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

譯者: Allen Kuo 審譯者: Twisted Meadows

My colleagues and I are fascinated by the science of moving dots.

我同事和我對移動的點 背後的科學非常著迷。

So what are these dots?

這些點是什麼？

Well, it's all of us.

是我們每一個人。

And we're moving in our homes, in our offices, as we shop and travel

我們在家、在辦公室裡走動，

在整個城市裡、 甚至世界各地旅遊和購物。

throughout our cities and around the world.

And wouldn't it be great if we could understand all this movement?

我們若能夠瞭解這些動作， 不是很棒嗎？

If we could find patterns and meaning and insight in it.

如果能從中找出模式、 意義和背後意涵的話。

And luckily for us, we live in a time

而我們有幸

活在一個擷取自身資訊 非常容易的時代，

where we're incredibly good at capturing information about ourselves.

So whether it's through sensors or videos, or apps,

無論透過感應器、影片或應用程式，

we can track our movement with incredibly fine detail.

我們都能非常精細地追蹤自己的動作。

So it turns out one of the places where we have the best data about movement

然後我們發現，最適合 獲取動作資訊的一個地方，

is sports.

就是運動場。

So whether it's basketball or baseball, or football or the other football,

無論是籃球、棒球、橄欖球或足球，

we're instrumenting our stadiums and our players to track their movements

我們都能在場館裡、甚至球員身上 安裝儀器，追蹤他們的動作 --

每個瞬間的動作。

every fraction of a second.

So what we're doing is turning our athletes into --

所以我們要做的 就是把運動員變成──

you probably guessed it --

你們大概已經猜到了──

moving dots.

移動的點。

So we've got mountains of moving dots and like most raw data,

我們收集了海量的移動的點， 但就像大部分的原始數據一樣，

it's hard to deal with and not that interesting.

它們不易處理、也不甚有趣。

But there are things that, for example, basketball coaches want to know.

但藏在數據裡的是，舉例來說， 籃球教練想知道的事。

And the problem is they can't know them because they'd have to watch every second

而問題是他們無法得知這些事， 因為他們得看著每一秒鐘的比賽，

of every game, remember it and process it.

記住內容並處理它。

And a person can't do that,

沒有任何人能做到這件事，

but a machine can.

但機器可以。

The problem is a machine can't see the game with the eye of a coach.

問題是，機器無法從 教練的角度觀看比賽，

At least they couldn't until now.

至少在此之前，它們都做不到。

So what have we taught the machine to see?

所以我們教會了機器看些什麼呢?

So, we started simply.

從簡單的開始。

We taught it things like passes, shots and rebounds.

我們教它判斷傳球、 投籃、搶籃板等動作，

Things that most casual fans would know.

一些大部分普通球迷都知道的事。

And then we moved on to things slightly more complicated.

然後我們進入稍微複雜一點的動作，

Events like post-ups, and pick-and-rolls, and isolations.

像是低位單打、擋切和清空單打。

And if you don't know them, that's okay. Most casual players probably do.

如果你不知道這些動作，沒關係。 打球的人大概都清楚。

Now, we've gotten to a point where today, the machine understands complex events

接著，我們到達今天的地步， 機器已經可以讀出複雜的動作，

like down screens and wide pins.

例如：向下掩護和無球掩護(wide pin)，

Basically things only professionals know.

一些基本上是專業人士才懂的動作。

So we have taught a machine to see with the eyes of a coach.

我們教會了機器 用教練的角度來看比賽。

So how have we been able to do this?

我們是怎麼做到的?

If I asked a coach to describe something like a pick-and-roll,

如果我請教練形容 某個動作，例如擋切，

they would give me a description,

他們會給我一段敘述，

and if I encoded that as an algorithm, it would be terrible.

如果我把這個敘述寫成 一個演算法，大概會慘不忍睹。

The pick-and-roll happens to be this dance in basketball between four players,

擋切在籃球中，恰如 四個球員之間的舞蹈，

two on offense and two on defense.

兩個進攻方、兩個防守方。

And here's kind of how it goes.

大概是這樣的過程：

So there's the guy on offense without the ball

有一個未持球的進攻球員

the ball and he goes next to the guy guarding the guy with the ball,

他跑到持球球員的旁邊幫他掩護，

and he kind of stays there

在原地稍作停留，

and they both move and stuff happens, and ta-da, it's a pick-and-roll.

然後他們都移動，事情就發生了 ——嗒啦——這就是擋拆。

(Laughter)

(笑聲)

So that is also an example of a terrible algorithm.

剛剛我示範了一個差勁的演算法。

So, if the player who's the interferer -- he's called the screener --

如果擋人那名球員──我們稱掩護者──

goes close by, but he doesn't stop,

慢慢靠近，但他並未停留，

it's probably not a pick-and-roll.

這可能就不是擋切。

Or if he does stop, but he doesn't stop close enough,

或是他有停留，但距離不夠近，

it's probably not a pick-and-roll.

這可能也不是擋切。

Or, if he does go close by and he does stop

或是他慢慢靠近、也確實停留，

but they do it under the basket, it's probably not a pick-and-roll.

但這發生在籃下，可能也不是擋切。

Or I could be wrong, they could all be pick-and-rolls.

也可能我判斷錯誤，這些全都是擋切。

這一切取決於精確的 時機、距離和位置，

It really depends on the exact timing, the distances, the locations,

and that's what makes it hard.

這也正是困難的地方。

So, luckily, with machine learning, we can go beyond our own ability

很幸運地，透過機器學習技術， 我們得以用超越自己的能力，

to describe the things we know.

來描述我們知道的事情。

So how does this work? Well, it's by example.

如何做到這個技術？舉個例。

So we go to the machine and say, "Good morning, machine.

我們跑到機器面前說：「早安，機器。

Here are some pick-and-rolls, and here are some things that are not.

這裡有些擋切的例子， 也有些不是的例子。

Please find a way to tell the difference."

請找出區分它們的方式。」

And the key to all of this is to find features that enable it to separate.

而一切的關鍵在於找到 可以進行區別的特徵。

So if I was going to teach it the difference

如果我要教它區分

between an apple and orange,

蘋果和橘子的差異，

我可能會說： 「不妨用顏色或形狀來區分?」

I might say, "Why don't you use color or shape?"

And the problem that we're solving is, what are those things?

而我們要解決的問題是， 類似這樣的特徵是什麼？

What are the key features

哪些是能讓電腦判讀這些移動的點時， 能暢行無阻的重要特徵？

that let a computer navigate the world of moving dots?

So figuring out all these relationships with relative and absolute location,

所以搞清楚每件事情的關聯── 包含相對和絕對位置、

距離、時機、速率──

distance, timing, velocities --

that's really the key to the science of moving dots, or as we like to call it,

絕對是研究這些移動的點的重要關鍵， 或者用我們喜歡的稱呼方式：

spatiotemporal pattern recognition, in academic vernacular.

「時空模式識別」這樣的學術用語。

Because the first thing is, you have to make it sound hard --

因為最重要的是， 必須讓它聽起來很難，

because it is.

因為它真的很難。

The key thing is, for NBA coaches, it's not that they want to know

重要的是，對NBA教練來說， 他們想知道的

whether a pick-and-roll happened or not.

不是擋切是否發生，

It's that they want to know how it happened.

而是擋切是怎麼發生的。

And why is it so important to them? So here's a little insight.

為什麼這對他們如此重要? 這裡有一些發現。

It turns out in modern basketball,

原來在現代籃球中，

this pick-and-roll is perhaps the most important play.

擋切可能就是最重要的戰術。

And knowing how to run it, and knowing how to defend it,

知道如何執行、如何防守擋切，

基本上是大部分比賽輸贏的關鍵。

is basically a key to winning and losing most games.

So it turns out that this dance has a great many variations

所以結果是，擋切這種舞步變化多端，

and identifying the variations is really the thing that matters,

真正重要的是要辨別這些變化，

and that's why we need this to be really, really good.

所以我們需要有非常完善的演算法。

So, here's an example.

這裡有個例子。

There are two offensive and two defensive players,

兩個進攻球員和兩個防守球員

getting ready to do the pick-and-roll dance.

準備進行擋切的攻防，

持球者可以選擇利用或拒絕擋切，

So the guy with ball can either take, or he can reject.

His teammate can either roll or pop.

他的隊友則可以選擇切入或後撤。

The guy guarding the ball can either go over or under.

防守持球者的球員可選擇 從前繞開、或從後繞開。

His teammate can either show or play up to touch, or play soft

他的隊友可選擇上前補防、 隨球盯人或向後消極防守，

and together they can either switch or blitz

他們也可以選擇換防或夾擊。

and I didn't know most of these things when I started

一開始我並不知道大部分的動作，

and it would be lovely if everybody moved according to those arrows.

覺得如果大家能照那些箭頭 的方向移動就太棒了，

It would make our lives a lot easier, but it turns out movement is very messy.

這會讓我們的生活更加容易； 但我們的動作往往非常雜亂。

人的動作有大量扭動，要在精準度和完整度上

People wiggle a lot and getting these variations identified

精確辨識這些變化，是相當困難的，

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.

因為唯有如此， 才能取得專業教練的信任。

And despite all the difficulties with the right spatiotemporal features

而儘管找到這些正確的 時空特徵困難重重，

we have been able to do that.

我們還是做到了。

教練們信任我們機器 辨識這些變化的能力。

Coaches trust our ability of our machine to identify these variations.

We're at the point where almost every single contender

我們已經達到，今年幾乎每一個 爭奪NBA冠軍的隊伍

for an NBA championship this year

is using our software, which is built on a machine that understands

都在使用我們的軟體， 安裝在可以讀懂籃球場上

the moving dots of basketball.

移動的點的機器裡。

So not only that, we have given advice that has changed strategies

不只如此，這些隊伍也根據 我們的建議改變一些戰術，

that have helped teams win very important games,

幫助他們贏了一些很重要的比賽，

and it's very exciting because you have coaches who've been in the league

這令人感到非常興奮， 因為我們讓這些在聯盟裡

打滾了30年的教練， 願意聽一台機器的建議。

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.

不只擋切戰術，更讓我們興奮的是，

Our computer started out with simple things

我們的電腦從簡單的開始，

and learned more and more complex things

學會越來越複雜的動作，

and now it knows so many things.

現在它已經有豐富的知識。

Frankly, I don't understand much of what it does,

老實說，它懂得已經比我多了，

and while it's not that special to be smarter than me,

但由於比我聰明也沒什麼特別的，

we were wondering, can a machine know more than a coach?

我們更想知道， 機器有可能懂得比教練還多嗎？

Can it know more than person could know?

可能懂得比人類還多嗎？

And it turns out the answer is yes.

結果答案是：可以。

The coaches want players to take good shots.

教練都希望球員掌握好的投籃時機，

So if I'm standing near the basket

如果離籃框很近，

and there's nobody near me, it's a good shot.

旁邊沒人防守，就是好的投籃時機。

如果我離籃框很遠，又被防守者包圍， 通常就是很差的投籃時機。

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.

但我們從來無法從量化數據得知， 「好」有多好、「差」有多差。

Until now.

但現在不同了。

So what we can do, again, using spatiotemporal features,

所以我們可以，同樣地， 利用時空特徵條件，

we looked at every shot.

檢視每一次投籃。

We can see: Where is the shot? What's the angle to the basket?

我們可以得知：投籃位置在哪？ 和籃框的角度是幾度？

Where are the defenders standing? What are their distances?

防守者站在哪裡？距離多少？

What are their angles?

角度多大？

For multiple defenders, we can look at how the player's moving

防守者不只一個時， 我們可以觀察球員如何移動

and predict the shot type.

來預測投籃類型。

We can look at all their velocities and we can build a model that predicts

我們可以觀察速率，建立一個可以預測

what is the likelihood that this shot would go in under these circumstances?

在此情況下的命中率模型。

So why is this important?

為什麼這很重要？

We can take something that was shooting,

我們可以將投籃

which was one thing before, and turn it into two things:

這種過去的單一行為，轉化為兩件事：

the quality of the shot and the quality of the shooter.

投籃動作本身的品質，和投籃者的品質。

So here's a bubble chart, because what's TED without a bubble chart?

這裡有一張泡泡圖， 沒有泡泡圖還像TED嗎？

(Laughter)

(笑聲)

Those are NBA players.

這些都是NBA球員。

The size is the size of the player and the color is the position.

泡泡大小代表球員體型大小， 顏色代表他打的位置。

On the x-axis, we have the shot probability.

X軸是進球的機率，

People on the left take difficult shots,

左邊的球員做了許多勉強的投籃動作，

on the right, they take easy shots.

右邊的球員在有空檔時才會出手。

On the [y-axis] is their shooting ability.

Y軸是球員的投籃能力，

People who are good are at the top, bad at the bottom.

擅長投籃的球員在上方， 不擅長的在下方。

So for example, if there was a player

舉例來說，如果有個球員，

who generally made 47 percent of their shots,

平均命中率大約47%，

that's all you knew before.

這是過去所有你知道的資訊。

But today, I can tell you that player takes shots that an average NBA player

但今天，我能告訴你以 這個球員出手投籃的狀況，

NBA球員的平均命中率是49%，

would make 49 percent of the time,

and they are two percent worse.

他比平均低了2%。

And the reason that's important is that there are lots of 47s out there.

這之所以重要，是因為 有這麼多47%命中率的球員。

And so it's really important to know

重點就是要搞清楚，

if the 47 that you're considering giving 100 million dollars to

如果你要用100美金 簽下一個47%的球員，

is a good shooter who takes bad shots

應該要找能投得準但出手時機不佳的，

or a bad shooter who takes good shots.

還是不那麼準但出手時機很好的球員。

Machine understanding doesn't just change how we look at players,

機器的理解力不只改變了 我們對球員的看法，

it changes how we look at the game.

也改變了我們對比賽的看法。

So there was this very exciting game a couple of years ago, in the NBA finals.

兩年前在NBA總冠軍系列戰， 有一場非常刺激的比賽。

Miami was down by three, there was 20 seconds left.

邁阿密熱火隊落後3分， 時間還剩20秒。

They were about to lose the championship.

他們即將把冠軍拱手讓人。

A gentleman named LeBron James came up and he took a three to tie.

一位叫勒布朗·詹姆士的先生 出手一顆三分球企圖追平比賽，

He missed.

球沒進。

His teammate Chris Bosh got a rebound,

他的隊友克里斯·波許搶到籃板，

passed it to another teammate named Ray Allen.

傳給另一位隊友雷·艾倫。

他命中了一顆三分球， 將比賽帶入延長賽，

He sank a three. It went into overtime.

They won the game. They won the championship.

最後他們贏了比賽，拿到冠軍。

It was one of the most exciting games in basketball.

這是籃球場上最刺激的球賽之一。

And our ability to know the shot probability for every player

而因為我們可以得知每一個球員 在每一秒鐘投進的機率，

at every second,

以及每一秒鐘他們搶到籃板的機率，

and the likelihood of them getting a rebound at every second

讓我們得以用前所未有的方式 窺見這個時刻的全貌。

can illuminate this moment in a way that we never could before.

Now unfortunately, I can't show you that video.

很可惜，現在我無法播放那段影片，

But for you, we recreated that moment

但為了各位，我們重建了那個時刻，

at our weekly basketball game about 3 weeks ago.

就在大約三週前 我們每週例行的籃球比賽裡。

(Laughter)

(笑聲)

And we recreated the tracking that led to the insights.

我們也重建了讓我們窺見 比賽全貌的追蹤數據。

So, here is us. This is Chinatown in Los Angeles,

所以，這就是我們， 在洛杉磯的中國城，

a park we play at every week,

我們每週都在這個公園比賽。

and that's us recreating the Ray Allen moment

我們正在重建雷·艾倫的經典時刻，

and all the tracking that's associated with it.

以及所有相關的追蹤數據。

So, here's the shot.

這就是那經典的一球。

I'm going to show you that moment

我將和各位展示那個時刻，

and all the insights of that moment.

以及那個時刻背後的一切。

The only difference is, instead of the professional players, it's us,

唯一的不同是，表演者是我們， 不是那些職業球員。

and instead of a professional announcer, it's me.

還有是我在播報，不是職業播報員，

So, bear with me.

所以請大家見諒。

Miami.

邁阿密熱火。

Down three.

3分落後。

Twenty seconds left.

剩下20秒。

Jeff brings up the ball.

傑夫帶球過來。

Josh catches, puts up a three!

喬許接到了球，三分出手！

[Calculating shot probability]

[計算命中率]

[Shot quality]

[投籃品質]

[Rebound probability]

[籃板機率]

Won't go!

球沒進！

[Rebound probability]

[籃板機率]

Rebound, Noel.

諾爾搶到籃板。

Back to Daria.

向後傳給朵莉雅。

[Shot quality]

[投籃品質]

Her three-pointer -- bang!

她三分出手... 球進！

Tie game with five seconds left.

追平比賽，剩下5秒！

The crowd goes wild.

觀眾陷入瘋狂。

(Laughter)

(笑聲)

That's roughly how it happened.

事情大概就是這樣發生的。

(Applause)

(掌聲)

Roughly.

大概啦。

(Applause)

(掌聲)

That moment had about a nine percent chance of happening in the NBA

這個時刻發生在NBA 賽場上的機率大約是9%，

and we know that and a great many other things.

我們能算出這件事 和其他許多事的機率。

I'm not going to tell you how many times it took us to make that happen.

我絕對不會告訴各位 我們試了幾次才成功。

(Laughter)

(笑聲)

Okay, I will! It was four.

好啦，告訴你們，四次。

(Laughter)

(笑聲)

Way to go, Daria.

幹得不錯，朵莉雅。

But the important thing about that video

但重要的並不是這則影片，

and the insights we have for every second of every NBA game -- it's not that.

也不是它對NBA每場比賽 每一秒鐘的意涵。

It's the fact you don't have to be a professional team to track movement.

重要的是，不是只有職業球隊 才能追蹤人的動作，

You do not have to be a professional player to get insights about movement.

也不是只有職業球員 才需要這些動作背後的意涵。

In fact, it doesn't even have to be about sports because we're moving everywhere.

事實上，它也不是只能應用在運動場上， 因為我們隨時都不斷地在各地移動。

We're moving in our homes,

我們在家裡移動、

in our offices,

在辦公室裡移動、

as we shop and we travel

購物和旅遊、

throughout our cities

穿梭在我們的城市裡

and around our world.

以及全世界。

What will we know? What will we learn?

我們可以知道什麼？可以學到什麼？

Perhaps, instead of identifying pick-and-rolls,

或許，除了辨識擋切戰術之外，

a machine can identify the moment and let me know

機器還能辨識出感動時刻，讓我知道

when my daughter takes her first steps.

我女兒何時踏出她的第一步。

Which could literally be happening any second now.

這真的是每一秒鐘都可能發生的事。

Perhaps we can learn to better use our buildings, better plan our cities.

或許我們能夠學會更善加 利用建築物、做更好的都市規劃。

I believe that with the development of the science of moving dots,

我相信藉由移動的點的科學進步，

we will move better, we will move smarter, we will move forward.

我們將能更好地移動、更聰明地移動， 並真正向未來移動。

Thank you very much.

非常感謝各位。

(Applause)

(掌聲)