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The Math Behind Basketball’s Wildest Moves | Rajiv Maheswaran | TED Talks

October 10, 2019

My colleagues and I are fascinated
by the science of moving dots. So what are these dots? Well, it’s all of us. And we’re moving in our homes,
in our offices, as we shop and travel throughout our cities
and around the world. And wouldn’t it be great
if we could understand all this movement? If we could find patterns and meaning
and insight in it. And luckily for us, we live in a time where we’re incredibly good
at capturing information about ourselves. So whether it’s through
sensors or videos, or apps, we can track our movement
with incredibly fine detail. So it turns out one of the places
where we have the best data about movement is sports. So whether it’s basketball or baseball,
or football or the other football, we’re instrumenting our stadiums
and our players to track their movements every fraction of a second. So what we’re doing
is turning our athletes into — you probably guessed it — moving dots. So we’ve got mountains of moving dots
and like most raw data, it’s hard to deal with
and not that interesting. But there are things that, for example,
basketball coaches want to know. And the problem is they can’t know them
because they’d have to watch every second of every game, remember it and process it. And a person can’t do that, but a machine can. The problem is a machine can’t see
the game with the eye of a coach. At least they couldn’t until now. So what have we taught the machine to see? So, we started simply. We taught it things like passes,
shots and rebounds. Things that most casual fans would know. And then we moved on to things
slightly more complicated. Events like post-ups,
and pick-and-rolls, and isolations. And if you don’t know them, that’s okay.
Most casual players probably do. Now, we’ve gotten to a point where today,
the machine understands complex events like down screens and wide pins. Basically things only professionals know. So we have taught a machine to see
with the eyes of a coach. So how have we been able to do this? If I asked a coach to describe
something like a pick-and-roll, they would give me a description, and if I encoded that as an algorithm,
it would be terrible. The pick-and-roll happens to be this dance
in basketball between four players, two on offense and two on defense. And here’s kind of how it goes. So there’s the guy on offense
without the ball the ball and he goes next to the guy
guarding the guy with the ball, and he kind of stays there and they both move and stuff happens,
and ta-da, it’s a pick-and-roll. (Laughter) So that is also an example
of a terrible algorithm. So, if the player who’s the interferer —
he’s called the screener — goes close by, but he doesn’t stop, it’s probably not a pick-and-roll. Or if he does stop,
but he doesn’t stop close enough, it’s probably not a pick-and-roll. Or, if he does go close by
and he does stop but they do it under the basket,
it’s probably not a pick-and-roll. Or I could be wrong,
they could all be pick-and-rolls. It really depends on the exact timing,
the distances, the locations, and that’s what makes it hard. So, luckily, with machine learning,
we can go beyond our own ability to describe the things we know. So how does this work?
Well, it’s by example. So we go to the machine and say,
“Good morning, machine. Here are some pick-and-rolls,
and here are some things that are not. Please find a way to tell the difference.” And the key to all of this is to find
features that enable it to separate. So if I was going
to teach it the difference between an apple and orange, I might say, “Why don’t you
use color or shape?” And the problem that we’re solving is,
what are those things? What are the key features that let a computer navigate
the world of moving dots? So figuring out all these relationships
with relative and absolute location, distance, timing, velocities — that’s really the key to the science
of moving dots, or as we like to call it, spatiotemporal pattern recognition,
in academic vernacular. Because the first thing is,
you have to make it sound hard — because it is. The key thing is, for NBA coaches,
it’s not that they want to know whether a pick-and-roll happened or not. It’s that they want to know
how it happened. And why is it so important to them?
So here’s a little insight. It turns out in modern basketball, this pick-and-roll is perhaps
the most important play. And knowing how to run it,
and knowing how to defend it, is basically a key to winning
and losing most games. So it turns out that this dance
has a great many variations and identifying the variations
is really the thing that matters, and that’s why we need this
to be really, really good. So, here’s an example. There are two offensive
and two defensive players, getting ready to do
the pick-and-roll dance. So the guy with ball
can either take, or he can reject. His teammate can either roll or pop. The guy guarding the ball
can either go over or under. His teammate can either show
or play up to touch, or play soft and together they can
either switch or blitz and I didn’t know
most of these things when I started and it would be lovely if everybody moved
according to those arrows. It would make our lives a lot easier,
but it turns out movement is very messy. People wiggle a lot and getting
these variations identified with very high accuracy, both in precision and recall, is tough because that’s what it takes to get
a professional coach to believe in you. And despite all the difficulties
with the right spatiotemporal features we have been able to do that. Coaches trust our ability of our machine
to identify these variations. We’re at the point where
almost every single contender for an NBA championship this year is using our software, which is built
on a machine that understands the moving dots of basketball. So not only that, we have given advice
that has changed strategies that have helped teams win
very important games, and it’s very exciting because you have
coaches who’ve been in the league for 30 years that are willing to take
advice from a machine. And it’s very exciting,
it’s much more than the pick-and-roll. Our computer started out
with simple things and learned more and more complex things and now it knows so many things. Frankly, I don’t understand
much of what it does, and while it’s not that special
to be smarter than me, we were wondering,
can a machine know more than a coach? Can it know more than person could know? And it turns out the answer is yes. The coaches want players
to take good shots. So if I’m standing near the basket and there’s nobody near me,
it’s a good shot. If I’m standing far away surrounded
by defenders, that’s generally a bad shot. But we never knew how good “good” was,
or how bad “bad” was quantitatively. Until now. So what we can do, again,
using spatiotemporal features, we looked at every shot. We can see: Where is the shot?
What’s the angle to the basket? Where are the defenders standing?
What are their distances? What are their angles? For multiple defenders, we can look
at how the player’s moving and predict the shot type. We can look at all their velocities
and we can build a model that predicts what is the likelihood that this shot
would go in under these circumstances? So why is this important? We can take something that was shooting, which was one thing before,
and turn it into two things: the quality of the shot
and the quality of the shooter. So here’s a bubble chart,
because what’s TED without a bubble chart? (Laughter) Those are NBA players. The size is the size of the player
and the color is the position. On the x-axis,
we have the shot probability. People on the left take difficult shots, on the right, they take easy shots. On the [y-axis] is their shooting ability. People who are good are at the top,
bad at the bottom. So for example, if there was a player who generally made
47 percent of their shots, that’s all you knew before. But today, I can tell you that player
takes shots that an average NBA player would make 49 percent of the time, and they are two percent worse. And the reason that’s important
is that there are lots of 47s out there. And so it’s really important to know if the 47 that you’re considering
giving 100 million dollars to is a good shooter who takes bad shots or a bad shooter who takes good shots. Machine understanding doesn’t just change
how we look at players, it changes how we look at the game. So there was this very exciting game
a couple of years ago, in the NBA finals. Miami was down by three,
there was 20 seconds left. They were about to lose the championship. A gentleman named LeBron James
came up and he took a three to tie. He missed. His teammate Chris Bosh got a rebound, passed it to another teammate
named Ray Allen. He sank a three. It went into overtime. They won the game.
They won the championship. It was one of the most exciting
games in basketball. And our ability to know
the shot probability for every player at every second, and the likelihood of them getting
a rebound at every second can illuminate this moment in a way
that we never could before. Now unfortunately,
I can’t show you that video. But for you, we recreated that moment at our weekly basketball game
about 3 weeks ago. (Laughter) And we recreated the tracking
that led to the insights. So, here is us.
This is Chinatown in Los Angeles, a park we play at every week, and that’s us recreating
the Ray Allen moment and all the tracking
that’s associated with it. So, here’s the shot. I’m going to show you that moment and all the insights of that moment. The only difference is, instead
of the professional players, it’s us, and instead of a professional
announcer, it’s me. So, bear with me. Miami. Down three. Twenty seconds left. Jeff brings up the ball. Josh catches, puts up a three! [Calculating shot probability] [Shot quality] [Rebound probability] Won’t go! [Rebound probability] Rebound, Noel. Back to Daria. [Shot quality] Her three-pointer — bang! Tie game with five seconds left. The crowd goes wild. (Laughter) That’s roughly how it happened. (Applause) Roughly. (Applause) That moment had about a nine percent
chance of happening in the NBA and we know that
and a great many other things. I’m not going to tell you how many times
it took us to make that happen. (Laughter) Okay, I will! It was four. (Laughter) Way to go, Daria. But the important thing about that video and the insights we have for every second
of every NBA game — it’s not that. It’s the fact you don’t have to be
a professional team to track movement. You do not have to be a professional
player to get insights about movement. In fact, it doesn’t even have to be about
sports because we’re moving everywhere. We’re moving in our homes, in our offices, as we shop and we travel throughout our cities and around our world. What will we know? What will we learn? Perhaps, instead of identifying
pick-and-rolls, a machine can identify
the moment and let me know when my daughter takes her first steps. Which could literally be happening
any second now. Perhaps we can learn to better use
our buildings, better plan our cities. I believe that with the development
of the science of moving dots, we will move better, we will move smarter,
we will move forward. Thank you very much. (Applause)


  • Reply Zaldy Castro April 19, 2018 at 10:35 am

    James puts up the THREE… won't go! Rebound Bosh, back out to Allen, his three-pointer…BANG! Tie game with 5 seconds remaining! Spurs do not have a timeout!"

  • Reply Andrew Hubb April 23, 2018 at 4:07 pm

    @4:22 It's The Points Guy!

  • Reply MATHS SUPPORT April 30, 2018 at 8:26 am

    Nice video!
    Get fact of maths here

  • Reply Unspoken Voices Inside Media May 2, 2018 at 4:13 pm

    So, this is a dance based on a definition without including a key factor that their objective ability in programming the code. Would this have a role in the outcome when the data is inputed.? This can affect how players our evaluated in terms of their wages. Also removing natural creativity and skills set in which players develop over a time period and the physical body movements our different. Some art can be reproduced and others our just one of kind,

  • Reply Kiddman32 May 5, 2018 at 12:16 am

    Hmm… I am a complete and total basketball nut… But my eyes glazed over after about 4 minutes.

  • Reply From Me May 8, 2018 at 3:49 pm

    Where can I get this software?

  • Reply angel me May 9, 2018 at 5:25 am

    Wanna know why it doesn't really matter if we think we know who the good players are? Because most of them aren't really bad shooters or bad players…. they just play bad… intentionally. That way they can ensure that the match will end the way it's meant to be ended and the money will go to the pockets that they're meant to go in… There's not such thing as honest sports today. Not when there are money behind them.

  • Reply REDBLOX COMEDY May 16, 2018 at 10:38 pm

    2k could use that shooting probability software…

  • Reply iamillasfuck May 22, 2018 at 1:02 am

    this guy is a fucing reptillian globalist don't let his nerdy charm convince u otherwise

  • Reply Manifest Destiny May 22, 2018 at 6:48 pm

    Where is the wild moves part?

  • Reply Mohammad Al-Awadi May 23, 2018 at 10:47 am

    Someone get the football manager guys! Their video game database is now used by man football (soccer) teams in Europe

  • Reply Edwin Vargas May 25, 2018 at 5:13 pm

    That last part about tracking all kinds of movement sounds like a double-edged sword, very similar to how facebook data on its users were used

  • Reply Homo_Sapien June 2, 2018 at 3:56 am

    "down screens and wide pins basically only things professionals would know" chill maybe most people at this ted talk wouldn't.

  • Reply den long June 2, 2018 at 5:05 pm

    Indian, sr

  • Reply beterbutz June 4, 2018 at 11:58 pm

    Through meticulous study and careful analysis they have concluded that Lebron James is the best player in the world…

  • Reply Diego Weissel June 5, 2018 at 7:45 pm

    stupid occupation for those who can't play basketball or whatever sports, or can't have social lives, and try to find sense in their sedentary antisocial sick lives. Go do something, a real something instead of spreading stupidity in a world that needs much more than software, but awesome jobs made by awesome people, healing societies and ecosystems in the preocess

  • Reply christopher kettler June 7, 2018 at 12:27 am

    But its always this kind of tech that gets in the wrong hands

  • Reply GLoBaL June 21, 2018 at 11:01 am

    I still can't alley doe.

  • Reply Obichukwu Nwosu June 24, 2018 at 5:01 pm

    can yall explain steph curry shots please

  • Reply Ethan Corner June 25, 2018 at 9:59 pm

    Hockey would've been good for this I think

  • Reply Fishy Net June 28, 2018 at 2:20 am

    If you are good, work hard and smart. You’ll get good, even without these machines.

  • Reply Alexis Mamadou July 2, 2018 at 6:51 am

    Ray Allen caught the pass from CB and took a backward step behind the 3 pt line before swishing it. That would have taken more 4 tries.

  • Reply YesPlease ThankYo July 3, 2018 at 7:59 pm

    This would revolutionise sports betting

  • Reply Joan Brunet Verdaguer July 7, 2018 at 6:05 pm

    Allen took one step back I'm sorry

  • Reply Kabeluhh Lynx July 9, 2018 at 11:39 pm

    it doesn`t worry you that the gorvenment might use this to control the population?

  • Reply InfernoPlus July 15, 2018 at 6:30 am

    Making machines more smarter, or more dangerous?

  • Reply Jack July 20, 2018 at 10:42 am

    I have questions that I'm wondering if anyone will see and hopefully answer:

    1) Isn't a good shooter BY DEFINITION a shooter who takes good shots (and likewise for bad shooters)?
    2) How are things in your algorithms weighted? As in, what's more important: the angle of the defender of the distance between them and the shooter, and how did you decide how to quantify this? Is it effectively an educated opinion?

    The second question above is something I've wondered for so long, how do you choose the weighting of variables in an algorithm?? (I also don't know how to implement that but it's just syntax and not OPINION).

  • Reply matasuki July 21, 2018 at 4:32 pm

    If anyone has a link or some advice how to get into this I would like to know. I am relatively new to the world of machine learning and programming and would like to learn more about this work. Thanks in advance

  • Reply Goku Black July 23, 2018 at 2:15 am

    Lebron is with the illuminati

  • Reply allen7in July 24, 2018 at 7:15 am

    Hindsight is always 20-20. Easy to 'predict' the game after the game is over. the machine gives Lebron 33% chance to make the shot which means 67% chance of missing it, and 88% chance of not getting an offensive rebound and 63% for Ray Allen not to make the tying 3. If you were to ask the machine before the play if Miami would win the game (a yes or no answer), there's 100% chance that the machine's prediction would be wrong. How's that for machine learning? A machine can't learn, it can't predict, a machine can process an extremely large amount of data, that's all.

  • Reply Don'tCallMeStupid July 24, 2018 at 9:14 pm

    Thats a good point in his closing statement about how this could help design buildings and cities with better traffic flow

  • Reply Daniel Munoz August 6, 2018 at 8:59 pm

    When Ray Allen hit the shot it was a 4vs4? Lol other then that this is pretty informative 👍

  • Reply Nic Harenda August 8, 2018 at 6:22 pm

    Do they know that a basketball game consists of two teams of 5?

  • Reply EVERYTHING ! ! August 16, 2018 at 12:59 am

    Thought this would teach me something

  • Reply Tan Wanli August 16, 2018 at 8:15 pm

    This was quite a bit of a clickbait. There was no real math, and a pick and roll isn't a wild move in basketball.

  • Reply fabien normand August 16, 2018 at 10:20 pm

    i didn't get anything. #imustberetarded

  • Reply Percival Sweetwater August 22, 2018 at 2:41 pm

    I could have done without the ad that appeared before the talk which promoted Global Climate change sponsor Exxon. Otherwise, a cool topic.

  • Reply Brian Arbenz October 8, 2018 at 5:45 pm

    So that's how Christian Laetner hit that shot to beat Kentucky in 1992 — he out-spatiotemporal patterned the Wildcats!

  • Reply f1yon1x ////\ October 15, 2018 at 5:46 am

    This is horeshit

  • Reply sean davy October 23, 2018 at 1:38 am

    "if he goes by close enough, doesn't stop, it's probably not a pick and roll"; "if he does stop and doesn't stop close enough its probably not a pick and roll"; " or i can be wrong they all can be pick and rolls….. my mans just showed me slip ball screen and a drag screen… they still pick and rolls tho…..

  • Reply Somebody November 1, 2018 at 6:26 am


  • Reply Philip Shirk November 3, 2018 at 7:14 pm

    Summary: analyzing movement is complicated, but it can be helpful. There are no interesting examples. There are no novel insights.

  • Reply Sean Sankey November 13, 2018 at 1:39 am

    Unusually clickbaity title for TED … “… wildest moves”??!!

  • Reply hallamittuna November 15, 2018 at 10:07 pm

    I miss sports before technology, mountains of money.. & drugs.

  • Reply Floyd Mayweather 50-0 November 15, 2018 at 10:41 pm

    As a spurs fan this talk made me sad

  • Reply Steven Chen November 23, 2018 at 11:52 am

    It’s 9% chance for the shot to happen and go in? A computer can’t detect a persons instincts or whether or not and how much someone has practiced a certain shot for these moments.

  • Reply Yoshi SBX November 24, 2018 at 7:49 pm

    Didn't think i would enjoy this so much then got scared at the end when i realized this was a Sky Net commercial…

  • Reply Ara Erfan November 25, 2018 at 2:42 pm


  • Reply Omer Pasternak November 25, 2018 at 7:58 pm

    That is seriously a bad lecture.

  • Reply Michael Lawrence November 25, 2018 at 8:09 pm

    The way pressure effects individuals is impossible to model as it varies on a day to day basis even within the individual. Some coaches who can read this and see who is "feeling it" on a given play will still be necessary.. So integrate this stuff cyborg style and we have the best teams ever

  • Reply Samuel Cahill Farella November 26, 2018 at 12:59 am

    Pretty amazing data, although it did tick me off that the defender wasn't nearly close enough in the remake of the shot. Allen rose up right in that guy's face and he had to backpedal first, which made it A LOT more difficult. Still, this was pretty cool.

  • Reply Romeo Carter November 27, 2018 at 7:24 am

    So this software wants to put a chip on people and track the dots.

  • Reply SuperGamer87 November 27, 2018 at 12:15 pm

    "Rajiv Maheswaran and his colleagues are analyzing the movements behind the key plays of the game, to help coaches and players combine intuition with new data."

    Basically, nerds who could never play sports, want in on the multi-billion-dollar business of sports, that's generally getting less competitive and seeing more predictable results, thanks to a growing overuse of sabermetrics and biomechanical analysis.

    Not against "math for sports." It has its place, even in sports. Just don't like how there's this constant push (advertisement) of such concepts that sports somehow better need something that sorta defies the whole point of human competition sometimes.

    "Sabermetrical" and analysis-heavy sports teams like the Boston Red Sox are becoming almost TOO predictably the winners of everything. To the point where you almost ask, "Why even bother? They math away the human guesswork."

  • Reply faccosh 264 November 27, 2018 at 7:22 pm

    PnR is important because it is abused by moving screens. Fact.

  • Reply DatIsraeliGuy November 27, 2018 at 9:44 pm

    Daria didn't take the right shot though, it was a three

  • Reply Seshadhri Subramanian November 29, 2018 at 9:31 pm

    Steph destroyed that predictability part of shot taking

  • Reply Chris November 30, 2018 at 1:11 am

    ill take the info from a great basketball coach/player over his team and his software any day

  • Reply Mad Cem November 30, 2018 at 8:44 am

    useless analyse ….. He has never see a basket match i think

  • Reply Clash Of Moba November 30, 2018 at 9:34 am


  • Reply aras ozkan November 30, 2018 at 11:32 pm


  • Reply Shakeem Diggz December 5, 2018 at 6:28 pm

    Clearley he never played sports. Sports is emotions a d the feel of the game. Every night is different

  • Reply Anton Hamilton December 5, 2018 at 7:13 pm

    Great Post The Michael Jordan Of Opportunities

  • Reply HUJAMBO Korodani December 5, 2018 at 10:35 pm


  • Reply mnati25 December 6, 2018 at 7:28 pm

    Very insightful

  • Reply Horst Tristan von Wittenbach December 7, 2018 at 10:40 am

    So what's the dot, uhm, point??… 😅

  • Reply Tathagat Verma December 7, 2018 at 1:17 pm

    The title is a bit misleading, involving something like "data analysis" or "machine learning" would be better

  • Reply Cliffinho Kisero December 8, 2018 at 9:32 am


  • Reply G Katsikogiannis December 8, 2018 at 10:09 pm

    Moving dots aka Championship Manager 2001.

  • Reply Syn Stilo December 10, 2018 at 9:32 pm

    I didn’t realize this was uploaded 3 years ago and the first thing I thought of when I saw the bubble chart was that orange bubble at the bottom was Ben Simmons 😂😂😂

  • Reply kiefer court December 11, 2018 at 3:38 am

    I want a link to that chart

  • Reply Addison Osborn December 11, 2018 at 3:39 am

    4:24 – is that @thepointsguy?

  • Reply OneBuccaneer December 11, 2018 at 10:29 am

    While I love data, this (money being the motor) ruins what sports is about.

  • Reply dark man December 11, 2018 at 3:10 pm

    No one laughing at his jokes.

  • Reply Frank Gregus December 11, 2018 at 11:42 pm

    2:10 because only a professional knows what down screen is

  • Reply Jason Clark December 12, 2018 at 5:00 am

    That was the points guy at 430

  • Reply wuxxxxxx December 12, 2018 at 11:59 am

    All this to get a ball through a hoop. Lets apply this energy to health services.

  • Reply Sergio Ferrero Pérez December 12, 2018 at 4:15 pm

    When he says that almost every single contender for the Championship uses his software, does he mean that the Nets doesn't???

  • Reply noitall man December 13, 2018 at 11:55 pm

    SImmer down stat geek… First of all, in regards to pick-and-rolls, or anything for that matter, coaches don't want to know "how it happened". They want to know what happened as a result of it or everything before the result.

    You say a machine can know more than a coach, but it really depends upon what "knowing" means. A machine can certainly calculate and store much more data than a coach. But, a machine cannot understand the human element, the other variables that cannot be translated into data, and inherent understanding of the game.

    You data collection software is only as good as the person analyzing the data, and if that person is a math guy, and not a basketball guy, then we are all in trouble.

  • Reply Tim V December 17, 2018 at 3:21 am

    Look if you need a software program that was developed by guys who know nothing about basketball if a player is a good shooter then wtf are you doing coaching ball?!?!?

  • Reply Justin Hibbler December 18, 2018 at 8:49 am

    Trippy AF

  • Reply bignardo95 December 20, 2018 at 8:28 pm

    This is the future of tracking humans and predicting where they came from, where they will be, and which way they'll travel to come and go. Think about that for a minute.

  • Reply dwayne jamal December 23, 2018 at 2:55 pm

    Wtf is this.

  • Reply kingkongstrong December 25, 2018 at 4:40 am

    So basically Big boys want to track our every movement. Good luck with your personal freedom.

  • Reply Daratasourus December 26, 2018 at 6:07 am

    how do we know that the clip he showed isnt edited

  • Reply Jane Za December 29, 2018 at 12:17 pm

    More variations as that in balling, go predict the art.

  • Reply azwabi December 31, 2018 at 12:26 pm

    "the other football" – thank you 🙂 but i prefer american football.

  • Reply Andrew Hanson January 2, 2019 at 7:15 pm

    There are probably thousands of factors that go into every move in a basketball game enacted out by 10 individuals with free will.

    * tracks court position

  • Reply yankeeslakers4ev January 6, 2019 at 4:34 pm

    is there anyone who can explain the meaning of the chart at 8:25 in Chinese? Plz~

  • Reply Mike Lee January 10, 2019 at 3:00 am

    Abolish refs and have it be a computer!

  • Reply Sam Sutare January 11, 2019 at 2:00 pm

    That last clips of people moving with their circles above their heads made it look like a Black Mirror episode.

  • Reply Sahr Lebbie January 13, 2019 at 4:41 am

    Good talk. There are things machines still can’t quantify or predict and may never be able to do so but this helps give you a ball park.

  • Reply Casey Foster January 14, 2019 at 6:30 pm

    The points guy @ 4:24

  • Reply Russell Kanning January 17, 2019 at 3:19 am

    fun in basketball … scary across society

  • Reply Dominic Caciappo January 19, 2019 at 2:14 am

    Can these guys make the next 2k game please.

  • Reply Redapple January 19, 2019 at 10:56 am

    god damn its a fuking 12 minutes ad. I just realized it around 6th minute.

  • Reply Nosy Rosie January 19, 2019 at 3:02 pm

    Thank you very much too for sharing!

  • Reply herasucks January 24, 2019 at 12:02 am

    Wow his commentary on the park game was taken straight out of game 6 of the 2013 finals.

  • Reply Andrew Bender April 1, 2019 at 9:50 pm

    If this guy is so on point, can he explain why the people who move the best tend to be the least interested in math and science?

  • Reply Adi Da Gamer April 4, 2019 at 8:59 am

    Okay is he implying?

  • Reply Livingstone Germain June 2, 2019 at 2:42 am

    Professor X

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