Speaker: 00:00:02

Today I am joined by Jacob.

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Buffa, the senior director of performance science and player development for the Houston

Astros.

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Growing up with a deep -rooted passion for sports in St.

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Louis, Missouri, Jacob's journey from aspiring baseball player at Missouri State

University to leading player development and performance science is nothing short of

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inspiring.

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Jacob discusses the critical role of nutrition and conditioning in athlete development,

emphasizing the innovative

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of education and visual communication tools to help athletes understand how their dietary

choices impact performance.

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He also explains how Bayesian stats play a pivotal role in analyzing player performance

and managing injury risks, and delves into how complex concepts like Bayesian analysis are

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communicated effectively to coaches and players,

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they understand the uncertainties and limitations of the models used.

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Finally, Jacob and I discuss emerging trends in baseball science, such as biomechanical

analysis and the application of computer vision algorithms.

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This is Learning Basics Statistics, episode 114, recorded June 20, 2024.

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Welcome Bayesian Statistics, a podcast about Bayesian inference, the methods, the

projects, and the people who make it possible.

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I'm your host, Alex Andorra.

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You can follow me on Twitter at alex -underscore -andorra.

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like the country.

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For any info about the show, learnbasedats .com is Laplace to be.

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Show notes, becoming a corporate sponsor, unlocking Bayesian Merge, supporting the show on

Patreon, everything is in there.

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That's learnbasedats .com.

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If you're interested in one -on -one mentorship, online courses, or statistical

consulting, feel free to reach out and book a call at topmate .io slash alex underscore

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and dora.

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See you around, folks.

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and best patient wishes to you all.

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And if today's discussion sparked ideas for your business, well, our team at PIMC Labs can

help bring them to life.

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Check us out at pimc -labs .com.

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Hello my dear fans, I'm coming to you with fantastic news because Learn Based Ads is going

live.

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We're indeed going to have the two first live shows of Learn Based Ads history.

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It's going to happen very soon in Stankham 2024 in Oxford, UK.

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We're going to have two panel discussions.

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We're going to kick things off amazingly on September 10 with Charles Margossian, Steve

Bronder and Brian Ward.

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talking about the past, present and future of Stan.

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And then on September 11, Elizaveta Semenova and Chris Wyman are gonna make science look

really cool because we're gonna talk about how Bayesian stats are used in the very

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important field of computational biology.

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So if that sounds like fun, if you wanna ask us embarrassing questions, if you wanna meet

us in person, if you wanna have exclusive LBS stickers, well, get your StanCon tickets now

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and...

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Honestly, I can't wait to meet you all on September 10 and 11.

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See you very soon, my dear patients.

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Jacob Buffa, welcome to Learning Bayesian Statistics.

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Hey Alex, how are you doing?

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I am doing very well, thank you so much for being on the show Jacob.

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So as I said in the introduction, you work for the Houston Astros, which I'm sure the

American listeners know about for non -baseball listeners.

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Houston Astros is a big MLB...

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team so baseball and thanks a lot actually to JJ Robbie for putting us in contact.

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JJ was here on the show damn a few years ago.

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I don't even remember the number of the episode but for people curious about what JJ is

doing at the Astros he was not at the Astros at the time but you'll get an idea of what

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he's doing he's doing absolutely tremendous job.

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in the R &D department.

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So yeah, I referred to that episode.

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I put in the show notes the link to the sports analytics playlist.

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And I'm sure if you're into sports, that's going to be worth your time.

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But today we have Jacob with us and I'm having you on the show because you're doing a lot

of different things and your background is actually super interesting.

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So yeah, maybe

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Tell us what you're doing nowadays, but mainly how you ended up working on these because I

know your path is marked by a passion for baseball, sure, but it was still a bit senior in

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random.

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So I love that.

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Yeah.

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So currently I serve as the senior director of player development and performance science

for the Houston Astros.

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My path to here was definitely unique.

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I played baseball in high school and then actually went to Missouri State University for

baseball as well, but wound up very quickly realizing that I was much smarter than I was

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good at baseball.

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so wound up actually pursuing an interest in just overall human performance.

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I was very passionate about

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basically, you know, training to be bigger, faster, stronger.

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so, you know, wound up spending a lot of time around the strength and conditioning staff

there, you know, wound up doing some, some internships and really learning as much as I

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could actually outside of school.

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You know, I chose my, my degree is actually marketing and then wound up adding economics

in there.

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But

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was never really big on learning like inside the classroom.

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It was just something that was not a passion of mine.

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So through college, you know, was able to gain a lot of knowledge around just general

kinesiology, strength and conditioning principles.

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And actually, I think it was like my junior year, I was approached by a friend of mine

named Denton McRomey, who was like, hey, man, like,

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we should start a gym, you know, after college, like that's what we should do.

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And actually at first I was like, you're crazy, like starting a business, like that's, I

don't know how to do that.

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But he kind of talked me into it.

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And so that's, you know, after graduating in 2016, moved back to St.

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Louis, Missouri.

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And, you know, we had some connections.

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We played baseball together in high school.

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He went off to play at Rockhurst, but we had some connections in the St.

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Louis area with

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baseball teams and we wound up leveraging those to be able to start training some kids and

got a building and basically kind of step by step, you know, figured out, you how to do

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it, how to run the business.

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And one of the things that we did that turned out to be relatively unique there was, you

know, I was very, we were very passionate about identifying what underlying physical

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qualities we, you know, were truly being impacted.

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to help improve on field performance.

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Because deadlifting more or squatting more is definitely important, but there's not

necessarily like a causal relationship to throwing five miles an hour harder.

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But there are certain first principles that we're trying to impact.

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So this is where I started to learn a lot about force plate research and just general

linear physics.

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And we purchased a set of force plates ourselves.

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started jumping athletes, really diving into the movement signatures, the force velocity

profiling.

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And we started testing guys' bat speed, their throwing velocity, and just started keeping

all this information with players.

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And over the course of a couple years, know, wound up, you know, being able to have some

research around why we do what we do, and we're really enjoying it.

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And then the Houston Astros in 2019 opened up a job called a performance coach.

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And this was traditionally what baseball would call a fourth coach or a development coach,

which coaches first base, know, maybe coaches defense and base running.

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But this role, they actually expanded to help in performance science.

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So the Astros were actually the first organization to have a sports scientist in baseball.

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So they were very passionate about this.

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part of this role was helping to do the sports science testing, helping to do the workload

monitoring, a lot of the grunt work, quite frankly, but it was definitely insights into

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multiple departments.

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it was something that I, given I never had actually a formal degree in kinesiology or

anything like that, I actually felt like this was my first shot.

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to actually work professionally or work for someone, work for an organization or in sport.

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So I applied and wound up getting the job actually.

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I actually remember Bill Fricke, Pete Petilla and Jose Fernandez were the three who I

interviewed with and who wound up hiring me and I'm forever grateful to all three of them

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for taking a chance on me because my resume was nothing spectacular.

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And so I wound up doing that for 2019.

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In 2020, they actually are after that season, they offered me a position as a sports

science analyst.

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So I accepted that role, moved down to West Palm Beach with my wife, where the spring

training complex is, and was a sports science analyst for two years.

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And then in 2022, you know, the Astros decided that they wanted to make a bigger

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more formal investment in biomechanics and sports science.

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So they started a performance science department and they asked me to be the director and

build it out.

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So I was very grateful for that opportunity.

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In 2022 and 2023, I was the director of performance science, building out that team and

trying to get that research off the ground.

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then just this past year, at the end of the year, they

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as to expand my responsibilities again to oversee player development.

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So that is the long story of how I wound up where I'm at.

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Yeah, I love it.

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I love it.

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It's absolutely, absolutely fantastic.

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that's also why I wanted to have you on the show.

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Because as you were saying, also you did quite a lot of weightlifting, which I am

personally very interested about.

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I do that very amateurly in my local gym.

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But something I discovered when digging into the science of weightlifting is

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And that was surprising to me because like, I didn't know anything about that before doing

that myself, diving into the science of it and basically conducting small RCTs on me at

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the gym and, know, coming up with my own macro cycles and so on.

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So something I was really, really surprised by is by the importance of nutrition.

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actually, you know, because when you're like, when you start a training like that, you're

like, yeah, the training is like 90 % of the results, right.

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But actually, I discovered nutrition is extremely important and is an integral part of the

training program.

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So I'm also curious if that's the case in sports teams.

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like baseball and then like, yeah, basically how do you apply that kind of knowledge that

we have from a much more controlled sport like weightlifting?

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How does that help you in your job today?

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Yeah, that's a really good question.

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absolutely, like nutrition plays a huge role in, I think all professional sport, but

definitely within our organization, we do take it very seriously.

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And yeah, I think that there are, you interesting parallels, you you talked about

weightlifting specifically, you know, I did spend probably three, three, four years

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competitively weightlifting.

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And, you know, like one example of something that is, it's just a staple in weightlifting

is you have to make a weight class.

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And so, you know, one of things that you have to do is you have to be able to manipulate

your body weight to essentially be

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the lowest body weight that you can possibly be while like lifting the most weight that

you can possibly lift.

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And, you you have weigh ins at a certain time and, you know, so you wind up needing to

basically weigh in at a certain time and then understanding this is what I need to eat and

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when to be able to, you know, lift at my fullest capacity, you know, over X number of

hours later.

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And while the exact scenario is

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significantly different than baseball, right?

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There's no weight classes or anything like that.

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The general principle of being able to understand essentially, you know, what your body

needs to perform at its highest level and how long that takes to get in your system and

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get out of your system is extremely valuable, right?

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And so, you know, on like something like that, that is certainly applicable is, you know,

even something as simple as like caffeine intake.

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You know, we play night games and so we know how important sleep is for overall

performance.

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And it could be very easy for someone to take extreme amounts of caffeine before the game,

you know, because they don't know how long it takes for caffeine to actually get through

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their system.

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And so they wind up actually it not being that useful, you know, for the first portion of

the game.

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And then they wind up basically not being able to sleep for several hours post game.

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So I think even basic principles like that, understanding what to put in your body and

when is extremely impactful.

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Yeah.

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Yeah.

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That's a very good example.

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I'm actually very curious.

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How do you follow that?

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Because like, you cannot be behind the players all the time, right?

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So here you have to also rely, I guess, own professional, professional character of the

player.

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So I'm guessing there is variation on that.

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How do you guys handle that?

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Because, yeah, in the end, we know about that stuff, but also there is a lot of personal

variation, not only as you were saying on caffeine intake and the timing, but also effect

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of caffeine on people.

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I'm personally very sensitive to caffeine.

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So that's cool because it wakes me up in the morning.

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But definitely I know that if I take caffeine after more or less 12 p I'm gonna have

troubles at night.

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I'm wondering how, yeah, how do you implement that stuff once, like how do you implement

the science on the players?

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Yeah, you know, I'm not gonna lie and say that we have it down perfectly or that all of

our players, you know, follow

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everything to a T.

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We largely rely on education.

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And I think that that's something that resonates with me.

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you know, I think for anyone that has kids, it's not significantly different in that you

can tell them the right thing over and over and over again, but until they believe it

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themselves, they may not do it.

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And so, yeah, to your point, we don't have oversight over these guys.

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all the time, nor do we want to have to.

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So the best thing that we can do is essentially educate them on why it's important for

their performance, why it's important for their careers, and trying to distill complex

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science into very simple but impactful infographics and try and communicate things

visually and essentially get them to believe and understand that if they want to improve

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their performance.

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this is something that they should do.

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And definitely when players do that, you can definitely see it because they take ownership

over their careers and we definitely see changes on the field as well.

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Okay, yeah, I see.

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That must be super interesting.

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So you basically get the players somewhere together and you go through the application of

the science.

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I don't know, like today is about caffeine, tomorrow is about sleep, and next week is

going to be about meal timing, stuff like that.

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Is that how that works?

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Yeah, essentially.

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You know, we have the draft coming up here, July 14th to the 16th, and that's a great

example of like after the draft, we have an onboarding process for all of our players.

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And so they will learn about the Astros' philosophies.

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In many areas, they'll learn about what our hitting philosophy is.

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They'll learn about what our defensive philosophy is.

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They'll learn about what our strength and conditioning philosophy is.

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And one of the things that they'll learn about is our nutrition philosophy.

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And it's definitely on the education side.

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It's why are carbs important?

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Why are fats important?

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Why is protein important?

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How much of that should you intake?

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What are the proper sources?

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And ultimately, you know, we always try and tie it back to on -field performance, you

know.

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So, you know, for example, you know, we can educate players that if, you know, if you're

playing in the field, know, carbs are important for essentially like high bouts of energy,

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right?

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And if you, one of the key performance indicators of basically being a good defender in

the outfield is how fast you can run.

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and how much ground you can cover.

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if multiple balls hit you, can you do that multiple times?

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And so, it's a non -trivial thing to be able to fuel your body correctly for maximum

effort sprints multiple times over several hours.

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And so, if we can tie it back to basically what they value, I think it has a better chance

of landing.

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Okay, yeah, that's definitely super interesting.

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I love that.

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And yeah, that...

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Also, personally, that timing of things is, I can see very interesting.

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You have also to understand, know, like there are definitely some moments of the days of

the day where I'm more efficient at the gym than like I'm definitely much more efficient

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in the morning than in that at night.

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Right.

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So I never now I almost never train at night or the evening if I don't have to.

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And I much rather do that in the morning.

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Also, because I have the caffeine.

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boost, you know, some like, and going to the gym after a full day of work is just like,

that's hard.

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You know, I much prefer go for a walk, or something like that.

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But definitely something I resonated with, and that's like, that's very anecdotal.

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But you're saying that there are some late night games, right?

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And so you have to take your caffeine at the right moment so that it

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gives you the boost for the game, but at the same time doesn't disturb your sleep.

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So it's a completely different field.

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But I do some stand up from time to time.

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And stand up shows are at night.

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And so I actually have the same issue.

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I I came up with that, that timing stuff, like very nerdy caffeine timing the other day,

just before a show because I wanted to have that but I knew if I if I

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took my caffeine too late, I would have like I would not sleep for instance, before like

three or 4am which happened to me before.

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So like that that made me that made me laugh when you talked about that because I was

like, well, not only you know, high sports professional have that issue.

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So thank you so much, Jacob for for all the work you do.

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And that's that's actually useful to much, much more people than you thought.

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That's good to know.

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You see?

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Well, that's actually the same issue.

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I mean, for any people who have to do some stuff at night where they need to be alert, I

guess that will be useful to them.

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Now, I'm curious also about what you do, the kind of work you do for analyzing player

performance and injury risk, because I know these two topics are extremely important for a

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professional sports team.

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I'm wondering how Bayesian stats are applied here and how they can be helpful.

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Yeah, I think that there's a significant way that just the overall Bayesian framework is

applied.

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And I think if we think about the components of professional sports, being successful in

professional sports, some of them being skill acquisition, cognitive processing, in -game

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strategy, and then obviously kinesiology.

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you know, injury risk.

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Kinesiology is probably the most publicly researched area, you know, of all of them.

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If anyone wants some answers, it's easiest, you know, to Google how to make a player

bigger, faster, stronger, or, and you'll get dozens of research articles that are

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applicable, which, you know, in my area means that

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we can leverage that information as priors and then be able to apply our observations from

our population to both improve the resolution of the insights that we glean from the data

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that we have, but also to be able to infer maybe where our specific processes or our

specific population might differ from the research population.

247

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Okay, okay, I see.

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That's in what's the what would you say is the state of the science on these on on these

fronts?

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My are we somewhat confident?

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Or is that something that's really at the frontier and that's evolving almost every year?

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I think that there there are aspects of it that we are very confident in.

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And there are aspects of it that are definitely evolving.

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So an example of aspects that we are confident in is like we are very confident in how

specific musculature and their functions apply to injuries and human performance.

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Very confident in the static state.

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You know, I think that we are one area that we that the research is improving in is

understanding maybe how these function in a

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in a dynamic state.

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And an example of that would be, know, it's maybe easy to take a look at hamstring

strength, right, and player's hamstring strength and then track that over a season and

258

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see, okay, who hurts their hamstring more or less, right?

259

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But it's, you know, there are certainly aspects to like sprint mechanics, that impact

that.

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that maybe are less obvious because there's not quite as much quantifiable information on

it right now.

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It also requires essentially getting more nuance and understanding what is the muscle

doing at the time of injury.

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And given that injuries are relatively sparse in nature when compared to non -injured

instances, that type of information is tough to come by.

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But there are definitely people doing good work and trying to understand how

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coordination fits into injury mitigation.

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So that's one area that we're improving.

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But I do think it's very good and we're very confident in overall, how does musculature

impact injury risk?

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Okay.

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What is a question or topic in particular in that realm that you'd love to see answered in

the coming month?

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that you're really curious about.

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Well, I guess, you know, don't know if this is specific enough.

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It's definitely not in the coming months.

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But you know, one thing that like we are always pursuing in the baseball industry is one

of the things that is most important to a pitcher being successful on the field is how

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hard they throw.

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That's, that's like pretty common.

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The harder you throw, generally, the better the results are going to be.

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However, we also know from

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external research that how hard you throw is pretty much the driving factor to whether or

not you're going to get hurt.

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You you put more torque on the elbow and more strain and that winds up essentially

escalating your injury risk a ton.

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And so like one of the things that I think we've been trying to look at is

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tendon and ligament adaptations and trying to understand, can we periodize workload of a

pitcher to be able to maximize their in -season performance and mitigate their injury

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risk?

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Because ultimately, the answer of throw the ball slower is not gonna work.

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I think baseball has tried to take the approach of

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just throw less overall and injuries continue to increase.

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So, you know, I think that there's, I don't know the answer to the question.

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I don't think external research will get to it.

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Hopefully, you know, we're able to get to it internally.

288

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Yeah.

289

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Yeah.

290

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I guess that's, that would be quite, be quite interesting, I'm guessing.

291

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And what about the, so I guess you talked a bit, a bit about that right now, but what do

you,

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See like how to Bayesian models help in predicting the impact of training loads on the

athletes Well -being and performance in general like not only injury.

293

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Yeah You know, I think when it comes to training loads, you know, we we know that there

are broad truths About how stress, you know impacts the human body

294

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We also know that there are nuances around how specific people or players adapt to

stresses.

295

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So we can essentially use those broad truths to overcome sparse data where we may not have

a whole lot of information on any specific player.

296

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But we do have a few observations.

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And then if we combine that with something like a multi -level model where we can

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then really glean some robust insights where maybe robust data actually doesn't exist.

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I see.

300

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Yeah.

301

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Yeah, for sure.

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I mean, that's definitely where, where hierarchical models would definitely be super

helpful.

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Like if you can relate the different, the different positions and the different players

and the different population of players, definitely super powerful.

304

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And what about the, so what you do also some, like you also work on, on

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athlete conditioning, right?

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And you, you, you do that, like you use the science of that to improve the training of the

players that right?

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Yes.

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Yeah.

309

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Okay.

310

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So how do you use how do you use, like, how do you do that?

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And how do you use Bayesian approaches here?

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Yeah.

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Good question.

314

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So I mean, I think it's not unrelated to the last answer that I gave, but one of the

limitations of overall injury prevention is the amount of data that can be collected.

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We only have so many players that come through our system in any given year or even

through a couple of years.

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And then we only have so many samples even within a given player.

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And especially on an injured population, right?

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The injured population is significantly less than the healthy population to the point

where, you know, if you have one or two players who maybe got injured with what looks like

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healthy data, you know, it can be difficult to discern.

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you know, even we go back to leveraging previous research, you know, I think

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If we take the example, stick with hamstring strength and hamstring injuries.

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If we have hamstring strength information on players, we can absolutely take information

from research and say, we believe within a certain degree of certainty that this is what a

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healthy hamstring signature or force profile would actually look like.

324

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And we can play around with how confident we are in that.

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you know, to basically see what gets us closest to the actual outcomes.

326

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And then that allows us to, you know, obviously be more confident in what we're looking

at.

327

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Yeah, yeah, that makes sense.

328

00:32:20,333 --> 00:32:27,595

That, I mean, that sounds pretty challenging, but that does make sense.

329

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So from all that you're seeing here, really something I can see is that, yes, if you look

at the

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You know, like one question in particular, the data can be limited.

331

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But if you look at the overall amount of data, and definitely in comparison to other

sports, baseball is quite rich in data.

332

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Because you have inputs from game statistics, you have player tracking systems, have

physiological data, you have a lot of these sources, how, so how do you integrate these

333

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diverse data sources to then provide interesting insights?

334

00:33:14,694 --> 00:33:28,841

Yeah, I think it, from my perspective or just my opinion on it, I think it starts by

layering the data properly, which I think to me means understanding what level of

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information is important depending on the question being asked or what level of

information do we need to start with.

336

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And so, for example, if we want to know, let's say how we can make someone a better

outfielder, right?

337

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First, we jump right to, well, what's their reactive strength index from the force plates

and, the reactive strength index is low, hamstring strength is low, I think we're going to

338

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lose a lot of people, right?

339

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There's not going to be a whole lot of people that will immediately make that connection

and say,

340

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yeah, that makes sense.

341

00:34:05,490 --> 00:34:07,892

We fixed that, he'll be a better outfielder.

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But if we start with maybe asking the question, how many runs is this player worth as a

defender?

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How many runs has he saved as a defender?

344

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Which may come from our ball tracking data, right?

345

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That may come from understanding which balls were hit to them, were hit to him.

346

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How many other defenders would have actually made that play on average?

347

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Something simple like that.

348

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you know, then we can maybe work backwards to the next level of information and say, well,

it looks like maybe he doesn't catch quite as many balls as the average outfielder because

349

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he's not as fast.

350

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Like he's slower than average as well.

351

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And we know that the amount of ground that you can cover is certainly important.

352

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Then I think you can make the next step to the physiological data and say, he's like,

doesn't produce a whole lot of force and he's not super strong.

353

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So now,

354

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people start to actually link the two and say, okay, now I can see how improving his

hamstring strength and his force production qualities makes him a better outfielder.

355

00:35:12,973 --> 00:35:14,444

Okay, yeah, that's fascinating.

356

00:35:14,444 --> 00:35:20,756

it's like, yeah, different hints basically that you're picking up from the data.

357

00:35:20,756 --> 00:35:28,159

Yeah, yeah, essentially, and making sure that basically each one is applied at the right

time.

358

00:35:28,460 --> 00:35:32,001

Yeah, yeah, And well, I think that's...

359

00:35:32,339 --> 00:35:42,415

And a question I have that's related to that also is then what what do you think are the

most significant challenges that you face?

360

00:35:42,415 --> 00:35:53,901

Not only you, but the whole, you know, science team that which are these challenges that

you face when you're applying patient stats in baseball science?

361

00:35:53,901 --> 00:35:56,562

And how do you address them?

362

00:35:58,023 --> 00:35:59,464

really good question.

363

00:35:59,464 --> 00:36:02,425

I mean, actually, I, I think that

364

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The largest challenge is actually getting people that are extremely familiar with Bayesian

methods and fluent in Bayesian methods.

365

00:36:14,629 --> 00:36:23,675

And I would not consider myself a Bayesian expert by any means.

366

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And the field of sports science doesn't teach this.

367

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It's very limited in the statistical methods.

368

00:36:32,513 --> 00:36:33,674

that it actually teaches.

369

00:36:33,674 --> 00:36:46,558

so I actually think one of the, I guess maybe another tangent, like it's related, is

people in the field of sports science tend to be very tied to what previous research,

370

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methods that previous research have done, right?

371

00:36:48,671 --> 00:36:54,657

So they'll come in and they'll say, I want to do project X and...

372

00:36:54,657 --> 00:36:58,059

this paper, these two papers were written on this project and they did it this way.

373

00:36:58,059 --> 00:36:59,991

So this is exactly how I want to do it.

374

00:36:59,991 --> 00:37:02,743

These are the statistical methods that were used.

375

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And a lot of times these papers are written by very, very intelligent strength

conditioning coaches or, you know, exercise physiologists, but they're, they're very,

376

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they're not written by people with strong stats backgrounds.

377

00:37:17,713 --> 00:37:24,557

So I think getting people in the field that are actually familiar with this type of

approach.

378

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is the largest obstacle.

379

00:37:26,947 --> 00:37:37,313

But I do think once we get people with that skill set, there's actually very few barriers

to it, just given, I think, two things.

380

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The first one being the amount of tools that are available to use Bayesian methods across

both Python and R with very simple syntax and are computationally fast has expanded

381

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tremendously.

382

00:37:54,091 --> 00:37:58,143

you know, just over the last six or seven years since I've been paying attention.

383

00:37:59,704 --> 00:38:07,808

And I also think that how we communicate, how we communicate Bayesian stats generally

aligns with how people think.

384

00:38:07,808 --> 00:38:12,241

People know that there are uncertainties around every decision that is made.

385

00:38:12,241 --> 00:38:16,593

And we know that some uncertainties are wider than others.

386

00:38:16,593 --> 00:38:23,356

And depending on our risk tolerance, you know, that may factor in more so than just a

single point estimate.

387

00:38:24,157 --> 00:38:30,481

And so I do think that overall, communicating them, I think that's actually one of the

strengths of Bayesian approaches.

388

00:38:30,481 --> 00:38:30,942

Okay.

389

00:38:30,942 --> 00:38:31,882

I see.

390

00:38:31,882 --> 00:38:33,433

Yeah, that's very interesting.

391

00:38:33,433 --> 00:38:49,374

it's like, it's a mix of like not only the data and the availability of those, and also,

guess, the importance of having at least a part of the organization focused on that, but

392

00:38:49,374 --> 00:38:53,429

it's also a technical side in the sense that

393

00:38:53,429 --> 00:39:07,211

You definitely need people who are able to work on these with these kind of methods that

you're using a lot and Bayesian stats are definitely a very important part of that

394

00:39:07,211 --> 00:39:07,721

workflow.

395

00:39:07,721 --> 00:39:09,443

Yeah, yeah, absolutely.

396

00:39:09,443 --> 00:39:10,024

Yeah.

397

00:39:10,024 --> 00:39:21,073

And actually how, like, because you have to communicate, as you were saying, your findings

and the results of your models to a lot of different stakeholders.

398

00:39:21,073 --> 00:39:22,694

So how do you do that?

399

00:39:22,694 --> 00:39:26,455

I know from experience that it can be challenging.

400

00:39:26,455 --> 00:39:39,741

So how do you communicate these complex statistical concepts like those from Bayesian

analysis to coaches and players to ensure that they are effectively utilized?

401

00:39:39,821 --> 00:39:45,924

Yeah, that's a non -trivial task as well.

402

00:39:45,924 --> 00:39:49,125

I do think one of the things that we try and do is

403

00:39:49,931 --> 00:39:53,763

we do communicate it in different ways to different groups of people, right?

404

00:39:53,763 --> 00:40:07,568

I think when talking with JJ's group and R &D, we're actually gonna wanna be as technical

as possible because we actually want their input on the methods and they're gonna wanna

405

00:40:07,568 --> 00:40:14,071

know, I trust these results based off of the process?

406

00:40:14,311 --> 00:40:18,213

If I'm communicating with a coach or a scout,

407

00:40:19,241 --> 00:40:20,883

they don't care about that, right?

408

00:40:20,883 --> 00:40:33,333

If I'm communicating with them, it's actually more so like one of the general approaches

that we take is, we distill the information that we have down to as few dimensions as

409

00:40:33,333 --> 00:40:33,884

possible?

410

00:40:33,884 --> 00:40:46,645

So, oftentimes what that looks like is maybe at most three or four dimensions where

obviously if we're relaying it in a graph, we have our X, Y axis and then maybe it's

411

00:40:46,977 --> 00:40:52,450

you know, gradiented with a specific color and faceted by different positions, right?

412

00:40:52,450 --> 00:41:07,028

So, you know, for example, if we're trying to communicate injury risk of a elbow injury

risk of a pitcher, you know, we might take a look at, we might take a look at the, you

413

00:41:07,028 --> 00:41:15,681

know, x axis being shoulder strength, the y axis maybe being lower body strength or

something like that, it may be gradiented out.

414

00:41:15,681 --> 00:41:20,604

by injury risk or probability and it may be faceted by how hard you throw.

415

00:41:20,744 --> 00:41:30,949

So that way, we can communicate four different variables, but very, very simply put and

hopefully easy to distill down.

416

00:41:31,930 --> 00:41:32,991

see.

417

00:41:32,991 --> 00:41:43,557

And what do you, in your experience, what are the most common challenges of consumers of

these models?

418

00:41:43,713 --> 00:41:49,077

be players, be coaches, be people from the business side.

419

00:41:49,478 --> 00:41:56,143

What do you see as the main difficulties and what would you recommend?

420

00:41:56,203 --> 00:42:01,527

What would you your advice to listeners who have to do the same at the work?

421

00:42:02,068 --> 00:42:13,587

Maybe not for coaches and players, but for other stakeholders who are not part of the

model building team, but have to use the models.

422

00:42:13,587 --> 00:42:15,037

in their own work?

423

00:42:16,878 --> 00:42:23,940

Yeah, so I think that there are two obstacles and they're actually kind of probably

competing obstacles.

424

00:42:24,420 --> 00:42:30,722

I mean, the first one is, you know, we want to be as concise, as quick as possible, right?

425

00:42:32,222 --> 00:42:39,674

We don't want to say, okay, you know, look at this visual, then this visual, then this

visual, then this visual to make your decision, right?

426

00:42:39,674 --> 00:42:43,063

If we can encompass it all in a single visual or

427

00:42:43,063 --> 00:42:47,035

you know, a single pillar of philosophy, that's what's going to resonate.

428

00:42:47,035 --> 00:42:53,181

Otherwise, you know, they may forget or if it gets too complex, they may not even try and

use it.

429

00:42:53,482 --> 00:43:06,432

The second obstacle is actually, you know, related to that is when we do that, I think we

run the risk of glossing through or like smoothing through a lot of information, maybe

430

00:43:06,432 --> 00:43:12,197

meaningful information and maybe nuanced, but nuanced cases do come up, right?

431

00:43:12,393 --> 00:43:19,318

And so we don't want to overgeneralize in an effort to simplify too much.

432

00:43:19,898 --> 00:43:31,206

so, you know, like one of the things that we have tried to do, and I'm not saying that we

are great at it, so maybe other people have better approaches, but we have tried to keep

433

00:43:31,206 --> 00:43:40,933

the information or the philosophy or the tagline as simple as possible, but then try and

highlight, you know, these scenarios.

434

00:43:40,991 --> 00:43:50,887

maybe possible scenarios where it's worth, if the results don't look intuitive to you, ask

a question.

435

00:43:50,968 --> 00:43:58,713

And we just try and highlight where these possible scenarios could go wrong, where

certainly we want people to actually think through it.

436

00:43:58,713 --> 00:44:08,130

And if they see a result that says, I don't think this is right, this doesn't make any

sense to me, as an expert in their field, just ask the question, or please just don't take

437

00:44:08,130 --> 00:44:10,341

these at face value all the time.

438

00:44:10,719 --> 00:44:12,400

Hmm, yeah, definitely.

439

00:44:12,400 --> 00:44:14,793

think it's something very useful.

440

00:44:14,793 --> 00:44:23,780

So in my experience, making sure to communicate not only what the model can do, but also

and maybe most importantly, what it cannot do.

441

00:44:23,901 --> 00:44:31,607

And that way, that will mitigate a lot of these issues of over or under confidence in the

model.

442

00:44:31,607 --> 00:44:38,613

Because I mean, we definitely as humans and it's well documented in the science that

443

00:44:38,867 --> 00:44:49,160

And humans have a different way of handling uncertainty around algorithm decisions, right?

444

00:44:49,160 --> 00:45:05,904

We tolerate much more the fact that a human is gonna underperform and be wrong in a

special case, but algorithms, when they are wrong in just one instance, then people will

445

00:45:05,904 --> 00:45:08,149

lose trust extremely fast.

446

00:45:08,149 --> 00:45:09,530

in the algorithm.

447

00:45:10,611 --> 00:45:26,572

yeah, I can think it's something to be very careful of when we communicate our model

because well, people will be way more, will be way harsher on the model than on a scout,

448

00:45:26,572 --> 00:45:27,843

for instance, right?

449

00:45:27,843 --> 00:45:37,729

A scout can be wrong much many more times than a model for recruiting players can be

because of that.

450

00:45:37,729 --> 00:45:39,380

bias that humans have.

451

00:45:39,380 --> 00:45:48,815

So I think it's very important to communicate that as you were saying, and also to

communicate that the model is not just a machine.

452

00:45:48,815 --> 00:45:50,956

The model is made by humans.

453

00:45:52,077 --> 00:45:54,278

be a bit kinder to it, Yeah.

454

00:45:54,658 --> 00:45:55,738

Yeah.

455

00:45:55,819 --> 00:46:01,662

I I think a good example of that, least for us, you put it well, communicating what the

model can't do.

456

00:46:02,182 --> 00:46:07,245

For us, that's actually our injury risk models, I think,

457

00:46:07,745 --> 00:46:18,328

for a lot in that category where like, you know, if we were to actually communicate, if we

actually communicated the exact probabilities that the model outputs of someone getting

458

00:46:18,328 --> 00:46:25,070

hurt, it's almost always going to say that the odds are they don't get hurt because those

are the true odds, right?

459

00:46:25,070 --> 00:46:30,311

That at any given time, if someone goes out there and plays, the odds are that they won't

get hurt.

460

00:46:31,152 --> 00:46:36,033

And so then, you know, we can communicate that like this, model that we're using is,

461

00:46:36,493 --> 00:46:42,133

not necessarily to make the prediction whether or not that this player is going to get

hurt.

462

00:46:42,153 --> 00:46:52,973

It's to infer what physical qualities or what features are actually important that we can

impact that lead to more or less risk.

463

00:46:52,973 --> 00:46:58,193

And so maybe it's less about is this player at 45 % risk or 35 % risk.

464

00:46:58,193 --> 00:47:06,053

It's more about what do we deem as important that would put that player at more or less

risk and then is that worth it?

465

00:47:06,241 --> 00:47:06,681

Yeah.

466

00:47:06,681 --> 00:47:06,992

Yeah.

467

00:47:06,992 --> 00:47:13,947

So basically communicating all the uncertainties around the decision to make.

468

00:47:13,947 --> 00:47:14,337

Nice.

469

00:47:14,337 --> 00:47:14,717

Yeah.

470

00:47:14,717 --> 00:47:15,077

Cool.

471

00:47:15,077 --> 00:47:22,713

Well, I think I've already asked you about a lot of that, like very precise, you know,

science questions.

472

00:47:22,713 --> 00:47:28,808

So maybe now to play us out a bit more looking towards the future.

473

00:47:28,808 --> 00:47:33,881

Are there any emerging trends?

474

00:47:33,889 --> 00:47:44,637

that you see in baseball science that you believe will significantly impact how teams

manage training and performance in the near future.

475

00:47:45,738 --> 00:47:55,706

And yeah, are there also some breakthroughs that you would really want to see?

476

00:47:55,706 --> 00:47:56,327

Yes.

477

00:47:56,327 --> 00:47:58,908

So actually, as far as future,

478

00:47:59,681 --> 00:48:04,423

you know, I guess, more or less like innovations in this field.

479

00:48:04,584 --> 00:48:13,939

One of the things that makes me very excited about my role is I actually do believe like

performance science in general fits into that category.

480

00:48:13,939 --> 00:48:19,152

And I guess more specifically as it relates to biomechanical information.

481

00:48:19,152 --> 00:48:24,364

So like we've talked a lot about just general kinesiology and physiology in this

conversation.

482

00:48:24,364 --> 00:48:29,617

you know, the last I think was three or four years ago, you

483

00:48:29,653 --> 00:48:37,346

Major League Baseball rolled out Hawkeye information, which is tracking the individual

joints of every single player.

484

00:48:37,346 --> 00:48:47,680

And that is where a lot of injury research comes from, especially in baseball field around

the torque of the elbow and things like that.

485

00:48:48,141 --> 00:48:54,303

So I do believe, like I, I'm very excited at that data set.

486

00:48:54,303 --> 00:48:58,589

And I believe that that's where, that's where the arms race.

487

00:48:58,589 --> 00:49:03,272

is in baseball is who can leverage that information the best.

488

00:49:03,973 --> 00:49:12,799

As far as breakthroughs that I'm hoping for, I don't know, maybe I could probably change

my answer if you would like me to change it.

489

00:49:12,799 --> 00:49:26,769

But I actually think that not necessarily on the research side, but the quality of the

computer vision algorithms and the player, the tracking, I'm hoping that

490

00:49:27,281 --> 00:49:35,486

breakthroughs occur there and maybe even more specifically the speed at which those

algorithms or those models are processed.

491

00:49:35,486 --> 00:49:38,188

And I guess that's for two reasons.

492

00:49:38,188 --> 00:49:52,976

First of all, when we're talking about elbow torque, the difference of one inch of the

wrist placement is exponentially more in degrees, which is exponentially more in force or

493

00:49:52,976 --> 00:49:53,396

torque.

494

00:49:53,396 --> 00:49:55,017

And so

495

00:49:55,093 --> 00:50:00,375

if a model misses by an inch, that's significant.

496

00:50:00,636 --> 00:50:03,877

And that's a very high standard for a computer vision model.

497

00:50:03,877 --> 00:50:05,798

It's a high standard for the human eye.

498

00:50:07,039 --> 00:50:14,332

But ultimately, if you want to get the most precise information possible, that's where I

think some of the innovation will come from.

499

00:50:14,332 --> 00:50:20,585

And then in a practice setting, there's a lot of research around

500

00:50:21,221 --> 00:50:31,017

feedback loops and skill acquisition and basically being able to provide a target and then

just providing that player with feedback of whether or not they hit that target and how

501

00:50:31,017 --> 00:50:32,147

far they were.

502

00:50:33,428 --> 00:50:45,965

And just given the complexity of the computer vision models and the size and the compute

power, those results, those biomechanical results don't come back for an hour or two,

503

00:50:45,965 --> 00:50:48,957

which is fast, but it's not, you

504

00:50:49,289 --> 00:50:51,590

we could use it inside of a minute, right?

505

00:50:51,590 --> 00:50:55,552

To really get to apply it in a practice setting.

506

00:50:55,552 --> 00:51:06,857

And so, yeah, those are maybe not specific kinesiology or physiology innovations, but I'm

hoping that somebody can figure that out in the next several years.

507

00:51:06,857 --> 00:51:08,927

Yeah, mean, yeah, for sure.

508

00:51:08,927 --> 00:51:13,239

That's like, I agree, that sounds absolutely amazing.

509

00:51:13,519 --> 00:51:17,281

So listeners, you've heard Jacob like...

510

00:51:18,145 --> 00:51:24,347

get going on that if you're if you're a fan of computer vision algorithms in baseball.

511

00:51:24,628 --> 00:51:27,569

Definitely that would be used by the Astros.

512

00:51:27,589 --> 00:51:30,530

And I'm guessing a lot of other teams.

513

00:51:30,850 --> 00:51:31,891

Yeah, that's super cool.

514

00:51:31,891 --> 00:51:33,311

I completely agree.

515

00:51:33,311 --> 00:51:39,674

And, well, I think that's that's the show, Jacob.

516

00:51:39,674 --> 00:51:45,416

I mean, that's I think we've already covered a lot of topics.

517

00:51:45,917 --> 00:51:47,487

Before we close up,

518

00:51:47,733 --> 00:51:51,754

I have the last two questions I ask everybody, of course, at the end of the show.

519

00:51:51,754 --> 00:52:00,486

But is there a topic you would have liked to mention but I failed to ask you about?

520

00:52:01,797 --> 00:52:05,548

I actually think that we covered it.

521

00:52:05,548 --> 00:52:12,830

mean, these are probably my three favorite topics of baseball, human performance, and

maybe statistical methods.

522

00:52:12,830 --> 00:52:15,660

So I think we hit on it all.

523

00:52:16,361 --> 00:52:17,687

Well, I'm glad.

524

00:52:17,687 --> 00:52:19,058

to hear that.

525

00:52:19,420 --> 00:52:21,863

So then, let's play a sandwich.

526

00:52:21,863 --> 00:52:28,413

First question, if you had unlimited time and resources, which problem would you try to

solve?

527

00:52:28,413 --> 00:52:29,714

Yeah, I...

528

00:52:30,796 --> 00:52:34,471

Is this specific to my field or just in general?

529

00:52:36,395 --> 00:52:37,865

Now, Justin Shanerl.

530

00:53:05,239 --> 00:53:07,730

Yeah, at a limited time and resources, I'd probably dive into that.

531

00:53:07,730 --> 00:53:23,289

But then more specifically, like in my field, I would absolutely love to be able to solve

the elbow injury risk with pitchers.

532

00:53:23,289 --> 00:53:27,761

I think it's something that is just an extremely complex problem.

533

00:53:27,761 --> 00:53:30,522

And I very much enjoy complex problems.

534

00:53:30,623 --> 00:53:35,157

And there's an extremely high return on investment.

535

00:53:35,157 --> 00:53:38,048

I think for someone I can help with that.

536

00:53:38,048 --> 00:53:46,190

Yeah, I mean, I'm really impressed at because the players play such an amount of games per

year.

537

00:53:46,190 --> 00:53:48,240

It's absolutely incredible.

538

00:53:49,241 --> 00:53:55,703

Me, like honestly, my I was anchored with European sports teams.

539

00:53:55,743 --> 00:53:58,413

So like in football, they play.

540

00:53:58,413 --> 00:54:04,205

I mean, soccer, they will play like on tops.

541

00:54:04,205 --> 00:54:10,945

let's say 50, 60 games per season, rugby is less.

542

00:54:11,605 --> 00:54:30,125

So like, yeah, when I started working in baseball and I saw the number of games that these

guys play per year at such a high level, I'm honestly surprised that they don't get

543

00:54:30,125 --> 00:54:32,105

injured more often.

544

00:54:33,107 --> 00:54:44,192

And yeah, like I understand why you're saying the elbow injury because like, yeah, that

was one of my first, that was one of my first questions when I started looking today.

545

00:54:44,192 --> 00:54:51,465

It was like, damn, but the pitchers must throw, I don't know how many thousand balls in

each season.

546

00:54:51,465 --> 00:54:54,926

And that's not even counting the training.

547

00:54:54,926 --> 00:55:02,169

So the amount of joint pain and risk that you have with that is absolutely incredible.

548

00:55:02,509 --> 00:55:06,989

I really don't know how they don't get injured more often, to be honest.

549

00:55:07,169 --> 00:55:08,469

Yeah, I agree.

550

00:55:08,469 --> 00:55:11,769

What they do and what they go through is impressive.

551

00:55:12,189 --> 00:55:16,289

Yeah, 162, that's a lot of games.

552

00:55:17,249 --> 00:55:18,249

damn.

553

00:55:18,468 --> 00:55:31,329

And is that actually, so maybe last question before the very last question, do you see

any, like is the pitcher position really the one that's the most at risk for injury or is

554

00:55:31,329 --> 00:55:32,435

that pretty much

555

00:55:32,435 --> 00:55:39,027

will widespread across the positions or do you have some positions that are much more

prone to injury?

556

00:55:39,027 --> 00:55:45,078

No, mean, it's pretty centralized at the pitcher position.

557

00:55:45,078 --> 00:55:58,792

There are definitely injury risks all over the field, but in terms of the biggest, mean,

the injury risk on the mound is exponentially higher than any other injury.

558

00:55:58,792 --> 00:56:01,413

I think if we look at the

559

00:56:01,975 --> 00:56:09,449

the game of baseball, the throwing motion is probably the only one that like truly pushes

the limits of the human body.

560

00:56:09,909 --> 00:56:16,433

know, sprinting, you know, no offense to any of my baseball players, love you guys, but

they're not the fastest in the world.

561

00:56:16,433 --> 00:56:19,194

You know, they're not pushing that barrier.

562

00:56:19,575 --> 00:56:28,139

They're not the strongest, you know, in the world, but that right or left arm and the

delivery is moving, you the fastest in the world.

563

00:56:28,139 --> 00:56:32,001

And so I think that's the one that pushes the boundaries the most.

564

00:56:32,001 --> 00:56:32,682

Yeah.

565

00:56:32,682 --> 00:56:33,072

Okay.

566

00:56:33,072 --> 00:56:33,612

Interesting.

567

00:56:33,612 --> 00:56:33,982

Yeah.

568

00:56:33,982 --> 00:56:40,327

I mean, I'm not, I'm not surprised, but that's, that's good to, to, to hear say that.

569

00:56:40,327 --> 00:56:40,657

Yeah.

570

00:56:40,657 --> 00:56:47,162

I mean, the, you amount of pitches they have, they have to make is just like, can't, I

can't believe that.

571

00:56:47,162 --> 00:56:49,473

It's just, it's just absolutely incredible.

572

00:56:49,794 --> 00:56:54,877

and also like, if you have any baseball players listening to that episode, well done.

573

00:56:54,897 --> 00:56:57,679

that's like, that's impressive.

574

00:56:57,679 --> 00:57:00,781

Like, you let me know if you have some.

575

00:57:00,811 --> 00:57:03,603

Houston Astros players listening to that episode.

576

00:57:03,603 --> 00:57:05,755

That's like great publicity.

577

00:57:05,755 --> 00:57:10,449

We need to like, you know, advertise that and then on the social media.

578

00:57:11,850 --> 00:57:12,521

It's like that.

579

00:57:12,521 --> 00:57:14,732

That'd be quite amazing.

580

00:57:16,995 --> 00:57:29,409

actually, you know, do you have do we have any study about then pitchers who retire and

how their joints age?

581

00:57:29,409 --> 00:57:39,998

Because I know for US football, for instance, that can be quite a big, they can still be

at a high injury risk even after their professional career.

582

00:57:39,998 --> 00:57:41,979

Is that the case also in baseball?

583

00:57:41,979 --> 00:57:44,241

Or do we not know about that?

584

00:57:44,261 --> 00:57:45,502

You know, that's a good question.

585

00:57:45,502 --> 00:57:47,704

I'm not gonna say that there's not research.

586

00:57:47,704 --> 00:57:50,366

haven't, know, there could be something that I'm not aware of.

587

00:57:50,366 --> 00:57:55,150

But I haven't read personally, you know, any, any research on it.

588

00:57:55,150 --> 00:57:58,313

So, yeah, I'm not aware of any.

589

00:57:58,313 --> 00:57:59,233

Okay, yeah.

590

00:57:59,233 --> 00:58:01,754

Yeah, I'd be interested in that.

591

00:58:01,874 --> 00:58:06,755

If anybody in the audience knows about that, let us know.

592

00:58:08,195 --> 00:58:11,976

And well, finally, last question for you, Jacob.

593

00:58:12,457 --> 00:58:19,998

If you could have dinner with any great scientific mind, dead, alive, or fictional, who

would it be?

594

00:58:20,099 --> 00:58:20,979

man.

595

00:58:22,099 --> 00:58:24,940

You know, I'm to go with fictional.

596

00:58:24,940 --> 00:58:29,077

And I'm going to go with Tony Stark as Iron Man.

597

00:58:29,077 --> 00:58:32,419

I'm a big fan of the Marvel movies.

598

00:58:32,719 --> 00:58:36,421

And so I think he's the one that I'd like to have dinner with.

599

00:58:37,002 --> 00:58:38,663

That's a great answer.

600

00:58:38,663 --> 00:58:41,044

I have never had that one on the show.

601

00:58:41,044 --> 00:58:43,046

So yeah, you're the first one.

602

00:58:43,046 --> 00:58:44,486

But I understand.

603

00:58:44,687 --> 00:58:51,100

That's definitely my favorite of all the Marvel superheroes.

604

00:58:51,100 --> 00:58:53,451

So yeah, I love that.

605

00:58:54,412 --> 00:58:55,755

Yeah, that would

606

00:58:55,755 --> 00:58:56,755

Definitely be super cool.

607

00:58:56,755 --> 00:59:01,667

Would you ask him if you can fly the iron suit?

608

00:59:01,867 --> 00:59:02,787

Definitely.

609

00:59:02,787 --> 00:59:05,608

And I'd hope that he would say no, but I would have to ask.

610

00:59:05,608 --> 00:59:07,608

Yeah, I mean, yeah, for sure.

611

00:59:07,909 --> 00:59:09,649

Yeah, I would definitely ask.

612

00:59:09,649 --> 00:59:14,391

Like you should probably also ask if you could play baseball with the iron suit.

613

00:59:14,391 --> 00:59:16,201

That'd be probably super fun.

614

00:59:16,201 --> 00:59:20,272

Yeah, that might be my only chance to make it professionally.

615

00:59:20,272 --> 00:59:23,371

Yeah, mean, with the iron suit.

616

00:59:23,371 --> 00:59:25,982

You must throw pretty fast.

617

00:59:25,982 --> 00:59:29,923

you like you should think about that, Jacob.

618

00:59:29,963 --> 00:59:32,403

That would mitigate injury risk a lot.

619

00:59:33,644 --> 00:59:35,984

Yeah, probably.

620

00:59:37,445 --> 00:59:41,506

Well, on that note, I think it's the perfect time to close.

621

00:59:41,506 --> 00:59:44,287

So thank you so much, Jacob.

622

00:59:44,287 --> 00:59:47,388

That was a pleasure to have you on the show.

623

00:59:47,388 --> 00:59:50,609

Thanks again, JJ, for putting us in contact.

624

00:59:50,669 --> 00:59:51,809

As usual.

625

00:59:51,937 --> 01:00:05,556

We'll add links to your website and socials and any resource that you think is interesting

for listeners who want to dig deeper and start learning about baseball science, sports

626

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science in general, and baseball analytics.

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Thanks again, Jacob, for taking the time and being on this show.

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Thank you very much, Alex.

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I really enjoyed it.

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This has been another episode of Learning Bayesian Statistics.

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Be sure to rate, review, and follow the show on your favorite podcatcher, and visit

learnbaystats .com for more resources about today's topics, as well as access to more

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episodes to help you reach true Bayesian state of mind.

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That's learnbaystats .com.

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01:00:40,346 --> 01:00:45,210

Our theme music is Good Bayesian by Baba Brinkman, fit MC Lars and Megharen.

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01:00:45,210 --> 01:00:48,352

Check out his awesome work at bababrinkman .com.

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I'm your host.

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01:00:49,557 --> 01:00:50,518

Alex and Dora.

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01:00:50,518 --> 01:00:54,741

can follow me on Twitter at Alex underscore and Dora like the country.

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You can support the show and unlock exclusive benefits by visiting Patreon .com slash

LearnBasedDance.

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Thank you so much for listening and for your support.

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You're truly a good Bayesian change your predictions after taking information and if

you're thinking I'll be less than amazing.

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Let's adjust those expectations.

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Let me show you how to be a good Bayesian Change calculations after taking fresh data in

Those predictions that your brain is making Let's get them on a solid foundation