Folks, you may know it by now, I am a huge

sports fan.

2

So needless to say that this episode was

like being in a candy store for me.

3

Well, more appropriately, in a chocolate

store.

4

Paul Sabin is so knowledgeable that this

conversation was an absolute blast for me.

5

In it, Paul discusses his experience with

non -stats stakeholders in sports

6

analytics and the challenges of convincing

them to adopt evidence -based decisions.

7

He also explains his soccer power ratings

and projections model, which uses a

8

Bayesian approach and expected goals, as

well as the importance of understanding

9

player value in difficult to measure

positions and the need for more accessible

10

and digestible sports analytics for fans.

11

We also touch on the impact of budget on

team performance in American sports and

12

the use of plus -minus models in

basketball and American football.

13

Paul is a senior fellow at the Wharton

Sports Analytics and Business Initiative

14

and I like truer

15

in the Department of Statistics and Data

Science at the Wharton School of the

16

University of Pennsylvania.

17

He has spent his entire career as a sports

analytics professional, teaching and

18

leading sports analytics research

projects.

19

This is Learning Visions Statistics,

20

Welcome to Learning Bayesian Statistics, a

podcast about Bayesian inference, the

21

methods, the projects, and the people who

make it possible.

22

I'm your host, Alex Andorra.

23

You can follow me on Twitter at Alex

underscore Andorra, like the country, for

24

any info about the show.

25

LearnBayStats .com is Laplace to me.

26

Show notes.

27

becoming a corporate sponsor, unlocking

Bayesian Merge, supporting the show on

28

Patreon, everything is in there.

29

That's LearnBasedStats .com.

30

If you're interested in one -on -one

mentorship, online courses, or statistical

31

consulting, feel free to reach out and

book a call at topmate .io slash alex

32

underscore and dora.

33

See you around, folks, and best Bayesian

wishes to you all.

34

Welcome to Learning Vagin Statistics.

35

a full conversation in French as we just

had before recording.

36

Well done.

37

It used to be though.

38

Go back two to three hundred years.

39

Maybe you just don't go to Africa enough.

40

That's where French is spoken a lot now

too.

41

Exactly.

42

But other than that, you can see French

used to be a very international language

43

because in my travels, almost all the time

people tell me, yeah, I studied French in

44

high school.

45

And the only thing they can say is just a

few words.

46

Which is normal, like if you don't use it,

right?

47

But yeah, you can see that because French

is still, or was still taught in high

48

school and now less and less.

49

So yeah, so well done Paul for that.

50

I know, I don't think French is an easy

language to learn.

51

What has been your experience?

52

I'm actually very curious.

53

You know, it's hard to say, so this is a

statistics pod or data science podcast.

54

So I guess I can't really, I can't really

compare it to anything else.

55

That's the only other language I've

learned besides my native English.

56

So, you know, I guess, you know, one

sample size for me, I took it in high

57

school as well.

58

I hated it.

59

I had, so, you know, coming from America,

you know, so the reason I chose, you know,

60

seventh grade is when I had to choose

whether I was taking French or Spanish.

61

And I'm the youngest of four kids in my

family growing up.

62

And my older siblings told me that the

Spanish teacher was really mean.

63

And that's originally why I took took

French.

64

and then I took it for the required two to

three years.

65

And then I was done.

66

I had in high school, I had this teacher

from Belgium and I still remember her

67

name, Madame Vendon Plus, and I couldn't

stand her, but come, come to find out

68

looking back in life that she was actually

a really nice person.

69

She was just Belgian.

70

And the cultural, you know, like Americans

think they're the best and the French

71

language in Europe people also think

they're the best because they ruled the

72

like they've ruled the world for the last

73

100 years.

74

And so when you get into a room together

and you think both of your cultures are

75

superior, you know, that doesn't go well

together.

76

But actually, so after that, I didn't...

77

speak French at all.

78

And then I did church service for my

church for two years and I lived in

79

Montreal, I lived in Quebec, not actually

in the city, I lived in a lot of rural

80

small town.

81

And so I studied French really hard.

82

I had to learn the very strong Quebecois

accent.

83

And then when I went back to school, it's

when I like really honed in my French.

84

I was very conversational, could speak

very fluently in Quebec, but then, you

85

know, I had to learn the grammar a little

bit more.

86

in depth.

87

So then I studied French as well at

university as well.

88

So, you know, immersing yourself and the

actually like learning languages because

89

when I learned it in school, it didn't

never made sense to me.

90

But when I studied it on my own and I

studied conjugation and all these things,

91

it became kind of like a math problem.

92

And so when I would speak a sentence in my

head, I'd always be like, I need a

93

subject.

94

I need to conjugate the verb.

95

And then I need to say like what I'm, you

know, just

96

do an adverb or an adjective after it.

97

And like it made sense in my head, but

that's not how I was taught in school.

98

I was taught, I had to memorize all these

words, like everything in the kitchen.

99

How do you say dishwasher?

100

How do you say refrigerator?

101

How do you say fork?

102

How do you say spoon?

103

I couldn't learn like that, but at like

living and like thinking about French as a

104

math equation, it made sense in my head

and I was able to pick it up.

105

You know, sure.

106

I made tons of mistakes and embarrassed

myself, but it wasn't too bad.

107

And that's how you learn.

108

Yeah.

109

So I'm guessing.

110

Like from that answer, I'm guessing people

already know why I invited you on the

111

podcast.

112

Very nerdy answer, your put languages,

that's perfect.

113

Thanks a lot.

114

And yeah, I completely relate actually.

115

I learned English and German in high

school and yeah, kind of the same.

116

I always hated formal language learning.

117

And like in the end I learned these

languages and Spanish that was the same

118

and Italian that was the same, just going

to the country basically.

119

And yeah, as you were saying, I think also

what it adds is you've got skin in the

120

game.

121

You're in the country, you're having a

conversation with someone.

122

If you're not able to talk, you look

extremely stupid.

123

So it's a very good incentive for the

brain to step up and learn.

124

And that's really awesome.

125

And then when you are in the situation

that you...

126

don't know what to say, you remember that.

127

And then when you learn, this is what I

should have said, it sticks with you

128

because it has an emotional attachment to

it.

129

Yeah.

130

Yeah.

131

No, exactly.

132

And I mean, and that's going to be a good

segue to my first question to you, but I

133

think it's also one of the situations in

life, where you can really, feel and see

134

your brain learning.

135

So that's why I also really love learning

new languages and going to countries to do

136

that because.

137

Like you arrive in the country, you don't

know how to say anything.

138

And in just a few weeks, your brain starts

picking up stuff and you can really,

139

really feel your brain doing its amazing

work that it's been like conditioned to do

140

from years of evolution.

141

And to me, that's just absolutely

incredible that the brain is able to do

142

that.

143

Even when you're like in your thirties and

beyond, you can do that.

144

And it's just, I found that absolutely

incredible.

145

And that's kind of like a Bayesian.

146

neural network, you know, so I mean, see

that segue, I should definitely have a

147

podcast.

148

So actually talking about base.

149

Yeah, I invited you on the podcast because

you do absolutely awesome work on sports

150

modeling.

151

And people know that I'm a big fan of a

lot of sports.

152

I love modeling sports and so on.

153

So I'm super happy to have you here.

154

And I have a list of questions that is

embarrassingly long.

155

But maybe can you tell us if you are

actually yourself using some basic

156

methods, if you're familiar with those or

not?

157

And yeah, in general, what does that look

like in your work?

158

Yeah.

159

So yeah, I mean, just a quick background

about myself, right?

160

I've worked in sports, what we call sports

analytics for almost 10 years now.

161

Out of actually, I was getting my PhD.

162

And statistics, and I, you got, there was

this job opportunity at ESPN, you know,

163

which is a sports broadcasting television

channel in the U S and a few other

164

countries.

165

And, you know, I got the job offer to work

on their sports analytics team where

166

essentially what the team there does is

make forecasts so that, you know, they can

167

show on TV, you know, on the bottom line,

like who's expected to win, or they can,

168

we will run simulations on.

169

you know, who's likely to win the

championship, you know, all throughout the

170

season.

171

And so, you know, you can tell stories

with that saying, you know, the team was

172

just like the beginning of the season.

173

No one thought they were going to be any

good, but just look how it, you know, they

174

got better or the opposite.

175

Like they were supposed to be really good

and everything just went wrong.

176

And so in my field in sports modeling, I

would think actually you can't, you can't

177

do it without being Bayesian.

178

And so when I would interview people, I'd

always focus on, on those.

179

So as people coming out of school,

sometimes they don't always learn Bayesian

180

methods very well.

181

And the reason is in sports, sample sizes

are very small and you have to make

182

forecasts with very limited data.

183

And the great thing about Bayesian is

statistics is that you actually have more

184

data.

185

You just haven't observed it.

186

You have expertise or you have opinions,

but those opinions actually matter.

187

And so maybe we'll get into this, but I'm

actually a very strong advocate because of

188

my field of being a subjective Bayesian

analysis.

189

It's okay to insert some information into

your models and it usually makes them

190

better.

191

Yeah.

192

Well, awesome.

193

couldn't have dreamt better and I have to

fully structure.

194

I didn't know Paul was going to answer

that because that's not really, I haven't

195

seen that in your, you know, on your

website or else,

196

So before, while preparing the episode, I

didn't know if you were already using

197

Bayesian methods or else.

198

But definitely, definitely happy to hear

that.

199

And so that people know that was not a

conspiracy.

200

I didn't know anything that Paul was going

to say.

201

OK, so that's awesome.

202

So I'm an open source developer, so I'm

always very curious about the stack you're

203

using.

204

What are you using actually when you're

doing Bayesian analysis of a spot model?

205

So in my career, I almost always use R and

Stan.

206

So if I'm doing Bayes analysis, I write a

lot of Stan code.

207

It's gotten easier with the Chat GPT.

208

It doesn't do it all the way, right?

209

But if it's like, hey, I want to build

this kind of model, it'll at least give me

210

a good framework.

211

And then I can adjust it and edit it as I

want from there.

212

Yeah.

213

Yeah.

214

And I mean, for sure, you cannot go wrong

with the.

215

with R and Stan.

216

So yeah, definitely.

217

And we've had the, one of the creators of

Stan, Andrew Gellman, was back on the

218

podcast a few weeks ago.

219

It was not released yet, but through time

travel, it's gonna have been released when

220

your episode is out.

221

So folks, you can go back to - Right,

because I am definitely a lesser draw than

222

Andrew Gellman is, but that's great.

223

No, yeah, so if people are curious about

what Andrew has been up to, lastly, it's

224

the third time he's been on the show and

he just released a new book, Active

225

Statistics, that I definitely recommend.

226

It's really fun to read.

227

It's like, it's how to teach statistics

with stories, which actually relates to

228

something you just said, Paul, about the,

like, cool and fun way to relate

229

statistics to...

230

non -stats people was to be able to tell

stories about a team's probability of

231

winning or any forecast like that.

232

So that's definitely interesting to hear

you talk about that.

233

And actually I'm curious because I've been

following that field of spots analytics

234

for a few years and I've seen it

personally mature.

235

quite a lot and evolved quite a lot when

it comes to the technology and the data

236

availability.

237

So I'm curious what an expert like you

think about that evolution of technology

238

and data availability and how that changed

the landscape of Spots Analytics.

239

Yeah, I mean, it's exploded in the last 10

to 15 years.

240

So I mean, if people are familiar with the

book slash movie Moneyball, which is

241

20, about 20 years, the book is about 20

years old now.

242

The movie is about 12, 13 years old now.

243

you know, back then in baseball, baseball

was the sport that sort of took off in

244

sports analytics.

245

I mean, for a couple of reasons.

246

One, the game is very discreet.

247

So their start and their stopping points.

248

So you can measure.

249

Right.

250

Discrete events very well in baseball, but

two, like they're the only sport that

251

actually had a really long running data

set.

252

And that went back and they've been

keeping statistics in baseball and you can

253

254

No other sport has that.

255

So that's, that's probably the reason why

baseball took off.

256

but since then, you know, every sport for

a while after that, every sport had what

257

we call play by play data, which is like,

this is what happens.

258

Soccer had a, a version that was called

event data.

259

So would people would.

260

watch a game and every time someone

touched the ball or made a pass, they

261

would mark, the ball was touched here on

the field and it was passed to there or

262

they dribbled from here to there.

263

So it was, they kind of were discretizing

soccer in a way to make it a similar

264

format.

265

But then about 10 years ago, we started

getting this player tracking data, which

266

is the location of everybody and the ball

or the puck on the field, you know,

267

depending on the sport, 10 to 25 times per

second.

268

And that's drastically changed.

269

the methodologies and things that are

used.

270

So, I mean, Bayesian analysis was great

for this play by play data or even, you

271

know, game by game data and measuring how,

how players or teams performed.

272

And then now we've started getting such

huge data sets that, you know, more of the

273

computer science world, neural networks,

things like that started becoming much

274

more prevalent in sports analysis just

because the data sets were so massive.

275

Not that statistics doesn't play a role.

276

It still does.

277

And I think.

278

People sometimes overly rely on these

black box methods.

279

They don't think about the implications or

the biases in the data, which are still

280

important.

281

But we have these huge amounts of data now

and it's just exploded to like, you know,

282

if you want all the data in a season in

the NFL, it's like over one terabyte of

283

locations of everybody on every field, 20,

every play of 25 times a second.

284

It's just massive.

285

Right.

286

So it's, it's really changed the way

people have done things.

287

Right.

288

And we started going from really simple

questions to huge big questions.

289

And the funny thing is now, I actually

think with the data being so large, people

290

are now actually going back to answering

more simple questions.

291

Like we're not trying to measure

everything all at once.

292

Let's try to measure very specific things

that we weren't able to measure before.

293

Hmm.

294

Yeah, that is definitely interesting.

295

and is that so first.

296

Is that availability of data, massive

availability of data, the case in all the

297

sports industry?

298

Or is it more, well, the most historical

ones, as you were saying, maybe more

299

baseball.

300

I know the data set are more massive there

and maybe other sports like soccer are

301

less prevalent, the data set are less

prevalent, less massive, or is that a

302

uniform trend?

303

First question.

304

And then second question is,

305

Where does that data leave?

306

Is that mostly open source or is that

still quite close source data?

307

Yeah.

308

So I mean, baseball is usually like the

cutting edge of everything because they

309

had a head start.

310

And basketball and then like kind of

American football, international soccer

311

football and hockey kind of trail behind.

312

But the data sets now in all those sports

are very massive.

313

Hockey just got

314

The NHL just got their player puck

tracking data just a couple of years ago.

315

Now baseball and basketball have moved on

beyond just knowing where players are on

316

the field.

317

They actually have data of what's called

pose data.

318

So they know where different joints and

their arms and the legs are of every

319

player on the field or on the court.

320

So that data is massive.

321

It's massive everywhere.

322

There's companies that are trying to

collect new data based on

323

video, so they're using computer vision

algorithms to do that, but largely to

324

answer your second question.

325

This is not open source data.

326

So the old school data, the play by play

data is open source.

327

You can find that on every sport pretty

much via an open source mechanism now.

328

But this huge, these huge data sets of the

tracking of the players, you know, 10 to

329

25 times per second.

330

It's usually all closed source.

331

There are a few.

332

releases of that here and there, you know,

the NFL does a competition where they

333

release some of that data each year, like

a very small set.

334

and a few other leagues have done

something similar as well.

335

If they know that's, that's kind of gives

you a taste.

336

if you have money, there are companies

that try to create that data themselves

337

and they'll sell it to you.

338

But you know, that's usually pretty

expensive for an individual person to buy.

339

So again, just that.

340

I see.

341

Okay.

342

Yeah, interesting.

343

Definitely.

344

Because like data is kind of oil in our

industry, right?

345

So it's definitely interesting to know

what's the state of the supply of oil in a

346

way.

347

Maybe for people who are less versed in in

sports modeling, can you give us an

348

example of how analytical insights have

349

directly influenced team strategy or

player selection in one of your consulting

350

roles.

351

Yeah.

352

So I mean, I'll just kind of talk broadly

at first.

353

I mean, so sometimes it's just the most

basic things, right?

354

So like in basketball, people shoot three

pointers more because all they did is

355

figured out the expected value was larger

for three point shot than it was for most

356

two point shots.

357

Not, not those layups and the dunks,

right?

358

Those are very high percentages.

359

So the expected value of a, of a high

percentage times two is, you know, is, is

360

pretty good.

361

But then even if.

362

The percentage drops off a lot when you

multiply it by three to get the expected

363

value of a three point shot.

364

You know, it's also pretty good.

365

So that means basketball has changed

drastically because of that.

366

and in my roles, I guess, you know, I

think in a lot of sports, there's just

367

been a lot of open questions.

368

People kind of move one way.

369

And then I think actually, I think the

sports analysis does really good job of

370

tackling very easy problems first.

371

But then I think there's actually a

tendency for the analysts themselves to be

372

overconfident in their analysis and

they're not factoring in all of the

373

sources of variation that might be there.

374

And something I'm also very curious about

it is what's your experience with non

375

-stats stakeholders?

376

So coaches, scouts, players, how do they

typically respond to the analytics and the

377

insights you provide and other...

378

differences in reception across sports,

maybe across roles.

379

Yeah.

380

So, I mean, it really does vary as in all

things, there's variance.

381

There are some typically younger, you

know, coaches or scouts that are a little

382

bit more receptive than people who have

been doing something for a long time.

383

And I think that's just human nature.

384

You're used to doing things a certain way.

385

You don't like.

386

You know, to stereotype, you don't like

some young person coming and telling you

387

how to do your job.

388

Right.

389

So you have to be really careful about

that.

390

and the, and the funny thing is, you know,

everything that I have learned or, you

391

know, I believe in, in terms of making

data driven decisions and don't

392

overestimate based on small sample sizes

goes out the window when I'm trying to

393

convince a stakeholder of something.

394

So for example,

395

If I have a model and I want them to use

it, and I think it's going to help them.

396

Of course, I've done the analysis to say,

you know, what over the long run, how it

397

would improve our efficiency, or if we

make a decision in this way, it'd be

398

better process, et cetera.

399

I've done that analysis and I've done it

over a larger sample size.

400

But when I, when I tell them what they

want to know is they want confirmation

401

bias, right?

402

They love confirming their beliefs.

403

So in order to get them to, agree with

what you're saying, it, this works so much

404

more better than saying, you know, out of

the thousand players that I did this in,

405

you know, you only were correct 60 % of

the time, but my model would have been

406

correct 70%.

407

Like they don't want to hear that.

408

They essentially say, well, my model, you

know, you love this player.

409

So does my model.

410

I find the one guy, even if it's literally

only one person, they're like, yeah.

411

Like, if your model can.

412

If your model can see that, then it must

be doing something right.

413

And then it's like, then they start to

trust you a little bit.

414

And over time you give them little pieces,

little crumbs of a cookie that they can

415

help, you know, get confidence in.

416

And then, you know, then is when you share

with them, okay, well, but it's also

417

suggesting this, which is different than

what you've been doing in the past.

418

Right?

419

So you don't ever start with, you know,

trust me.

420

because you might be wrong, because you're

a human.

421

I mean, like, you know, humans always make

mistakes, but we usually don't think we

422

make as many mistakes as we do.

423

And so I found just over time is if you

get people to trust you by confirming

424

their prior held beliefs, right?

425

It's another Bayesian concepts.

426

If you can confirm their prior beliefs,

they're going to accept your future

427

recommendations or future things that the

model might suggest more than if you start

428

with.

429

the differences upfront.

430

And so that's like a little bit of human

bias, right?

431

That you have just learned over time.

432

And some things are just really hard for

people to accept, but over time, if you

433

get people to trust you and you build that

relationship, there's a lot of human

434

elements here and then they trust your

work by confirming their prior held

435

beliefs, then they'll trust you and open

up a little bit more to being a little bit

436

more open -minded about other things as

well.

437

Because then like, okay, well, I know

you're not an idiot.

438

Like you could speak my language some.

439

now I might be more open to learning a

little bit of your language.

440

And that's just sort of a human

relationship thing that you have to always

441

work on.

442

Yeah, that is very interesting.

443

And I'm very, yeah, I'm always very

interested to hear about that because I

444

also face clients daily and have to

explain models to them.

445

And so as you were saying, that definitely

varies a lot in interactions to the model.

446

But that negative wisdom of maybe

indulging the...

447

the confirmation bias at the beginning and

then slowly go towards a bit more of

448

speaking the truth.

449

It's very interesting.

450

I had not thought of that, but that's

yeah, definitely I can see that being a

451

valid strategy when you also are in front

of someone who doesn't really understand

452

the value of the modeling, I would say.

453

Whereas when I

454

encounter clients who are already

convinced of what the models can do for

455

them.

456

They are usually looking for contradicting

what they already think.

457

And that's when they find the model

interesting.

458

So I find that really, really cool to see.

459

The contradictions are really where

there's value, right?

460

But there's no value in a model if no one

uses it, right?

461

Even if the model is really good, if no

one uses it, it has zero value.

462

If they use it, the contradictions are

valuable if they're right, correct?

463

So in soccer analysis, you know, I've

spent my career doing lots of different

464

sports, but there's this sort of, this

applies to every sport.

465

In basketball, we can call it the LeBron

test and soccer, we'll call it the messy

466

test, where it's essentially, if you build

a model and it's trying to evaluate

467

players and messy is not like one of the

top players in your model, then.

468

You're not going to share it with anybody

because no one's going to believe you.

469

Right.

470

That's like the first thing everyone does

is like, okay, well is messy up top.

471

And if like, if messy is near the top,

then like people, at least they'll listen

472

to you a little bit longer.

473

Right.

474

But they're not going to listen to you at

all.

475

If you're like, yeah, messy is an okay

player.

476

Right.

477

Like I don't care what your model says.

478

Right.

479

That's wrong.

480

Right.

481

That's that, that's what people believe.

482

So it's like a little bit of like, I need

to feed you like, no, no, no.

483

Like I'm taking a different approach than

what you do, but you know, my approach

484

also thinks that messy is the best.

485

Right.

486

And then I'm like, it's okay.

487

You know,

488

Okay, yeah, we agree.

489

He is really good.

490

Yeah, it's like a sniff test, right?

491

And it's like, in a way, it's like, well,

that's a strong prior.

492

And it's like, it's saying, well, I have a

very strong prior.

493

That message is really good.

494

To convince me, otherwise you're going to

need really, really good data.

495

It's like, well, the earth is very

probably somewhat round.

496

It's going to be very hard for you to...

497

move that prior from me and telling me

it's not, in a way.

498

Yeah.

499

And in sports, people have really strong

priors, right?

500

So, you know, those sniff tests do really

matter.

501

And as a modeler, even for myself, like,

I'm a human.

502

So like, I do the same thing.

503

If I'm building a model, I always want to

see the results.

504

And it's like, I don't look at the median,

like I do, but I don't look at who the

505

median result is in my model half the

time.

506

I usually look at the best and I look at

the worst.

507

And if I don't understand it, then I'm

like, maybe my model is doing something

508

wrong.

509

And I'm all like, gonna, I'm going to dive

in a little bit more.

510

If it like confirms my prior held beliefs,

I'm like, it's probably correct.

511

Right.

512

And even as a modeler, right, you have to

be careful of that.

513

But at the same time in sports, you know,

it's like I said, subjective analysis can

514

be helpful.

515

It's because people's subjective and I'm

like, there's wisdom.

516

People coaches have been playing a game

for.

517

20, 30, or coaching a game for 20 or 30

years to think that they don't have

518

something to offer a model is kind of

crazy in my opinion.

519

They might have biases and of course they

do, but their information that they can

520

provide is useful.

521

Yeah, definitely.

522

And that's where we go back to what we

were talking about at the beginning in the

523

value of Bayesian inference in that

context.

524

Because if you can leverage that deep and

hard -hearned knowledge,

525

from the coaches, from the scouts, and add

that to your model, it's like getting the

526

best of both worlds.

527

And that can make your analysis extremely

powerful and useful, as you were saying.

528

Yeah.

529

And people have done studies like this,

I've done studies like this.

530

If you build a model just on the data and

ignore the human element, right?

531

Or if you build a model just on human and

scouting analysis and ignore the other

532

data.

533

Right.

534

Neither one of those is going to do as

well as when you combine both.

535

And that's really, that's what, you know,

that's Bayesian analysis is you're

536

combining subjective belief with objective

data and then making forecasts based on

537

them.

538

And we know that if you have priors that

are not really, really bad, a subjective

539

Bayesian forecast is going to have smaller

error than a data, you know, what we call

540

maximum likelihood forecast, right.

541

And stats terms, right.

542

Or.

543

You know, just the human one, just the no

data, but, you know, feelings forecast as

544

well, right?

545

So there's the combination of the two,

always does better.

546

Yeah.

547

Yeah.

548

Yeah.

549

Preaching, preaching to the choir here for

sure.

550

And actually, I think that's a good time

now in the episode to get a bit more

551

nerdy, if we can, because I've seen you,

so you've obviously worked extensively

552

with.

553

soccer analytics and you have an

interesting soccer power ratings and

554

projections on your website that I'm gonna

link to in the show notes but can you tell

555

us about it and what makes these

projections unique in your perspective in

556

evaluating team and player performance and

don't be afraid to dig into the nerdy

557

details because...

558

My audience definitely liked that.

559

Yes.

560

Sure.

561

I'll dig in.

562

So what's on my website is...

563

Sorry if you can hear my dog there.

564

What's on my website is perhaps the most

simple power ratings forecast that I've

565

ever done.

566

So I say that, not that it's like stupid

or anything.

567

So when I was at ESPN, I build power

ratings in American football, both

568

professional and collegiate, and

basketball, professional and collegiate.

569

and hockey, I mean, like almost every

sport, right?

570

So what's on my website, I'll explain the

model very simply is it's a Bayesian model

571

where you have an effect for each team,

right?

572

And the response variable is the expected

goals for each team.

573

So usually when we do a power ratings and

we're trying to estimate for a team, you

574

know, there's two sort of.

575

things that we're trying to estimate their

offensive ability and their defensive

576

ability and then you assume essentially

that their overall team ability, you know,

577

if it's a linear model, right is the

combination of their offense and their

578

defensive abilities.

579

Okay, so you so essentially in each match,

right?

580

You have essentially two rows of data

where you have the expected goals for the

581

one team and then the expected goals for

the other and the reason we use expected

582

goals, although I actually have

583

lot of issues with the expected goals.

584

They are a better indicator of how, how

good the team performed on offense than

585

just the raw number of goals.

586

And right.

587

I don't need to go into details, right?

588

It's essentially a, it's an expected value

as opposed to an observation from a

589

Poisson distribution, which soccer scores

roughly, roughly reflect a Poisson or

590

pretty close to a Poisson distribution,

right?

591

The expected goals is that expectation.

592

And so essentially I have a hierarchical

Bayesian model where I actually.

593

I actually do a few things.

594

So I actually assume the expected goals is

the mean of a Poisson distribution.

595

The observed goals is the actual outcome

of the Poisson distribution.

596

And then I fit a linear model essentially

where I look, okay, I have team A was on

597

offense, team B was the opponent.

598

And this was team A's expected goals.

599

And I'm essentially fitting a regression

model, right?

600

A Bayesian regression model where I have

individual team effects.

601

I have a prior on each team.

602

each team's offense and each team's

defense.

603

And that prior, you know, rough, I don't

have to get too crazy.

604

You know, I just use a normal distribution

and, and, you know, sometimes I actually,

605

when I code in Stan, I actually like

using, distribution was a little, a little

606

bit thicker tails.

607

But I think for this model, I was just

trying to go simple, normal distribution

608

prior with a mean, you know, for my

expected, essentially each team's expected

609

goals per game, on offense versus.

610

Defense right and the defensive value I

usually use I usually do the subtraction

611

So it's team the offensive team minus the

defensive team and that way The the

612

defensive team's value is is is higher if

they're a good defense So essentially if

613

team a's, you know expect the goals and

they in a game against an average opponent

614

is like 1 .5 and the defense was Average

expected goals in the game was you know

615

that they allowed was 1 .4

616

then you would say, the difference is like

0 .1, okay.

617

I also include effects for being at home

in this model.

618

I think, actually, I think that's all I

do.

619

But in other models I've done, you can

look at things such as how much rest

620

they've had since their last match.

621

You can look at the difference between

each team's rest.

622

And those are not linear effects, right?

623

You have to do some sort of nonlinear

effects for that, right?

624

Because like one day of rest is, two days

of rest is not,

625

Like the difference between two days of

rest and one day of rest is very different

626

than seven days versus eight days of rest,

right?

627

Seven and eight days of rest are pretty

much the same thing, but two and one is

628

very different, right?

629

Like much bigger effect for having two

days of rest than just one day of rest.

630

And so you can do things like that, or how

far away they had to travel, those sorts

631

of things.

632

Now in European soccer, that's not a huge

deal, because especially in the

633

competitions within each country, no team

is traveling that far.

634

But in American sports, it is a pretty big

deal.

635

Like, you know, you, you have to fly five,

six hours across the country on short

636

notice.

637

Like that can, that can really affect

performance.

638

and, and other things, like I said, I

don't have this in the soccer model, but

639

I, if anyone's interested in modeling

sports outcomes, that people typically

640

tend to overlook is the, I liked always a

big proponent of elevation, meaning that

641

if there are certain sports where there

are certain teams that play at higher

642

altitudes,

643

And if you're not used to playing at

higher altitudes, it's actually a very

644

noticeable effect in a model that you're

going to have a lower offensive output and

645

you'll actually allow more points on the

other end due to fatigue.

646

And so the United States, it's the teams

that are playing in Colorado and in Utah.

647

But in Europe, it could be the teams that

have to go to Switzerland or the teams

648

that have to go to some of these alpine

regions that are higher up in altitude.

649

In Mexico, if you have to go to Mexico

City, it's extremely high.

650

Or Colombia, right?

651

I mean, depending on what you're doing,

these are very high altitude places that

652

have shown to have a measurable impact on

an opponent's performance.

653

Yeah, that's very fun.

654

My God, I love those kind of models.

655

That's so much fun.

656

And I would also guess that, I mean, at

least my per would be that there is a

657

reverse mechanism also for teams who are

used to playing altitude.

658

Do they get a boost of performance when

they play closer to the C level?

659

Because they could have had adaptation

that make them better when they go to the

660

C level.

661

Yeah.

662

I mean, I think there's certainly science

behind that.

663

I found that is a lot harder to show in a

model than the reverse.

664

Not that it might not be there, but I

think the effect size, if it is there, is

665

definitely smaller than the reverse.

666

Yeah.

667

That's what...

668

That's what I would expect to like.

669

I think the effect is here mainly because,

well, I've seen it.

670

Like it seems to be pretty well seated in

the science literature, but that doesn't

671

mean the effect is big.

672

So yeah.

673

Yeah.

674

I mean, I'm a runner and I know that all

of the distance runners that are training

675

for marathons that are elites and

professionals, they all train at higher

676

altitudes, right?

677

For the...

678

six weeks leading up to a competition and

then they travel to the competition at a

679

lower altitude.

680

And, you know, they think they have an

oxygen performance boost due to that.

681

Yeah.

682

Yeah.

683

Kind of like legal oxygen doping, legal

blood doping.

684

Yeah.

685

Yeah, exactly.

686

Yeah.

687

Yeah.

688

I mean, I think it seems to be pretty much

proven.

689

I would say maybe it has more of an impact

on individual spots like marathon running

690

or else, because it's more like, you know,

it's just like,

691

Even if you're winning just a few tenths

of a second, well, it can help you have a

692

better time in the end because, well, at

this level, just having the smallest

693

increase in performance could be the

difference between first and second place.

694

But maybe that's harder to see such a

small effect on a collective spot, a

695

collective game because, well,

696

Maybe there are some...

697

Maybe it's just not an addition.

698

Maybe it's actually the effect cancel out.

699

So in the end, you don't really see a big

effect.

700

But that would be...

701

Yeah.

702

I'd love to do an experiment on that.

703

Like an RCT.

704

That would be so much fun.

705

Yeah.

706

Well, good luck trying to do experiments

in sports.

707

It's hard.

708

Yeah, I know.

709

I know.

710

But that...

711

I mean, if the multiverse exists...

712

Then there is a universe where we can do

that kind of experiments.

713

And my god, these scientists must have so

much fun.

714

And yeah, so thanks a lot, first, for

detailing the model that clearly and in so

715

much details.

716

That's super cool.

717

So the results of the model are in a cool

dashboard on your website.

718

Do you have the model and data available

freely, maybe on your GitHub, that we can

719

put in the show notes?

720

Yeah, I'm not sure.

721

I think my GitHub, I don't know if my

GitHub model is in the model.

722

It's on GitHub.

723

I don't know if it's private or not, but I

can let you know.

724

You know, I use actually open source data

for that.

725

So I, I, let me double check.

726

I can actually double check and get back

to you after the show on if, yeah, if I

727

could have it in my public GitHub or not.

728

So, yeah.

729

Yeah.

730

But essentially it uses the, there's a

package called world football R and.

731

It uses data from there to build the

model.

732

So some of that data is just from, it's

scraped from like transfer market.

733

so I use, I use, I didn't really talk

about how I set priors means for each of

734

the teams, but very, a very simple, very

simple, hierarchical model is essentially

735

just to use the expenditures of the club

and use that as a prior mean for how good

736

the club will be going into the season.

737

And, and.

738

Unlike some other sports in soccer, world

football, how much a club spends is very

739

highly correlated with how successful they

are, which makes sense, but it's not true

740

necessarily in like baseball.

741

So, do you see these effects of budget?

742

So, yeah, first, before I go on a follow

up question, yeah, for sure.

743

Get back to me after the show.

744

And if that's possible, we'll put that in

the show notes because I'm sure.

745

A lot of listeners will be interested in

checking that out.

746

I personally will be very interested in

checking that out, definitely.

747

So that'd be awesome.

748

And second, that effect of budget that you

see on the performance of a team.

749

And so I guess in football performance

mean number of expect expectation of games

750

won.

751

Do you see that on Curse?

752

Do you see?

753

that much of an effect also in a closed

league system like the MLS?

754

Or is that so because my prior would be

the effect of budget would be even

755

stronger in open leagues like we have in

Europe because it's like there is no

756

compensation mechanism, right?

757

Clubs can go down and usually in Europe

the strongest clubs are the historical

758

clubs.

759

or the new clubs are just the ones that

were lucky to be bought by very, very

760

healthy shareholders.

761

And like, there is not a lot of switching

of the hierarchy and changing of the

762

hierarchy, mainly because of budget, as

you were saying.

763

But I would think that maybe the effect of

budget is less strong in a closed league

764

like the MLS.

765

Is that true?

766

Is that something you see or is it

something that's still in the air?

767

Yes.

768

So I haven't looked specifically at the

MLS, but in general in American sports,

769

which all have closed leagues, the budget,

well, for various reasons, the budget

770

effects are not super strong.

771

So, you know, in American baseball, there

is no spending limit.

772

So in some American sports, like the NFL

and football, like there's a salary cap,

773

meaning you can't spend more than a

certain amount.

774

So there is no relationship between

overall spending and winning because

775

everyone has to spend a minimum and

there's a maximum.

776

In baseball, there is no limit.

777

There's a tax.

778

If you spend too much money, they do tax

you.

779

But there's still not a huge correlation.

780

And then in MLS, like I said, I'm not

entirely sure.

781

Most of the clubs, they are constrained

about how much they can spend.

782

And so there isn't as much variance also

in spending.

783

So like, you know, Messi going to Inter

Miami, it wasn't that Inter Miami could

784

pay him a lot of money.

785

They actually, you know, there's a couple

of exemptions that an MLS club could use

786

to pay an international player.

787

They have, they're called, you know, a

couple of exemption players they have.

788

And that's originally started when David

Beckham went to Los Angeles and they kind

789

of made that rule essentially just so he

could, they could afford paying him what

790

he was used to or close to what he was

used to being paid in Europe.

791

and, and the MLS is still kind of the

case.

792

You have one or two players you're allowed

to have on these exemptions and.

793

The way Messi was able to make it work is

he's getting paid from Apple for his

794

Apple's broadcasting the MLS games.

795

So they're paying him essentially to play

in the MLS because they're hoping, more

796

people are going to watch our broadcasts

are going to pay us.

797

And so we're going to give you a

percentage of that.

798

And that's where actually a lot of his

salary or like his earnings are coming

799

from is from a, a deal with Apple versus

the actual MLS club in Miami, which can

800

only pay him so much.

801

So my guess is, my prior is, I haven't

looked specifically at the MLS with this,

802

but my prior is yes, that there isn't a

huge relationship in the MLS between

803

winning and spending just because there's

not much of a variance.

804

In order to see those correlations, you

have to have a large enough variance in

805

the spending to notice the relationship,

right?

806

So.

807

Yeah, definitely interesting.

808

I mean, I love also looking at these, you

know, the...

809

how the structure of a league impacts the

show and the wins is extremely

810

interesting.

811

That can seem very nerdy and I think

that's my political science training that

812

kicks back here, but really how you

structure the game also makes the game

813

what it is and the results and the show

you're going to get.

814

I find that extremely interesting to see

how the American games, the US games are

815

structured.

816

Because ironically, it's a system where

there is much more social transfers, if

817

you want, like we have in Europe for

social security and health and education.

818

American sports are socialist, and

European sports are capitalist.

819

But typically, we consider Americans to be

more capitalist and the Europeans to be

820

more socialist.

821

So it's an interesting inversion.

822

Yeah.

823

No, definitely.

824

And I mean, I think...

825

Honestly, that's going to be interesting

in the coming years to see what's

826

happening on the European side because

there are more and more debates about

827

whether we should have a closed European

wide league, which would basically be an

828

extension of the current Champions League.

829

And honestly, I think it's going to take

that road because more and more

830

championship, at least all the

championship, I would say, for the

831

exception of the Premier League.

832

get more and more concentrated on just a

few clubs.

833

And just from time to time, you have one

club that bumps onto the top, like

834

Leverkusen this year in Germany, Monaco in

France a few years ago, Montpellier.

835

But that's like really exceptions.

836

And in the end, you almost always get the

same clubs that win all the time.

837

And so the idea of open leagues is not

really true for the top of the leagues.

838

It's definitely true for the bottom, but

the big clubs never go down.

839

And...

840

And so I think at some point, this

illusion of the open leagues is going to

841

disappear and probably we'll get a

European wide championship where like

842

basically the leagues are going to get a

bit more even because I think it's better

843

for the show and that's going to make more

money.

844

And in the end, I think that's what the

question is also.

845

Yeah, you might be right, but I hope, I

hope not.

846

I really, as an American, always have

dreamed of Americans doing relegation and

847

promotion just because...

848

You know, in America, we have this problem

where we call it tanking, right?

849

Because we have the socialist draft system

where if the worst teams are incentivized

850

to lose because they know they're not

going to win.

851

So they want to get the best possible

players in the draft the next season.

852

And so they're incentivized, you know, to,

to lose a little bit more.

853

And so that really does kind of, you know,

the promotion relegation is nice because

854

it solves that, you know, if you keep

losing, you lose a lot of money because

855

you get sent down.

856

so everyone's motivated even at the bottom

of each league to keep winning games,

857

right?

858

As much as possible.

859

Otherwise they lose a lot of money.

860

And in American leagues with the closed

system, it's like, well, Hey, you know,

861

it's actually, we talk about sick sickle.

862

He, and one thing that sports analytics

analytics have done is essentially say,

863

it's really hard to go from an American

sport being an average team to a really

864

good team.

865

And the reason is.

866

is the draft system.

867

So in the draft system, people are always

overconfident in how good the players are,

868

but there's really thick right tails of

how good a player can be.

869

So when you get a new player who's young

and you can draft them at the top of the

870

draft, they might not pan out, but they

also have a really thick right tail,

871

meaning that if they do pan out, you could

go from being one of the worst teams to

872

one of the best teams really quickly.

873

And so,

874

You know, it's this other analysis of

like, well, if you don't ever have an

875

option opportunity to draft someone in a

position where there's that right tail,

876

where, you know, once out of every five

years, you get a player who's transcends

877

everyone else that comes in, then you

can't move up from average to really good,

878

but you can go from being bad to really

good.

879

So often teams and the smarter teams, if

they're really good, they say really good.

880

But once they start noticing the players

are getting older, they just trade

881

everybody away.

882

They get rid of all their best players and

they just stink for a year or two and

883

hopefully they can get some good draft.

884

They get a lot of draft picks.

885

Essentially.

886

They try to trade their players away, get

more draft picks, and then it becomes a

887

sample size problem.

888

And it says, well, if we have more draft

picks, our probability of getting someone

889

on the right tail goes up.

890

And so that's all we're going to do is

we're just going to increase our odds of

891

getting that right tail player.

892

And if we get that player, then we'll be

good again.

893

Yeah.

894

Yeah.

895

It's like.

896

buying a lot of lottery tickets.

897

Yeah, that's what they're doing.

898

Yeah, now that's fascinating.

899

Yeah, I wasn't aware of these effects.

900

That's super interesting.

901

Because basically, what you're saying is

there is an incentive to be extreme,

902

basically.

903

Either you want to be among the top ones

or you want to be among the worst ones.

904

But being in the middle is the worst,

actually.

905

It is the worst.

906

Yeah.

907

Yeah.

908

That is extremely interesting.

909

And that's...

910

Yeah, I mean, I actually don't know which

system I prefer.

911

Honestly, I'm just saying I think Europe

is getting, is going there because we have

912

more and more basically concentration of

the wealth at the very top of the leagues

913

and that's going to make the national

leagues less and less interesting

914

basically.

915

But I don't know either if I prefer the

European wide championship.

916

Well, I think I would prefer European wide

championship.

917

for sure, but I think it would be great to

have it still open.

918

So where you could have, you know, like

basically countries would become regions

919

and then you get from like, if you, if

you're in the best in France, basically in

920

one year, then you get to the highest

level, which is the European one.

921

And then if you're among the worst, you

get down to your country the next year.

922

I think that would be very fun because

the, like, especially now that players can

923

be traded very easily between the, the...

924

continental Europe because it's basically

the same country legally.

925

That also makes sense that the teams, you

know, basically meeting PSG versus

926

Barcelona is much more tied than PSG

versus literally any team in France.

927

So yeah, that's going to be very

interesting.

928

But at the same time, I'm very, yeah, I

love hearing about the wrong incentives.

929

at the same time of the closed system.

930

So thanks a lot for that.

931

That's food for thought.

932

And that's again, like that's very close

to two elections, actually, like how you

933

count the votes impacts the winner.

934

And so here, like really in sports to how

you structure your game has an impact on

935

the winners.

936

And I think it's extremely important to

keep in mind because in the end, like how

937

the

938

the organization, so the MLS in the US or

the UEFA in Europe have actually huge

939

power over the game.

940

Well, thanks for that political science

parenthesis.

941

I wasn't expecting that, but that's

definitely super interesting.

942

To get back to the modeling because time

is running by and I definitely want to ask

943

you about the plus minus models because

you're using that also to...

944

estimate player value in American

football.

945

So I'm curious about that.

946

What is that kind of model?

947

Is that mainly for American football that

you're using that also for other sports?

948

Or if it's only for American football, why

is that particularly tailored to that

949

sport?

950

Yeah.

951

So plus minus models actually are

originated in basketball and they're, they

952

work the best in basketball.

953

They're not perfect.

954

And that sort of the concept in basketball

is you have 10 players on the court at

955

each.

956

at each moment and they substitute in and

out.

957

But while those 10 players are on the

court, you know how many points are scored

958

for each team, right?

959

So, you know, five players on the offense

side and five players on defensive side.

960

There's essentially just a big linear

model and you look at and you want to

961

adjust for how long they're on the court

or how many possessions they were on the

962

court for.

963

So you can say, okay, these 10 players are

on the court for two and a half minutes.

964

And in those two and a half minutes, this

team scored six points and their team

965

scored four points.

966

And essentially what you're doing then is

a plus minus model, essentially.

967

So sometimes you might see in a, in a

statistic after the game, like the total

968

difference in the net points for the team

when a player was on the court versus when

969

they're not.

970

Well, that's not too useful because

there's a lot of correlations, right?

971

You're playing with someone else a lot.

972

So what we call an adjusted plus minus

model, right, is a linear model that then

973

tries to fit those player effects of, you

know, you get a one when you're on the

974

court.

975

on offense and negative one year on

defense.

976

And we look at your team's efficiency,

right?

977

Your points divided by some denominator,

whether it's minutes or possessions.

978

Okay.

979

And that's sort of the basketball thing

over time.

980

They realized, okay, well, there's so much

correlation between who is playing

981

together.

982

We need to adjust for that.

983

So they used ridge regression.

984

And so that would divvy up the credit a

little bit better.

985

And you know, ridge regression is very

good at when there's

986

A lot of multicollinearity or correlation

between two effects, right?

987

And on the basketball team or all

basketball players, you have teammates

988

that play a lot together and they don't

play with other people a lot.

989

But Ridge Regression has done a decently

good job in basketball over a big sample

990

of estimating how effective players are.

991

And if you look at these things, you'll

see, we talked about the sniff test.

992

993

And he's the number one player for a lot

of the years, not so much anymore because

994

he's older, et cetera.

995

Right.

996

But that's sort of those sniff tests that

we get.

997

Well, some people in, in basketball and

I'm proponent of this, like, you know,

998

this is a Bayesian podcast is that ridge

regression, you know, for those unfamiliar

999

is, is a frequentist way to write a

Bayesian model.

That's very specific where you have a

normal prior on each player with a mean

zero.

Okay.

And that's ridge regression.

So we think about it from that perspective

with adjusted plus minus models.

What happens when you have a normal prior

with mean zero is that when you have

players that play less, we shrink more

towards the prior mean.

And it's only when we have more data for

players that we can deviate from that

prior mean.

Well, one thing we know about sports is if

you're not playing as much, that actually

is pretty useful information.

And what does that tell us?

You're not very good.

Because if you're good, you're going to

play more.

And if you're bad, you play less.

So other people have come around and, you

know, in the last 10, 15 years and said,

okay, well, instead of a ridge regression

model for basketball, we should do a

Bayesian regression model.

And instead of having a mean zero for a

player, we should have a mean of something

else.

So there's a few different versions that

people have done.

One thing, a very simple version is say

just everybody has a mean prior mean of,

you know, what we call a replacement

player.

Okay.

Someone that doesn't play very much.

If you're really good and you play a lot.

It doesn't matter what the prior mean is

too much because the data is going to

overwhelm the prior.

But if you don't play very much, we're

going to stick with that sort of negative

prior mean because it means you're below

average.

And so that's one thing you can do.

A more sophisticated thing sometimes

people will do is they'll build a

hierarchical model where you have

essentially a, a prior mean that is based

on other statistics that we observe.

So how many points you score or how many

assists you have.

And those that's called a box, a box score

prior mean or a box score plus minus.

So that's sort of the basketball.

So we gave you the what plus minus models.

So that's sort of the basketball approach.

Now.

Basketball is really nice because you have

lots of games in the NBA.

You play every team at least twice and you

substitute a lot and there's lots of

scoring.

Now my work in American football tried to

address a lot of these issues in American

football.

You don't play every team.

you don't substitute very much.

And if you do play, you only play with

certain people like all the time.

And then there's not a lot of scoring

compared to basketball.

There's some scoring, but you know,

there's, you know, American football point

scoring is unique, right?

You get six or seven points for a

touchdown, you get three points for a

field goal, you know, and then on more

rare occasions, you get these two point

safeties.

Yeah.

So there's roughly maybe 10 scoring events

in an American football game versus in

basketball where you have, you know, a

hundred to a hundred.

So there's, you know, about each two to

three points, each one there's, you know,

80 to 120 scoring events in a basketball

game.

Right.

So these models work a lot better.

My work in American football has been to

sort of, how do we take the basketball

model and make some modifications so we

can do a football model?

And so one of the things that is tricky in

football is.

that certain positions never get

substituted out.

So on offense, the quarterback plays every

single play unless they're hurt or they

stink.

So they get benched.

Well, the quarterback also always plays

with the same offensive line as long as

they're healthy and they don't get

substituted out.

So how does a model separate credit when

the same players are on the field all the

time?

And so my work in that was sort of to use

Bayesian statistics and take the...

the Bayesian regression model where we had

a prior mean, I used some information to

inform the prior mean for each player, but

I also did this unique thing where I

shrink.

So the prior variance is a function and is

actually, there's one prior variance for

all players and then it's multiplied by

another parameter, which is unique for the

position that they play.

And so quarterbacks have a different

shrinkage parameter, essentially, or prior

variance than.

a different position.

And then instead of just looking at

scoring plays in football, we have what we

call is expected points added.

So at each play, we look at on average,

how many points are you going to score if

you have the ball in this position?

And I look at the difference between two

plays, right?

And that tells you essentially how much

value you got in the result of the play.

So instead of using every scoring play, I

just use every single play in football.

And I do this unique shrinkage.

dependent on position and doing that, and

it's a huge model.

So I did this in college football, which

has way too many parameters because

there's like 16 ,000 kids.

But even in the NFL, I've done this and

you get interesting results.

Sometimes they match up with what you

think, sometimes they don't.

But the interesting thing is you can

actually estimate how much you should

shrink each position.

And so actually the model is nice because

it essentially tells you how much of the

variance in the outcome of the play.

is dependent on how good players are

across different positions.

So in football, we all know that

quarterbacks are the most impactful

position in the game.

And I did give somewhat subjective priors,

but not with, I still left a lot of

uncertainty around and the model very well

could see and estimate that quarterbacks

are in fact the most important position

because you shrink them the less they have

the largest variance.

So.

You could look at that.

If you look at the most impactful players

in football, it should be a quarterback.

But in the same measure, the worst players

in football are also quarterbacks because

in order to negatively hurt your team, you

can only hurt your team really a lot.

If you're a quarterback compared to other

positions, I mean, every position you can

hurt your team, but no one can hurt a team

as much as a bad quarterback hurts their

team.

Just like a good quarterback can help

their team better.

So that's sort of like a kind of rough

overview of, of my plus minus modeling in

football.

I think I do have, when I wrote the paper,

I have a version of that written in Stan.

The data set itself was not public, but I

did have a version of the Stan model

written and uploaded on my GitHub that you

can look at.

It's pretty massive.

In recent years, I've tried to expand it

and to do a state space model type

version.

So I have effects for each player for each

season over time.

Yeah, that was exactly what I meant.

Computationally, that gets a little bit

trickier.

And my dataset, actually, I was able to

scrape some data for that.

And then actually, I can't anymore.

The NFL just stopped releasing that.

So that work is on hold for now.

But I probably need to find a graduate

student that can help me finish it.

Yeah, definitely we should put that in the

show notes.

That's super interesting.

Your paper in the...

and the link to the GitHub repo.

That's for sure.

And that makes me think a recent episode I

did, and also a recent interest of mine, I

started contributing to that package

called Baseflow, where that's precisely

that could be useful in your case here,

because your model structure doesn't

change.

If I understand correctly, because well,

once you have the model structure, it's

kind of like a physics model.

It's not going to change when you have new

data, but the data sets do change.

So you have new data sets coming in.

And so that's where probably using these

kind of inference that's called amortized

Bayesian inference could be extremely

useful because you would basically, if the

bottle, the computational bottleneck would

just happen once.

That would be when you train the deep

neural network.

to learn the posterior structure and

parameters.

So instead of MCMC, you're using the deep

neural network to learn the posterior.

But then once you have trained the deep

neural network, then it's like doing

posterior inference is trivial.

And so for that kind of models where you

have a lot of data, but the model is the

same.

That's a very good use case for amortized

Bayesian inference.

So that could be something very

interesting here.

Yeah.

Yeah.

Yeah.

Yeah.

Happy to tell you more about that

afterwards if you're interested.

But yeah, I've started digging into that,

and that's super fun for sure.

So yeah, and I think this is a cool use

case.

Awesome.

Well, I still have a few questions, but

can I?

We are getting short on time, so can I

keep you a bit longer?

Yeah, just a few more minutes.

Sure.

Yeah.

Okay.

Awesome.

Yeah.