, is not as a direct expected value problem like this does, but rather to treat it as a diminishing marginal returns problem. Basically, the xth 3 point shot you select is more likely to go in than the x+1th. As a result, there is (well, technically this is "may be", since at sufficiently low enough expected values the curves might not cross -- that is not the case here) a point where you are better off selecting the 1st midrange shot, so you do end up with a Nash equilibrium in which all three ranges of shot are taken. Grant's question regarding increased usage (which is the term used for players taking more or fewer offensive touches) is actually also fairly well-studied. The easiest way to think about it is as an economics style trade-off between usage and points per shot, but that also becomes complicated by rubberbanding effects. It's fairly common for high volume players to record higher than expected points per shot because they're able to continue shooting after a poor start, where a lower usage player that misses his first 3 shots probably doesn't get to shoot again that day. While Tim's answer about sample size is important, it's also important to recognize that context effects are non-linear, non-monotone, and non-independent. Also, it's worth noting that the "location first" approach has been heavily criticized in recent years, because people (Kirk Goldsberry of ESPN chief among them) have argued that the homogeneity of distance is also creating homogeneity of play. However, the manner by which the ball gets to those locations is as diverse as it's ever been, so reducing it to just "oh the shots are coming from this exact distance" does a disservice to a game that we all love. As for the discussion on coaching and how to present numbers to decision-makers, that's a delightfully fun topic. I've been told stories by my peers in front offices of how they'll intentionally withhold specific information from coaches and players so that it doesn't get misinterpreted. For me a lot of the time I have to interact directly with players and families, and boy is the first time you have to sit down with a player and say "even though there are legitimate basketball reasons for this number to be low, you really do need to work on it" harrowing.

[@theepicosityofpizza]

Thank you for this! I think the prof actually did a disappointly poor job answering Grant's questions - this sheds some more light on how probability is accounted for

[@theepicosityofpizza]

Video was lacking some meat for people interested in statistics I think I'd love to hear more about this stuff from you!

[@christiang5209]

"This particular problem is one that's well-known in our canon. The best way to represent it, IMO, is not as a direct expected value problem like this does, but rather to treat it as a diminishing marginal returns problem. Basically, the xth 3 point shot you select is more likely to go in than the x+1th. As a result, there is (well, technically this is "may be", since at sufficiently low enough expected values the curves might not cross -- that is not the case here) a point where you are better off selecting the 1st midrange shot, so you do end up with a Nash equilibrium in which all three ranges of shot are taken." i have a little understanding problem with this, my first impression was tat the amount of shots taken are correlating with the shot quality ... So when you are 5 minute on court and you should try to hit the basket once during this timespan, you can wait for an easy oppurtunity ... While when you need to take 5 shots in the same time, you need to select harder shots. But just electing the first shot imho doesn't change the quality of shot taken, by both fictional players ... You maybe get some progression factors, out of the data to reduce the effect of the shooting quality. PS: sry for my spelling it is not my first language, and i don't use it much in scientific context.

[@twoqueersplay]

Always excited for a Matt Parker chart party.

[@deproissant]

I think Grant has a point. Prior to Warriors' run in 2015, three-point-shooting-centric offense was frowned upon because relying on at least one of your players to make > 35% of his threes, at a high enough volume, for almost 100 games, is ridiculous. Obviously then the Splash brothers came along, and advanced analytics (whose mass usage was at its early days at the time) supported the increasing usage of threes (and dunks), which I guess made threes cool even among big men.

[@marcm.]

It also tells me that the three-point line needs to be 7 ft farther back

[@michaelhaydenbell]

@@marcm. SEVEN feet??? Lol that's crazy.

[@TomCruz54321]

It's also worth noting the quality of the three-point shot. A wide open jump shot has better odds than a contested shot. This is the difference between the Warriors and the Celtics. The Warriors used their motion offense to free up Steph and Klay. The Celtics stand around the perimeter, run down the shot clock, and jack up a contested three.

[@luudest]

lol, one thing is in not mentioned in the video: The main reason why 3 pointers became so popular has to with a rule change: In 2004 „hand checking“ was banned. Afterwards as a defender you had be much more careful in order not to get a foul (see below). This made it easier for shooters to throw from outside. „A defender may not place and keep his hand on an opponent unless he is in the area near the basket with his back to the basket. A defender may momentarily touch an opponent with his hand anywhere on the court as long as it does not affect the opponent’s movement (speed, quickness, balance, rhythm)."

[@JakeMueller12]

Subtle parker square, great humor, killer lyrics. Keep it up!

[@morganmartino1071]

Matt Parker is channeling Jon Bois and I am HERE for it!

[@StephanieS13]

as a very non-sports person this was unexpectedly very interesting! would love to see the other-sports-mentioned versions of this video, particularly swimming!

[@e-naa4118]

Sports are pretty much IRL RPGs. And we've entered the min/max era. Even if the players aren't too nerdy themselves, there's someone who are and tells them what to do. Football Meta has a video on xG (expected goals) that is somewhat similar to this.

[@pedroscoponi4905]

After reading 17776, I have gotten very used to that feeling at this point.

[@keionadams01]

Sports are a lot cooler than people that aren't into them think, I think there's at least one sport for everyone if they're open to learning about it

[@TomCruz54321]

Would love to see some analytics on futbol, tennis, track and field, swimming, boxing, MMA.

[@HomeOnTheEdge]

Other ideas: Did you consider running an analysis evaluating distance and angle? S.T.: y = distance*x1 + angle*x2. This would allow one to find the 'highest scoring zones' on the court. It would also reveal whether there's a 'left-right' bias, perhaps due to players' handedness.

[@mikepower7419]

@Math66 That plot was just shot volume so it doesn't take into account how likely those shots are to be made.

[@madeiraafonso2835]

well, we already know that the highest scoring zones are the ones near the basket. if you are right-handed its easier to shoot of the dribble going left because its easier to angle yourself to the basket and the opposite aplies to left-handed people

[@1.4142]

You could make a heat map of accuracy of shots on the court to also see the effect of angle from the basket,

[@astropgn]

What angle? There are two points, the basket and the player. It is a straight line, wherever the shot is taken.

[@andrewtietjen7268]

The backboard

[@Qermaq]

@@andrewtietjen7268 Most NBA shots today don't even use the backboard, except for up close where the angle becomes trivial. If you see a 3 point shot hit the backboard, it's because the player wasn't precise.

[@Imperial_Squid]

​@@astropgnthe angle between the player-basket line and the edge of the court line??? They want to know whether players shoot nearer the edges or nearer the centre of the court obviously...

[@astropgn]

@@Imperial_Squid They throw from the edge because the 3 point line is not a perfect circle (Matt even discuss this, look at the diagram at 11:22), so the shots at the edges are shorter, maximizing the expected points per shot. The angle is irrelevant.

[@frogsinpants]

5:56 Nailed it. I can't be the only one who genuinely loves this cheeky posturing on a shot that goes wide.

[@AkiSan0]

a big thank you to Tim Chartier for stating that the questions makes the statistic, not necessarily the numbers. (which matt proved with his infamous stonehenge/woolworth (or whatever shop it was) video)

[@tmrogers87]

Grant is ripped holy moly!

[@rickseiden1]

"You shoot once and you make it, you're amazing, you're 100%." This is why you'll often hear stats like, "Dominik Hasek is the all time leader in save percentage for players with at least 200 career NHL games," instead of just, "Dominik Hasek is the all time leader in save percentage." There could be someone who got called up from the minors, played one game on the current first place team against the current last place team, so he didn't face a whole lot of shots, and had a shutout. His save percentage would be 1.00, beating Dominik Hasek's 0.922.

[@mattc3581]

This feels like a call for the Koo Dae-Sung video by Jon Bois. Possibly the greatest stats in baseball history against possibly the strongest average pitchers anyone ever faced :)

[@man4437]

This reminds me, when, during the 2020 European football championships, Finland won their first game (the one that was postponed due to Eriksen collapsing), meaning that for a brief period in time, Finland had a 100% win record in that tournament, in every major tournament they'd ever played (this was the first one), and they'd scored and kept a clean sheet in every game. In fact, unless I'm wrong, Finland also scored their ONLY shot and the goalkeeper saved a penalty, meaning Finland had a 100% penalty save record And shot conversion rate. Pretty crazy micro-stats example

[@chrismoore6359]

What I find most interesting about this is the "plateau" of accuracy against distance. I imagine that accuracy is a function of the probability of a shot going in *but* also the effect of defense. Because the probability of a shot going in decreases as a function of distance, that must mean that the effect of defense decreases as a function of distance. The decrease in defense as a function of distance makes all sorts of sense because in a "semicircle" like a court, defenders have to move farther distances when they are farther from the basket. What a cool video and data. Thank you.

[@rustyrapp5673]

Just surprised they didn’t mention that the delay in increased shot distance coincided with the first kids who watched NBA games with a 3 point line finally making it to the NBA.

[@brettchr777]

Note the "Parker" squared on the back of the jersey -- certainly a throw back to an earlier video with the "Parker Square." LOVE IT.

[@lasagnahog7695]

I'm very excited whenever Bec shows up. Grant is a special treat as well and I'll be equally excited for him as soon as the three of them start a podcast.

[@donniemorrow]

Part of the expected value is also the rebound percentage. Making 40% of your 3s may be offset by recovering the ball less often than close shots, which lets your team try again. The current maths take the assumption that you get zero points on a missed shot (guaranteed turnover). I wonder if that is a valid assumption?

[@PanzehVideos]

If the defense has the interior position for rebounds, the longer boards on 3 pointers actually favor the offense as well.

[@Vito-jr9wl]

39.6% somehow reminded me of the Standardnormal-distribution density at the center (1/sqrt(2pi))

[@rasuldzhakupov4980]

Central limit theorem kicks in, thus it is very logical that you may observe normal distribution's traits there

[@Dragostorm21]

​@@rasuldzhakupov4980 you could even say that everything is normal (with enough sample size)

[@KekusMagnus]

peak nerd moment

[@axp_bubbles]

As someone who uses data to provide insight and advice to clients for a living, there's a lot to be said for having a team of people who understand the data but not the context, people who understand the context but not the data, and people with a reasonable understanding of both. As someone from the first group (but steadily gaining the subject matter knowledge to move into the 3rd group), it's often frustrating when a client believes the data/insights are wrong because they do not conform to what they want to believe.

[@Asterism_Desmos]

I recently read “Humble Pi” and loved it! Found it at Barnes and noble and instantly decided which book I wanted. :D

[@Goku17yen]

That’s cool

[@Pyrozoid]

very interesting and pointed questions from Grant. I love how curious he is and how much he wants to get a better understanding of the topic. It felt like Prof. Tim was giving a thesis defence with Grant being the dept. head grueling him lol.

[@vigilantcosmicpenguin8721]

Grant is the honorary head of the mathematics department of KZbin.

[@Markd315]

Feel a little bit better about my 27% rate of draining threes in pickup basketball. Plus, when you play ones and twos, the mathematical leverage of making one is even higher! 2x as many points vs the 1.5x in the NBA.

[@flashspider-man3214]

As a big fan of both basketball and math, it's nice to see you make a video on the NBA. Great video, as always! Morey ball!

[@rafaelschipiura9865]

It's nice Grant gives us so much time to prepare for SoME, since we aren't not even in winter yet!

[@jucom756]

I love the contrast between Matt and Grant in the interview, Matt always has the "well the experts explained what they explained, on with the video" look, but then Grant asks another question, dogging in to the subject. I think this also kind of neatly demonstrates the difference between your channels, where Stand-up maths is more about exploring math and covering interesting new topics in an entertaining way every time, 3b1b is more about digging deeper and trying to get the viewer to understand one topic at a time.

[@rosieisla8286]

Somewhat random, but I'm glad to see the subtitles get more reliable! The chat at the end and the song lyrics weren't great, but they're way better than they used to be - I know there were ideas for a new subtitle system on the channel going around last year, so this is nice!

[@geo2739]

Thank you, Matt and Tim, this answers a question I have often asked myself

[@josephlance9262]

Great video topic as always. You’re great at picking varying topics of interest

[@racg174]

I'd love sequels to this on 2 point conversions in american football as well as fourth down descisions in the same sport

[@DanielHarveyDyer]

Chart Party by Jon Bois is the sort of thing you are looking for, if you aren't already aware.

[@Isaac_Essa]

Something important to note is the specific players that take long distance threes: most average three point shooters aren’t going to be taking 30 footers. The majority of those will come from guys like Steph curry, Damian lillard, all time level shooters. So there’s a good chance that inflates the points per shot the further out you go.

[@udishomer5852]

Correct. There are also players like Jokic who make 65% of their 2pt shots which is 1.3 pts/shot. So Jokic should clearly continue to shoot the 2pt shots.

[@Isaac_Essa]

@@udishomer5852 definitely. These graphs are interesting as an overview of the league, but it’s definitely more important to break down points per shot by player (and take into account the context of the possession, etc). A bailout KD midrange shot at the end of the shot clock holds a ton of value, even if it’s not technically a higher point per shot than an average open three.

[@Max_Griswald]

That was one of the most interesting videos I've seen in a while. Thanks!

[@MindstabThrull]

I just realized that Matt's jersey shirts include a PARKER SQUARE(d) Well played, Math Parker, well played.

[@adamplace1414]

I'm getting that delusional feeling that something (this video) was made just for me. Bec Hill and Grant Sanderson in a sports related Matt Parker video - really doesn't get more perfect than that.

[@cuanleahy2375]

Grant is absolutely yolked

[@witerabid]

The even more mathy (mathsy?) and updated version of the Chart Party video on this topic and I'm 100% here for it!

[@Bob-jn8jt]

Super interesting. Loved this video.

[@BTroit]

Particularly enjoyed the discussion on stats vs coachable metrics, and some accommodation for "trusting your gut". Would also recommend sports+math people check out "Baron Davis From 89 Feet" which is a great story on an extreme outlier data point.

[@entropie-3622]

You could explain the leveling off of the probability due to the interaction with the defense of the opposing team. Clearly it is also easier and more important to defend closer to the hoop. So this actually may be a game theoretical equilibrium where the advantage gained by going in deeper is negated by having to deal with a stronger defense.

[@TheFranchiseCA]

That's a good point, the defensive pressure is going to be greater the closer in that a shot is taken.

[@Arkhanno]

I love that you had Team Pi jerseys made.

[@CapnCrazy110]

Another part of the reason the trend toward more threes is so recent, is that the typical player in 2023 grew up in a world where it was well known that high volumes of 3 point shots were they way to go, and so they've spent a lot more time learning and training that skill. There were fewer skilled long-distance shooters in 1997 because when those players were growing up the 3 pointer was a new addition to the game and the skill wasn't really needed. That's especially true at the amateur level, since high school and college ball didn't adopt the 3 point line nationally til 7 years after the NBA.

[@josesanmiguel9212]

Grant makes very good points

[@krugerdw]

Love this - thanks for showing that data can be used for fun!

[@allank8497]

This is awesome bc Ive loved Stand up matchs for years, and I've loved working with NBA data for years. Wish I could get a hold of these datasets

[@sk8rdman]

When I saw Matt's Team Math jersey, I really wanted to see the rest of the team labeled with other mathematical constants.

[@matthewcoyle6429]

I always wondered how the Globetrotter Planet would come to be, and why they'd be so good at maths..

[@johnnyjohnson6643]

Outrageous how few likes that has. Underrated!

[@jeroenw9853]

This channel keeps answering questions I didn't know I had. Always interesting

[@jaysonbunnell8097]

So I’m a university student. I have finished calculus I and II and had a very very fun differential equations/linear algebra course. And while I love math, taking it out of theory myself is so tricky! seeing that 3-D plot around 4:30 was the tipping point though. I thought, "wouldn’t it be a neat metric to show the derivative of a linear fit of all the points at each position on a horizontal axis of time, to see how different places changed over time?" and felt like a math super genius lol. Thanks for the awesome vid!! I love math inspiration!!

[@RomanNumural9]

Math and basketball and all that but anyone else notice Grants massive biceps? :P

[@freescape08]

18:37 Here's an interesting thought, would you be able to re-do that graph with the darkness of each point being a confidence level of the athletes who made the shot? Confidence being what portion of their shots are made from that distance.

[@TheLoxely]

Well this is a great crossover between my love for the NBA & Maths. Great stuff

[@heighRick]

Thanks Matt, helps a lot!

[@Adderkleet]

Is "distances in INCHES" correct? 20 inches away and only 20% accurate?

[@jonasjoko294]

I think he lost a factor of ten in that plot, then it would also match the NBA plot better

[@lithiumdeuteride]

20 inches away, 200% accurate.

[@yonatanbeer3475]

hey don't shame a man like that

[@matthewnoriega7240]

Grant’s math jersey was a Parker Gift

[@SwagnerCountsThings]

As a maths and basketball fan I am so excited for this!!!!

[@thomascaldwell184]

Damn! Who knew Grant was so ripped? Also, I love that you can do anything you want with math, given enough creativity. I mean, since the Universe seems to run on math (or at least, that's the best way we have to describe the Universe) it makes sense. Yet another cool video! Thanks.

[@samuelculy655]

Watching this video is a valid reason to not be revising for my AS Maths paper, right?

[@rohanpatel7186]

Yes

[@FLPhotoCatcher]

Apparently it's "math" now. As an American, I usually hear "mass" when someone from the UK says "maths", so for me, at least, "math" is more comprehendible.

[@samuelculy655]

​@@FLPhotoCatcher He says, commenting on a video from Stand-up Maths... (no hate btw) Honestly, I've always called it maths, I see it as a valid contraction of Mathematics, I can see why you would see it as a valid contraction of Mathematics too. Everyone around me calls it maths, not much makes me want to switch to the American version, there are few scenarios I find myself in where someone else would think I said mass.

[@doublespoonco]

@@FLPhotoCatcherw*stoid 🤢🤢🤢🤢

[@JakeMueller12]

Letting you know about errors in the comments, as is tradition: Labeled your own/everybody shot graphs as "Distance in inches", should be ft obviously. We'll cough it up to being in silly freedom units.

[@TassieLorenzo]

Why is it not in metres?!

[@smithwillnot]

I heard about this exact stat (how much each distance is "worth") and it's great to see it visualized. Also it makes more sense seeing it on the graph rather than just hearing numbers.

[@marcoestevesjr1923]

Great video!! I think the variance of the accuracy has a lot of importance too. Only looking at the expected value may distorce the strategies. Congratulations for the excellent work.

[@sdspivey]

Where is the heat map of the whole court?

[@luminatihd2895]

Matt Parker x Jon Bois

[@vonriel1822]

Aww, the Parker Jersey was adorable. And I gotta wonder if I was the only one mad enough to look for a mistake in the printing. Sadly, there wasn't one.

[@Tyler-zs3ry]

When I was at the APS March meeting this year I saw a great talk where someone used density functional theory to model basketball, basically treating the players as interacting particles. Lots of cool math you can do with sports!

[@noelearlwatson2724]

You should have metric units on screen as well

[@alquinn8576]

this is 'murica

[@GoatsAndChickens123]

5:13 wait…. Distance in inches? Hoping this was feet.

[@sunie10]

I agree, in the graphs with MATT_SHOT and EVERYBODY the text for the X-axis says "distance in inches" instead of "distance in feet".

[@luismijangos7844]

Amazing video!!!!!!!!!!!

[@purplegill10]

This is like that one Jon Bois video except on steroids. I'm in love.

[@nocturnhabeo]

Soooo Grant is WAY bigger than his videos make him look.

[@belgaer4943]

Would have loved to have measurements in meters as well! Inches and feet are a little tough to parse

[@Kollum]

I would have to re-watch paying more attention to units, but the plot of accuracy of Mat shots versus distance is definitely mis-captioned. With immediately raised my question: is it a joke making fun of the US unit system, or is that just an unintentional mistake.

[@allank8497]

A huge thing to keep in mind is the strength of the defensive shot contest. I'm assuming the flat section of the shot-percentage/shot-distance curve in the mid range isnt actually about players being as good of shooters from 10 feet as they are from 20, but rather that opposing teams are much more happy to let a player walk into a deep mid range shot than a shot from floater range closer in, and so the defensive attention is a lot higher on the latter than the former, and then once the player gets out to 3 point range the defensive attention picks up. Defensive schemes like Drop pick'n'roll coverage explicitly aim to do this, first: making sure to fight hard through the screen to push ball handlers to within the three point line, and then once the ball handler is there, having the screener's man drop well into the paint to allow them to contest at the rim or those short mid range shots, with the goal being to concede semi-open long mid range shots.

[@floodo1]

Fascinating

[@eonoire]

Hot damn 3b1b is absolutetly ripped

[@flashrandom]

Very interesting, thank you

[@dasiro]

thanks matt for this great combo. As a center with a lower usage rate I completely understand where grant's question came from. I'm having a far higher efficiency compared to the forwards and certainly guards but get far less scoring opportunities, thus in the most basic stats (being the scoring sheet) its appears as if my contribution is far less than those of other players. I squeeze in the +/- stat to redeem myself a bit, but it would be far more obvious if things like rebounds, screen-assists and usage rate were taken into account. Stats can prove everything and nothing, but as a 6'9-6'10 player I'm still happy my teammates were excited for me to join their team even though I'm already in my 40's only to finish the season with a promotion :)

[@artswri]

Great video thanks!!

[@jbhelp4u]

Great video! Data Analysis has changed lots of "games". Professional video gaming teams also have mathematical analysis done on their games and competing teams!

[@doomtho42]

I’m a bit of a sports analytics junkie, so I had already seen all of this data a million times presented in a million ways, and I have to say that the data visualization in this video was really top-notch. In particular, the one showing yearly shot distribution plotted as 3d bars on a court overlay was probably the best presentation of that data I’ve ever seen.

[@ckq]

7:30, the NBA has these graphs (smoothed and shows frequency for each player on their shot chart page

[@robertthompson3447]

"A single metric basketball player" This is now my new favorite unit.

[@IanZainea1990]

22:48 I LOVE that he pointed out how it was much less touching. lol. Yeah. For a second there it def seemed like you only made one shirt for yourself haha. BTW, just in case it comes in handy in the future, you don't get the names printed. You leave the names blank and then you get iron on letters for the names.

[@Nicholas-cm6rx]

Grant's forearms @15:43 are heavenly

[@holly_hacker]

The reveal of 3B1B playing in the background was so cool :p

[@therocknrollmillennial535]

I just started the video, but it's bound to be a great one: Matt talking about sports and maths, two of my favorite things! Also, maybe I'm wrong but it doesn't seem like a coincidence that Tim Chartier is the one here talking about this phenomenon, seeing as he's a professor at Davidson College, where the NBA's king of 3's attended. Sneaky little addition to the video. Don't think we NBA nerds didn't notice, Matt! Edits to add commentary to points of the video that stuck out to me: 4:23: We call that DeMar DeRozan-land. 5:05: Today I learnt that Matt has that Shawn Marion jumpshot. 13:48: Okay, I guess I wasn't the only one to know that.

[@christianbaird8800]

I was just in NYC last week and walked past the Museum of Maths and was so sad it had already closed. What a timely video though!