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The Math Behind Sports Rankings and Golf Analytics

May 07, 2026 / 01:08:01

This episode of Wharton Moneyball features discussions on sports analytics, golf rankings, and the impact of strokes gained. Guests include Mark Brody, a professor at Columbia Business School and creator of the strokes gained concept.

Mark Brody shares insights on college golf rankings, explaining how they determine which teams qualify for regionals and nationals. He discusses the challenges of ranking systems and the biases that can arise, particularly for teams from different regions.

The conversation also touches on the World Golf Rankings, with Brody explaining the differences between predictive models and those that reward past performance. He highlights the importance of fairness in ranking systems and the adjustments made to improve accuracy.

In the second half, the hosts and Brody discuss various sports topics, including the impact of analytics on tournament design and player performance. They explore the use of AI in sports analytics and the complexities of ranking systems.

The episode concludes with reflections on the evolving landscape of sports analytics and the significance of Brody's contributions to the field.

TLDR

Mark Brody discusses golf rankings, strokes gained, and sports analytics in this episode of Wharton Moneyball.

Episode

1:08:01
00:00:00
Welcome, welcome to Wharton Moneyball. Welcome to a full hour of sports analytics
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here on the Wharton Podcast Network. This is Cade Massey hosting this week at the moment with my longtime friend and collaborator,
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Eric Bradlow. Shane Jensen is out this week, sadly, tragically, but Audie Weiner will join us just a
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little bit late. Audie is in transit at the moment. Some combination, as you guys know, some combination
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of us are here almost every week of the year and have been for more than 12 years now talking sports analytics with you
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guys. We are going to run our usual format this week. We're gonna run a guest in the first
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half hour and then we'll do open lines. In the second half hour, me, Audie, and
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Eric will kick around a few things. I am piped in from Austin, Texas. Eric is from Huntsman Hall, West Philly, on
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campus. Mark, I'm assuming it's New York. I don't know that for a fact.
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Mark Brody is our guest in the first half of the show. He is a longtime friend of the show
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and we're always delighted to get time with you. Mark, thanks for making time for us.
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Thanks for having me. And yes, I'm in New York, New York, and looking out over the Hudson River, which
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you can't see in my background because it's the way I'm looking, not behind me.
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Right. Mark, as some of you guys know, is at Columbia, the Columbia Business School there in
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New York. He is the Carson Family Professor of Business there. He came out of the quant finance world,
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but he is best known in the sports analytics world for his contributions to golf.
00:01:27
He flat out invented the concept of strokes gained, which is just kind of ridiculous.
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It's one of the great sports analytics stories of our lifetime and continues to be engaged
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in the sport at multiple levels. He has a great book, Every Shot Counts. We'd strongly recommend his book, Every Shot Counts.
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He consults to professional golfers and he has been involved with revising the ranking systems of
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various associations, including the World Golf Ranking System, which is like the biggie, but also NCAA
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ranking system. So something we wanna talk about at some point with Mark is that, that's a fun
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topic for us. But maybe we'll start, Mark, with just, this is kind of, in some ways, peak golf
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season. We're a few weeks post-masters, we're a week before the PGA, which is gonna be
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in the Philly area. The majors are all lined up now, one a month, which is fun these days.
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What is on your mind, what is on your docket right now in the world of golf? Well, I would say that I don't really
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follow golf as closely as some fans do, certainly not as closely as Rufus Peabody does.
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But I look at more kind of longer -term problems and actually my day-to-day stuff recently has been with college golf rankings
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and professional disc golf rankings. And this is the ranking season for college golf because, like the March Madness basketball tournament,
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the main use of college rankings, besides bragging rights throughout the year, is determining which teams
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go to regionals. And that's run by the NCAA. And then from regionals, you go to the
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nationals and then you crown the national champion. So it wasn't clear to me how this
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ecosystem worked until getting into the rankings, but the colleges, universities themselves choose their schedule and
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teams run their events. And it's kind of in coordination with the NCAA, but the NCAA isn't running all of
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these events. So we're keeping track of all that's going on and then ranking the teams throughout the
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year. And then at this point in the year, then the qualifiers for regionals are set.
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So there's some interesting problems there in the rankings. There's some interesting problems also, which is more
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operations research, I guess, than sports analytics, which is how do you assign the teams that
00:04:01
you have selected into the six regions? Okay. So that comes up in many sports, but
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I was involved in it this year in golf. This sounds like a ball, frankly. Let me say, interesting that you mentioned Rufus
00:04:18
at the top there. I happen to know that Rufus and Mark occasionally play golf in the New York area.
00:04:23
So these guys are friends. But yeah, Rufus, not a trivial part of his living is made watching golf, paying attention
00:04:31
to golf very closely. But one of the first things we ever did together when he was shortly after he
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was at Yale, the Yale women's golf coach at the time asked us if we could help develop a ranking system for women's golf,
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because they felt they were disadvantaged being in the Northeast, playing different tournaments, playing a different
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time of year. They thought whoever the cabal was in Oklahoma that ran the college golf rankings, maybe they're
00:04:58
still the cabal. Maybe you're in with the cabal now, Mark. I don't know.
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But that coach was not happy with it. And we dabbled a little bit. It was good fun.
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But I could imagine that's great fun to get into. It is absolutely great fun.
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And I would argue that the previous rankings did appear to be biased in certain ways
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that if you played a stronger schedule, that you would be ranked higher for an equal
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level of performance. But that requires some analytics in order to prove that. Right.
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So I've heard a lot from coaches, but then when I develop this new ranking system,
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which has been in place for, this is the third year, I then hear questions from coaches.
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And I realized that just because people are criticizing the ranking system, doesn't mean they're right.
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You really need to go into the analysis to figure out back then, was Penn, was it biased against teams in the Northeast or
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not, just because... And that's another thing that's almost as important
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as the analytics is being able to convey the underlying rationale and to communicate why it's
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fair and to convince people that it is fair. Because I don't know how many times coaches
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have come up with the question to me, we have beaten this other team twice in the season.
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By that means they played in the same event and they finished higher in the final
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leaderboard. We've beaten them twice, therefore we should be ranked higher than them, but we're not.
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Your system is messed up. And so it's like, well, how do you answer that question?
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And the most direct way I could find to answer that question was to show cycles.
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So I found in the data, just looking at wins and losses, team A has beat team B two or three times.
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Team B has beat team C two or three times. And if you argue that A has to be ranked better than B and B should
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be ranked better than C, then A should be ranked better than C, but C beat A two or three times total.
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And then you realize you can't use that logic. It's completely impossible to have a ranking system
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that would satisfy that criterion. Right, so I think it's the NFL that by some point in the season every year,
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the circle's complete, that everybody has beat somebody and transitive property takes us all the way
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around. Eric has a question. So I just want to say real quickly, Eric, you don't know, like you probably don't
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quite understand that he's hinting at the greatest playoff tournament format in sports, you know, the
00:07:37
one I get fired up about every May and June, the college golf tournament. Mark, I don't know if you've heard me
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rant, every year I make the guys pay attention because they play this, you know, three
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or four or five rounds of stroke play to identify the 16 or whatever it is, teams that play match.
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And it's just fricking brilliant in my opinion, but let's leave it there for now.
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Eric wants to jump in with a question. No, I just had a clarification question, Mark.
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Are the rankings, like literally it's a deterministic function on who qualifies based on the rankings
00:08:09
or it's used like in college football, like it's an input to some subjective committee.
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It's a clarification question. I'm just asking which one is it? It's more the latter.
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It's an input, not a rule, but in practice, more of the divisions follow the ranking
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exactly than don't, but where it comes up is usually in borderline cases, when you draw
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the line and you take a look at the teams right around that line and somebody will make an argument.
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And I think it could be a valid argument that the rankings aren't perfect. And there might be some reason to take
00:08:48
the team that's ranked one out rather than one in, you know, across the line.
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But also when you do that, then the committee that makes the ultimate decision needs to
00:09:00
justify it because it's the team that got kicked out that was inside the bubble is
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like, oh, well, you better have a good reason for not letting us get in. But I assume Mark that the distribution of
00:09:11
team, let's call them strengths or rankings is what we classically see that there's greater separation
00:09:17
out in the right tail, but that right near the cut score, there tends to be bunching.
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And therefore there's a significant number of teams that could argue, I should be above the
00:09:27
cut line or not. I assume that that follows for rankings as well. I think it happens in just about every
00:09:33
stat that I've looked at, including rankings. So you're exactly right there.
00:09:38
Mark, let's talk about, well, first one more thing on the college thing. You said it's interesting how they assign them
00:09:43
to regions. Yes. And you said this is kind of an OR question, but what are the considerations?
00:09:48
So you said there's six regions. What are the considerations? Yeah. So once you decide on the 72 teams
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and it's not in rank order because the conference champions get in. So Columbia women got in this year because
00:10:03
they won the Ivy league championship. And so conference champions get a free pass
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into the regionals. And when they're not ranked in the top 72, that means there's teams that are ranked
00:10:18
higher that get in place of other teams. But once you have the 72 teams, the six regional hosts, the six locations have been
00:10:27
determined years in advance. So now the question is, how do you put those 72 teams and assign them to
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six regions? And the multiple- Why don't we listen to, we're all math people here.
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Is there an objective function, literally a mathematical objective function that's maximized by that assignment?
00:10:47
Except it's an OR problem, there has to be an objective function, right? Well, the problem is there's three or four
00:10:52
objectives. Good, good. And the question is, how do you weight them? But by far the number one objective is
00:11:00
to make sure that the top six seeds, the top six ranked teams, which would be the number one seeds in each region have
00:11:09
the easiest and an equal shot of getting through. In other words, you wanna make sure there's
00:11:15
regional balance. You don't wanna put a bunch of strong teams in one region and a bunch of
00:11:20
weak teams in another. So the number one criteria is so that the number one seeds have the best chance
00:11:27
and a nearly equal chance of getting through and the same with the two seeds and
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three, four, five seeds. And even, so that's one objective, sort of this regional balance in terms of strength of
00:11:39
each region. The other that I found out that they care about is they don't want one region
00:11:46
to be overloaded with a bunch of teams from one conference. So it seems like it's a repeat of
00:11:51
a conference championship and they have to duke it out somehow. Somebody is gonna get left out just because
00:11:57
they happen to be in the same region as same conference. Well, Mark, let me ask you a question.
00:12:01
If I gave you the 72 teams, suppose we all agree, I'm not saying we're agreeing
00:12:07
on what those teams are, but I give you the list of 72 teams. Would you write down the criterion?
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Like you just mentioned, the top team should have the easiest path. We don't want too many teams in the
00:12:18
same. Would some algorithm now just pump out those 72 broken into the six or would there
00:12:26
still be subjectivity there? So yes, actually to both because the last one is travel.
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So I put that in as an objective, but it's less important than I had thought
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it would be. But I put it into an optimization problem and it will spit out an assignment.
00:12:44
And then they will look at that assignment in more detail and find reasons for doing
00:12:50
swaps. And because there are many, many assignments of these 72 to six regions that are nearly
00:13:00
comparable, this to me is a way of choosing among many good alternatives, but the algorithmic
00:13:08
viewpoint gets you to a really good starting place, which is very hard to do manually,
00:13:13
which is what they were doing before. So what the standard practice is called the
00:13:19
S-curve, which is teams one through six go into these regions and seven goes where
00:13:25
the six and then you go around. Right, right, right. So we made the algorithm so that it
00:13:34
starts with the S-curve and then when it does swaps, it preserves seeds so that only two seeds are swapped or three seeds
00:13:42
are swapped or four seeds. So in some sense, the S-curve isn't completely blown apart, which again would be harder
00:13:50
to justify or explain. This is a great example of man-machine collaboration and set the board with the algorithm
00:13:58
and then tweak as you need to tweak, but you're going to do so much better as a baseline if it's set with, look,
00:14:04
it's not Mark Brody deciding what the weights are. You had a long consultation about what those
00:14:09
weights were before you ran the optimization. Adi Weiner has joined the show and he
00:14:13
has a question from his office on a campus at University of Pennsylvania. Yeah, great to see you, Mark.
00:14:18
I just want to, just only one question based on my partial understanding of the conversation.
00:14:23
This seems like a job for AI, can it do it? At least get you at right towards a decent set of solutions pretty quickly?
00:14:32
I think AI is good at some things, but not this. No. It's like saying, let's give a traveling salesman
00:14:39
problem to AI and expect to get a better solution than our current algorithms? No.
00:14:45
It isn't. I would expect you to use the current algorithm. That's basically what I would expect.
00:14:48
Oh, sure, sure. Yeah, so yeah, if you think of it that way, but if you don't give AI
00:14:55
enough guidance and it goes to try and figure this out on its own, it's not going to come up with a good solution.
00:15:03
Right. And Mark, you just mentioned something that some of our audience will understand and some won't.
00:15:07
And it's worth pausing and explaining what is the traveling salesman problem?
00:15:12
Sure, so the traveling salesman problem is one of the most famous OR problems. And it says, if you have a list
00:15:18
of cities, think of a bunch of cities in the United States and you want a salesman to go on a tour, visit each
00:15:25
of those cities in some order, and you want to minimize the total travel that they
00:15:31
take. And it turns out if you have 20 cities, then there's 20 factorial, which is a
00:15:40
large, large number, possible orderings of these traveling salesman tours. And it's very, very difficult to find the
00:15:49
optimal solution. Well, 20 is pretty small now, so that can be done. But it's a problem that's in a class
00:15:56
of very hard problems. It means as the number of cities increases, it becomes harder and harder to find the
00:16:03
solution. But for any kind of reasonable set of cities that we have today, like the 72
00:16:11
college teams to assign them, that can be done relatively very fast on modern computers.
00:16:18
And Mark's making a general point that I think Adi set up quite intentionally, which is
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whenever we have well-established models and algorithms for a solution, then they do most of
00:16:30
the work. And unless they're fed it directly, AI wouldn't come up, because that's a well-honed, decades
00:16:37
-long optimized model. Okay, let's jump to the pros, because you're also involved with the World Golf Rankings.
00:16:45
And now we have a different set of problems, because this is, I was talking with
00:16:51
Rufus about this just a few weeks ago, actually. World Golf Rankings versus like Data Golf Rankings.
00:16:58
It's a little bit like the college football playoff debate that happens every season between best
00:17:04
versus most deserving. And the best is the predictive model, that's kind of the Data Golf model.
00:17:09
If you're gonna bet who's gonna win this weekend, you want a model like that.
00:17:13
Versus most deserving, which is what I take to be the World Golf Rankings. So I'm sure there's best in there, but
00:17:19
you're also trying to reward accomplishment. So it's more backward, it's at least some
00:17:24
backward looking, whereas the best, quote best, is gonna be strictly forward looking.
00:17:30
So that's the setup. And then can you talk to us about how y'all decide, talk about weights.
00:17:36
I mean, you gotta decide what weight to put on different levels of accomplishment in order
00:17:40
to fix these World Golf Rankings. And importantly, Mark, you weren't, you know, this
00:17:43
thing existed many years before you got involved. So what are the changes since you've been
00:17:46
involved? So Cade, you hit on the point that I think many people when they look at
00:17:54
rankings don't realize that the objective could be predictive, forward looking, or it could be backward
00:18:01
looking reward for performance. And it's easier to see the difference in the official World Golf Rankings if you just
00:18:10
used a who's the best, what's the most predictive, then you wouldn't give any special treatment
00:18:19
for majors beyond that they have a strong field. You wouldn't give any special reward for winning
00:18:26
by- Winning, yeah. One shot for winning, period. Because it could be, you know, you won
00:18:31
in a playoff and you didn't differentiate yourself from the other two or three players that
00:18:35
were in the playoff, whereas a predictive system, one stroke matters, not very much, but in
00:18:41
the official World Golf Rankings, winning means a lot. And winning majors means a lot more.
00:18:49
So the board of the official World Golf Rankings and the way it has been set up for, you know, since the 1980s when
00:18:56
it first started, is that wins are rewarded a lot, heavily, like the ratio is 100
00:19:04
for first, 60 for second, 40 for third. And that decline, that exponential decline really says
00:19:10
one stroke at the top matters a huge amount. Missing the cut, whether you miss the cut
00:19:15
by one stroke or 20 strokes, you get zero points, which in a predictive sense clearly
00:19:21
isn't gonna be good. So the official World Golf Rankings objective is clearly not to be predictive.
00:19:27
It's a reward for performance, kind of backward looking, but it's of course related to skill
00:19:33
because the better players win more often. But the biggest change was trying to make
00:19:41
it unbiased within this reward for performance system. So you wanna make sure if you're giving
00:19:47
points out this way, that a strong field gets the right total number of points compared
00:19:54
to a weaker field. So you can still have the same exponential payoffs, but the main question then is, how
00:20:00
many points do you give to a strong field versus a weak field event or between a PGA Tour event and the Hero World
00:20:08
Challenge, which is 20 players or between that and some Asian Tour event? So that's- How do you do that?
00:20:16
How do you do that? Let me clarify the question first. You're saying it's always gonna have this steep
00:20:20
decay, say 160, 30. So 1.6.3, that ratio off the top three. But for a minor tour event, it might
00:20:30
just be at a base of 10 points. Versus a PGA event might be, I don't know, 50, and then a major might be
00:20:36
100 or whatever. What's the ratio of those things? Yeah, we of course know, Mark, I don't
00:20:40
know if your system relates this at all, but it's not principled really in any way.
00:20:44
We know how they do it in tennis, for example, which is exactly that. It's 2,000 for the majors, 1,000
00:20:50
for the Masters 1,000, which is why they call them that. You know, ATP 500, there's 500 points, 250.
00:20:57
So how is it done in golf? And is it related at all to this kind of two for one system, two for
00:21:03
one ratio system? Definitely not. And that was the problem that that's kind of arbitrary and that leads to biases.
00:21:12
And there were biases that you could easily see in the old system. And so the question is, what's the principled
00:21:18
way to do it? And the idea is you take an unbiased measure of skill, in this case, a strokes
00:21:25
gained measure, and you actually have a curve which converts that into kind of points or
00:21:34
endowments that the players bring to an event. And that endowment, you know, weaker players that
00:21:41
have, you know, worse strokes gain bring fewer points to an event and stronger players bring
00:21:46
more. And that total endowment of the players in the field is the number of points that
00:21:52
are redistributed. And so then you get on average in any field, the players don't move up or
00:21:59
down because their points that they bring to the event are just redistributed. So the players that do well are better
00:22:07
than the points they brought, move up in the rankings, the players that do worse move
00:22:12
down. And that's- It's a standard system. It's a standard of any ranking system ought
00:22:17
to be that way that if your expected performance, if your performance matches your expected performance,
00:22:22
you don't change the rankings, right? And if you outperform your expectation due to
00:22:28
the rankings, then you should move up or move down. So it's a very- So Bradley Terry
00:22:32
is optimized using the EM algorithm and you just, if you're at your expectation, you don't
00:22:38
change. Well, so this is, it's lovely because you said principled and I was kind of like,
00:22:42
well, I want to see this because it wasn't clear to me how you're going to
00:22:45
come up with a principle for these ratios. How off was it before, Mark? Without throwing anybody under the bus or too
00:22:50
much shade, like how big an adjustment was that? Not just that, good, Kate. How the hell did Mark get them to
00:22:55
actually adopt that system? I want to hear that part of it too. Yeah, yeah, right.
00:22:59
Well, there's two parts of that question. So one is, I mean, we kind of showed with Dick Rendleman, a colleague of mine,
00:23:08
that there is great bias, but it's easier anecdotally to see that you could have a
00:23:13
particular player, in this case, say from the Japanese tour, and they used to have these
00:23:18
World Golf Champion events where they'd bring the top ranked players, top 72 or 75, and
00:23:27
invariably, players from some of these lesser tours that happened to just make it into the
00:23:33
top 75 would be destroyed in the tournament by many, many strokes. And you could see that they always, when
00:23:43
you got them together in head-to-head competition with the other players, you could see
00:23:50
that their ranks were misaligned, were out of whack. So to answer Eric's question, how did this
00:23:59
happen? Well, Dick Rendleman and I wrote this paper, and like academics, we thought this would affect
00:24:05
some change, but no, unlike, you know, we showed drive for show, putt for dough is
00:24:12
not right. Here, when we showed the official World Golf rankings in the past iteration were biased, people
00:24:17
said, yeah, we knew that. It was like, but then how do you get it to be fixed? And basically they got a, the official World
00:24:28
Golf Rankings Board decided that they needed a mission statement, and the mission statement was to
00:24:35
fairly rank golfers, not to just reward certain tours for one reason or the other.
00:24:41
And they did an analysis, independent of what Dick Rendleman and I had done, five other
00:24:49
groups did independent analyses that came to the same conclusion that the rankings as currently they
00:24:56
stood at the time were biased. And so now they had a mission statement, they want unbiased rankings, and they have independent
00:25:03
academic expertise saying they're biased, so what's the fix? And that's what led to the change.
00:25:11
It's interesting, so then there's an, so let me just check. I just want to think about this.
00:25:16
So if I'm a good player, I want Sheffler or potentially Sheffler or McElroy, well, when
00:25:25
they're not in the field, there's less than total points brought to that event, which means
00:25:30
there's less, I'll call it bonus for winning. So beating them, I mean, it's what you'd
00:25:35
want. You'd want that to be true, but of course your probability of winning goes down.
00:25:40
So have you ever thought of the problem of like, if I could, if I had, if I'm a, let's say I'm the number
00:25:45
10 player in the world, okay? I don't even know who that is, but let's, I could make up a name, but
00:25:50
let's say, I don't know, whoever. Let's say I'm the number 10 player in
00:25:53
the world. The number 10 player in the world golf rankings is Xander Shuffley. Okay, that's a great name.
00:25:59
So I'm Xander Shuffley. Should I want McElroy and Sheffler not to show up? Now, the bad news is they're not, those
00:26:08
points aren't coming their way, but of course my probability of being higher up the exponential
00:26:12
curve goes up. So which, have you thought about the problem of optimal field depending on where I am
00:26:19
in the rankings? Absolutely. So this was designed so that, that question that you just asked, you're indifferent between whether
00:26:28
Scotty and Rory show up or not if you're Xander Shuffley. Right, right. Beautiful.
00:26:33
Take it, but if you take it to an extreme and you say, we're going to give Eric Bradlow a sponsor's exemption into a
00:26:42
no-cut signature event, okay? Yeah. You would be, you would not be in the top 10,000 of the official world
00:26:52
golf ranking, yet because it's a no-cut event, you might get a few points and
00:26:58
that would be unfair. So it works for almost all events, but not if you take a large, large range
00:27:05
from, the Scotty Shufflers of the world to the 10,000th ranked player in the world.
00:27:10
So your point is academically, it's perfectly correct. In practice, you don't have that large a
00:27:17
dispersion in the quality of the field. I'm sorry, but just to be clarified, does
00:27:20
that mean that an expected value, it's sort of balanced? It's indifferent?
00:27:25
Yes. Okay, but not necessarily, but you could have other loss functions that could be optimized differently.
00:27:31
On average, when you, when players, professionals play in events, they neither go up nor down
00:27:38
in the rankings, unless like I said, you're Eric Bradlow on a sponsor's exemption, then on
00:27:44
average, you're going to go up. All right, Mark, one, I'm curious, especially now
00:27:50
that this has been jiggered a little bit, when it comes to like writer cup selection.
00:27:53
Yep. How did the world golf rankings play into that versus predictive models like data golfs?
00:28:02
And some of it, are the captains restricted or some guys automatically qualify, but that's a
00:28:07
world golf rankings automatic qualification. And then, but they've scrunched that down a
00:28:12
little bit to give the captains more discretion. Do you have any sense of whether captains
00:28:16
just want the predictive or do they put a little value in the most deserving? Cause they might think that it captures an
00:28:23
ability to win under pressure counting. So they've changed from like 10 out of
00:28:27
12 or automatic qualifiers now, like six out of 12. So the captains tend to have six discretionary
00:28:34
picks. And I would say most of them are based on predictive and looking forward.
00:28:40
And then the question is, well, something like strokes gained or the data golf rankings, whatever,
00:28:47
don't take into account necessarily course fit, recent play. And the question is, how do you weight
00:28:53
those factors? And so you're still trying to make it predictive, but you're including additional features that aren't
00:29:02
necessarily in the raw numbers. Okay. Okay. Mark, we are coming up on the time we'll need to let you go, but I
00:29:09
do want to ask one kind of general question about you and your experience with golf
00:29:13
analytics. When you created this concept of strokes gained, you probably could have only fantasized that it
00:29:19
would be as impactful as it has been. But I'm curious years on now, what is one place it's gone or something that's come
00:29:27
from it that has surprised you or that you never would have anticipated? Because it strikes me that it's this tool,
00:29:33
it's a method really, and any good method is going to find new and unexpected uses.
00:29:39
So I'm just curious your experience with it. Where has it gone that you might not
00:29:42
have anticipated? Well, I did not anticipate that most professional players and coaches and college coaches and college
00:29:52
players would be looking at this, but for the most part they are. I didn't really anticipate that it would form
00:29:59
the underpinnings of an official world golf ranking. And I didn't really anticipate that many betters
00:30:07
like Rufus would also be using this as step one in their betting system. So it has had a lot more uses
00:30:16
than I ever imagined. And also surprising when I started teaching the sports analytics course at the Columbia Business School
00:30:25
is the strokes gain concept is now in most modern stats that are coming out. So rushing yards over expected and many other
00:30:35
kind of new stats in football and many other sports have this idea of performance over
00:30:41
expectation. And that's basically what strokes gained is for golf. Well, it's XG in golf and in soccer.
00:30:49
Expected goals in soccer, expected goals in hockey. Guys, it's April or May, it's hockey.
00:30:55
Come on now, Eric. I just have to ask Mark one question. When I think, and this is one academic
00:31:01
to another. When I think of some of the things that I'm most quote unquote famous for in
00:31:06
academia, it's none of the things that are particularly the most technical of my work.
00:31:10
So can you just give us a sense briefly, like I assume strokes gained is not the most technical thing you've ever written.
00:31:17
And so does it bother you? It doesn't bother me at all. I'll just tell you.
00:31:21
But does it bother you at all that the thing you may become most famous, or you are most famous, I don't know, is
00:31:26
or the most cited for is something that isn't as technical as like your training?
00:31:32
No, it doesn't bother me because as academics, I think we try and come up with
00:31:37
ideas that have an impact. And this is an idea that's had way wider an impact, but not on academics, but
00:31:45
on the real world, at least as far as the golf world or the sports world is concerned.
00:31:50
So I'm not embarrassed at all. And I, you know, in many of my talks, it said, you know, how, who would
00:31:58
have guessed that you could get so much mileage out of a concept which is subtracting
00:32:02
two numbers? Right. Well, there you go. That's a good counsel. That's good counsel to us and some of
00:32:10
our listeners that it doesn't have to be the absolutely most technically proficient thing to make
00:32:14
a contribution. Why don't we leave it there? Mark, greatly appreciate your being with us.
00:32:19
Always enjoy the chance to visit with you. Thanks so much, Cade and Eric and Adi.
00:32:24
It's always a pleasure. Thank you. Mark Brody, Carson Family Professor of Business at
00:32:28
the Columbia Business School, the creator, literally the creator of Strokes Gained and a longtime friend
00:32:34
of Wharton Moneyball. Come back and join us after the break. We have another half hour still ahead.
00:32:41
Welcome back. Welcome back to Wharton Moneyball. Welcome to the second half of this week's
00:32:46
show. Tuesday afternoon, as it usually is when we're recording, show will go up bright and early
00:32:52
Wednesday. I think Dion gets this thing going early Wednesday. Eric Bradlow's in here with me.
00:32:57
This is Cade. Adi Weiner's in here now, rolled in to his office about halfway through the first segment.
00:33:03
Shane Jensen out and about doing Shane Jensen things. He'll be back. I think he's blood on a bloody committee
00:33:07
right now, the poor guy. He'll be back just off the line with Mark Brody. He always enjoyed talking Mark.
00:33:15
I didn't know he'd done all those golf rankings things. That was good fun.
00:33:18
And that's a neat little extension of his Strokes Gained. And tournament design as a result of it.
00:33:23
Yeah, it affects tournament design. That's great. We have a handful of topics to hit,
00:33:30
some big, some small, but I'd mentioned last week on the show that he had done
00:33:34
a little work on the ABS. Original primary research that Adi is prone to do on occasion just kind of spins it
00:33:40
off. Some of us eat lunch kind of naturally, some of us drink coffee, some of us
00:33:44
go for walks. And Adi just spins off original primary research on things like the challenges in baseball.
00:33:50
So what do you got, Adi? Yeah, so it's really, it's all new. So we're really interested in trying to figure
00:33:56
things out. And lots of analysis are being done. In fact, the MLB has its own website
00:34:02
devoted to challenges created by, as usual, Tom Tango, who is not a real name. That's a real person, that's not a real
00:34:09
name. And he's looking at essentially challenge rates and success rates, but he kind of creates his
00:34:17
own denominator of challengeable pitches, and he's kind of have his own thing.
00:34:21
So what I ask the question is, think about a universe where every wrong play was
00:34:28
turned to the right one. Okay, good. And now accumulate all the, what I call run expectancy flip, caused by flipping the wrong
00:34:37
play to the right play. We're just talking about called balls and strikes now.
00:34:41
Exactly. And only when they're challenged. Well, no, no, no. No, no, no. All of them.
00:34:46
All of them, right? And so every team will have a run, a defensive set of run expectancy they could
00:34:52
reclaim by challenging, and offensive run expectancy that they can reclaim by challenging.
00:34:58
So why I wanted to ask the question, how much of that pile, if you will, that's available to them, are they reclaiming?
00:35:05
Okay, first, great, cool. But give us some context. How big is that pile? And how's it distributed?
00:35:11
Well, it's actually pretty big. It balances out. So your opponent is missing or is being
00:35:18
denied about the same amount that you are. So it's not like, it's a bias.
00:35:22
But if you can recover more than your opponent, that's actually an advantage, substantial.
00:35:27
Per game, it's getting close to about a quarter to a half a run. All right. So just remind me, per team?
00:35:37
Yeah, per team. It balances out. So it's equal, so it's not like one side is advantage.
00:35:41
That's like 5% of the number of runs that are scored. So that's a lot. It's a little less than that, but yes,
00:35:48
it's a lot, yeah. Okay, and just correct me if I'm wrong. How many, before I answer your question on
00:35:53
percent, can you just remind me of how many challenges I get and when, if I get it right?
00:35:59
Because it matters. Because if I could infinitely challenge, and that's a different thing, but obviously I cannot.
00:36:04
Obviously, you'll get all of it if you can infinitely challenge. Right. You just keep challenging until they make it
00:36:09
right. And at that point, you give up the system and you just let the robots determine
00:36:13
all the value. But that's not the system. The current system allows you two.
00:36:18
And every time if you make a mistake, your amount is decremented. So you can do as many as you
00:36:23
can until you hit two errors. So it's a classic. So that's a wonderful system.
00:36:28
It is a good system. Because it actually is a lot of fun to sort of think about from a operational,
00:36:34
strategic perspective, what should the teams do? And the players are kind of working them
00:36:39
out. Now we've learned a few things. We've learned that catchers are much better than
00:36:43
hitters and pitchers. Catchers are best at this. They're the best view. They also don't have the emotion.
00:36:49
Jazz Chisholm is the worst. He has challenged pitches right down the middle. And he's already an internet meme for like
00:36:56
looking at the camera going, oh, what am I doing? Most players- Catchers have caught a million
00:37:04
pitches. And so they're calibrated for this. Exactly. But they make errors as well.
00:37:09
The catcher error rate is around 60%. And the position player- Zero? No, no, sorry, getting backward.
00:37:15
Success rate is around 60%. And the position players are in the mid 40s. Well, that already gives us some information.
00:37:22
So because look, the two factors that help me determine reclaim percentage is the hit rate
00:37:29
or how successful am I when I challenge, but also the distribution of when I ask
00:37:34
for it, because I want to ask for it, for example, if it's bases loaded and it's three, two count and a marginal pitch
00:37:40
comes in, I should challenge that pitch because that's potentially worth a lot in terms of
00:37:46
expected number of runs. Absolutely. So people have recognized that your decision to
00:37:53
challenge depends on two factors, your probability that you're right, which is how bad the call
00:37:59
was. And of course, the run expectancy that would flip. Didn't I just say that?
00:38:03
Exactly right. And people have recognized that, but people have not. There's no algorithm that anyone has made as
00:38:08
yet. And I'm working, our team is working to create that. We don't know the algorithm right now because
00:38:14
there's a problem. You only get a resource of two. So you have to husband that resource and
00:38:19
think about it properly. So the question that I went out to answer and did answer is a very simple
00:38:25
one, which is what percentage of the run expectancy that is out there for you to
00:38:31
reclaim are you actually getting? And among the amount that you're missing, are
00:38:36
you missing it because you're running out of challenges and therefore you can't challenge?
00:38:40
That's really horrifying, by the way, if you're watching baseball and it's the eighth inning and
00:38:43
there's a strikeout and it's a bad call and you're out of challenges that you're pulling
00:38:47
your hair out. So how much of the missing challenge is cost is, missing RE is caused by lacking
00:38:54
the ability to challenge because you're all out. And how much is it missed because you're
00:38:58
just not challenging? Can I ask you a clarifying question? Sure. Why you decided to study runs as opposed
00:39:04
to win probability? Eric Bradlow with the home run question. The answer is it's a lot more stable
00:39:14
and it doesn't depend on context and it'll be the same no matter what inning you're
00:39:20
in. And it is just, and there's a lot more data on it that's reliable. So win probabilities can barely move with a
00:39:29
strike in the first inning, but a run expectancy is a measurable and determined quantity.
00:39:35
So it really is a statistics argument. Yeah, the only reason I'm asking because I
00:39:39
think it's a good question, I'm glad you thought of it, obviously, but also the reason
00:39:43
why you might see a percentage lower than one might expect is because you've created a
00:39:50
metric, but the team, I'm being generous, the team may be trying to reclaim win probability,
00:39:56
not runs. And therefore that's why you see a lower percentage in your metric than you might expect.
00:40:02
Actually, real quickly, you could imagine psychologically regret is more closely associated to win probability than
00:40:08
runs. Even though I 100% agree with what Adi's saying and doing. And by the way, that's something Adi has
00:40:14
said over the years about expected points versus win probability in different sports.
00:40:19
So I kind of knew where he was coming from, but you could imagine regret, like even the hair pulling out in the eighth
00:40:23
inning, that's a little bit closer. All right, do you want my answer, Adi, on the percent?
00:40:26
Let me just before, just to respond on that as well, like in fourth down decision
00:40:31
-making, the right thing to do is win probability. In decision-making in football, everything should be
00:40:36
win probability, but a lot of decisions are made on expected points. And one of the reasons for that is
00:40:41
there's just many more independent possessions. Possessions are valued on the point basis.
00:40:47
Win probabilities are all related, right? So you have much more data to accurately
00:40:51
estimate things when you're dealing with possessions and the points rather than win probability.
00:40:55
And so we know much more about run expectancy than we know about win probability.
00:41:00
And so we have to recognize the limits of our data. So also one of the things that I
00:41:03
also tell my students, start with the easy thing, for God's sakes. No, I don't.
00:41:09
All right, so you want to make some guesses? What percentage of the available RE is being
00:41:14
reclaimed? I got it. I understand the question. And give me a defense and an offensive
00:41:19
number. Well, clearly we know that defensive is going to get more because catchers are better.
00:41:26
Yeah. I don't have a calculated answer, but my intuition is like just a very small fraction.
00:41:31
I don't know, 10%, 15%. Eric? I was going to guess a third. Okay, so you're both in the ballpark.
00:41:38
It is small. And no one is at a third, but defense is around 27% and offense is just around 19.
00:41:47
And that's only through April 29th when I ran the data. Eric, we should have asked if we could
00:41:52
pool our guesses and we would have hit it. You would have nailed it. Yeah, exactly.
00:41:56
Model average. That would have been the right thing to do as you guys all know. Ensemble, we just have to demonstrate it.
00:42:01
Now the real question is, the second question, which I know the answer to, is how
00:42:05
much of the missed challenge, which is roughly between 75% to 80%, how much of that missed challenges are caused by not having
00:42:13
challenges? Small number. Quarter to a third. I'm going to guess more than that.
00:42:23
I'm not going to, I was going to say half. Now we're going to average. Which side?
00:42:28
That doesn't matter. Eric's half is this. So how much is lost of the remaining
00:42:32
chunk that we're missing? X, take out the ones you're getting. Yeah, if I had more challenges, I could
00:42:38
regain half of that. That's my thought. Okay, so I'm not asking the question, that's
00:42:43
a different, that's a totally different question. If I had three challenges, how much can
00:42:46
I regain? I'm asking you just an observational question of the challenge run expectancy that you have not
00:42:52
reclaimed, how much of it is missed during the periods of time where you have no
00:42:57
challenges? Yeah, yeah. Then it's small. Then I'm going to go back to what
00:43:02
Kate's saying. I'm going to go with a quarter. It's actually much smaller than that.
00:43:09
Much smaller. They are barely missing any challenge because they don't have it.
00:43:15
It's about 5%. So they happen to pick the right number of attempts too? No, I just think they're underusing their challenges.
00:43:21
That's my guess. They're underusing their challenges. That's another explanation.
00:43:26
I got plenty of challenges because I'm not using them. They're just not using them.
00:43:29
And when they use them, but they don't use them enough. I think the teams, once they blow one,
00:43:35
are just under, I just think they underuse them. And particularly later in the game, I think
00:43:40
they're underusing them. Seventh innings, eighth inning, and the ninth. I mean, come on.
00:43:46
Just use the goddamn challenge. Is this the same as like sitting your guy with two fouls in the first half?
00:43:52
Yes. You're trying to preserve something and you're being too conservative about the preservation.
00:43:57
Yep. Or it's like, you're starting actually to see Adi's point actually in the NBA now.
00:44:02
Like you're starting to see at the end of games, like you know it was a foul, but what the hell?
00:44:08
Let's challenge this thing and see what happens. There's 15 seconds on the clock.
00:44:11
And you know what? We're going to lose the game if this thing isn't overturned.
00:44:15
There's no cost for me to see. You know, maybe some gets in the ref's eye and he says, no, that's not a
00:44:20
foul. You know, who knows? Actually, I'm starting to see it in the playoffs.
00:44:24
I've seen ridiculously bad challenges in high leverage situations. Are there no penalties for over?
00:44:32
You get a certain number. But it's just the end of the game. You're going to lose the game if this
00:44:36
isn't reversed. Give it a shot. So that's the real question. So the answer, the unknown now is what's
00:44:43
the right policy. Right. Yeah, right. Don't know it. Are you observing different teams following different policies?
00:44:51
Is there much heterogeneity? Is there already learning? Oh, Adi could have been talking about two
00:44:55
different things, Adi. Do you mean MLB's policy? Or do you mean what Cade was talking
00:44:59
about, which is the team policy? I'm not changing MLB. Oh, okay. By the way, so I'm able to rank
00:45:05
teams by their ability to recover challenges. And actually Philadelphia is very good on the
00:45:09
offensive side. They've been recovering a lot of challenge. They may be doing that because they're actually
00:45:13
challenging a lot. And in fact, a lot of, I mean, this gets to the psychology. When you challenge and are wrong, they often
00:45:21
feel the heat for that. And I think in a way that's probably not deserved. A good challenging team should be not ending
00:45:29
the game with challenges. That's, you screwed up if you did that. Which means that you have to bear the
00:45:33
brunt of what might be considered silly challenge. Can you tell us the probability?
00:45:38
If I have on the Y-axis, the probability of successful challenge, and on the X -axis, the distance from the strike zone, what
00:45:45
does that curve look like? I actually have, so I don't have that number because it's very correlated with that.
00:45:55
But I'll start with the first number, which is, I can tell you the probability of
00:45:59
an umpire error as a function of the distance from the strike zone. Okay. I fit that curve.
00:46:04
And by the time you get to three inches, the probability is nearly zero. Yeah. And it interpolates fairly linearly.
00:46:12
What is the diameter of a baseball? Just under three inches. All right, so it's basically, once it gets
00:46:18
to more than a baseball outside of the zone. They tend to be very, very good. That's good.
00:46:24
I'm glad, thank you. The umpires, by the way, the umpires are awesome. Yeah.
00:46:28
I mean, we laugh at them and think, oh, 92.5 is their success rate. Do you have any idea how many pitchers
00:46:35
are right on the border? These are professional pitchers we're talking about.
00:46:39
They throw it on the corners and on the edges. And when you're on the edges, their probabilities
00:46:44
are roughly 50%. I mean, it's very hard to get right. The trouble is, and this is one of
00:46:49
the reasons the challenge system is so great, is that there are outliers. I mean, there are human beings.
00:46:53
And the outlier, if you can zap those, then you've made a lot of progress. Why don't we let that sit there for
00:46:59
now? This sounds like an ongoing project. I'll be able to come back to us on some things.
00:47:03
I have some other, I'll do some other baseball trivia for y'all. Trivia is the wrong word.
00:47:07
I'll put you through your paces a little bit. Did y'all happen to see this Wall
00:47:10
Street Journal article about the Brewers the other day? They looked at how over-performing they are
00:47:15
over the years. So, FanGraph's preseason predictions for number of wins over an 11-year period of time, 2015
00:47:23
through 2025. So 11 seasons. The Brewers have been the most outperforming of the FanGraph's expectations.
00:47:29
And you can go to like Pakoda, you can go to somebody else's system. They're also the top there.
00:47:34
What do you think the average number of wins above expectation the Brewers have achieved over
00:47:40
the last 11 years? Five. So what is the, in wins? How far in wins above expectation?
00:47:49
Observe your wins minus FanGraph's expected wins. Sum it over 11 years and divide by
00:47:54
11. Yeah, and I've guessed five. I would guess three. Seven and a half. What?
00:48:02
Right? And that's 11 years set. Dodgers are five, 5.1. Astros are 4 .8. You're Yankees, who seem like underachievers to
00:48:10
me, are actually four. But the Brewers are 7.6. And- Does that say more about their model than
00:48:16
anything else? Well, the key, I think the article, is it Jared Diamond? He's always doing these kinds of articles.
00:48:23
I'm not sure if it's him. Let me look real quick. Yeah, Jared Diamond, as a matter of fact.
00:48:26
This is May 4, so yesterday. They say it's development. You know, this is a small market team,
00:48:33
small budget team. And they say they are turning, making players better more than they're expected to and more
00:48:42
than other teams are. And if that's true, I just- They're also relying heavily on youngsters because if they're
00:48:48
not youngsters, they would be priced into the preseason expectation. So if I'm getting this right- Unless
00:48:54
they're just turning them into, they take a veteran and they make them better than they
00:48:58
were before in some way. I mean, this was the story for the Astros all those years.
00:49:01
Like Astros were first into development. Now we talk about baseball being this way.
00:49:04
But apparently, seemingly, at least by this article, they're ahead of the league on that.
00:49:10
But Adi's got a good point in that, like when residuals like this tend to be
00:49:14
persistent, any good statistician would go back to the model and say, I'm missing something here,
00:49:21
you know? But what if it's a team effect? And then you're just going to put your
00:49:23
thumb on the scale and have a real Brewer's Fixed Effect? That's not the way you want to go.
00:49:28
That's a big number. That's seven and a half. That's a big number. Right?
00:49:31
Yeah, no, because listen, they don't tell us what their forecasting system is.
00:49:34
Yeah. I don't know what that is. That is a very big number. And it is time for us to just
00:49:39
shout out a former student of ours, Eric Babitz, who is the Director of Player Acquisition
00:49:43
for the Brewers and has been there since he graduated five, six years ago. At the Brewers?
00:49:48
At the Brewers. Oh, how about that? Well, heck, let's get him on the show and find out whether Jared Diamond's article is
00:49:53
actually capturing what's going on. I mean, he's right in the middle of that stuff.
00:49:56
Because he's charged with finding people that aren't going to break the bank because they're a
00:50:00
small budget team, and yet they believe they can make better. That's his charge.
00:50:04
That's his charge. That's interesting. Okay, let me give you one other baseball
00:50:07
question. I don't know how I wasn't calibrated for this, but top, so the women's softball season
00:50:14
is winding down. Their postseason is great fun. Top shortstop in the country, Issa Torres, Florida
00:50:22
State. She's got a big bat, she makes offensive contributions, but she's also great defensively.
00:50:27
What do you think, just let's say, I don't know if this is true, but let's
00:50:31
say she has the top fielding percentage in the country. What do you think her field, a shortstop,
00:50:35
women's college softball shortstop, what do you think the top fielding percentage would be?
00:50:41
And I'll give you the number of, well, you might even guess, what's the number of
00:50:43
chances? There's a simple thing to guess. How many games are there in a season?
00:50:46
30 or so? About 30, yeah. And I would guess chances are probably in the, there's so many strikeouts, probably between six
00:50:54
or seven chances a game. So I'd go for about 150, so. You're dead on, 142.
00:51:00
I thought it'd be higher, 142. So Issa Torres, 142 chances this season, led the country in fielding percentage.
00:51:06
What do you think it was? So I bet she got about 138 of those 143, would be my guess.
00:51:14
So that's 97, 98%. That's what I was, I was gonna guess somewhere between 95 to 98%.
00:51:19
What's your upper limit? Well. 100. Well, I know that's your true max, but
00:51:27
we do agree. She's 100%, she had no errors this year. She had no errors, that's amazing.
00:51:32
Playing shortstop. Now, let me ask you a question about that. So let's suppose you have a known statistic.
00:51:38
So let's imagine there's a play that happens now or whatever during the season.
00:51:43
And the scoring person says, you know what, let's tilt this to the no side. First baseman should have scooped that ball.
00:51:52
Yeah, exactly. That was not a bad throw. Okay, that is wonderfully cynical, Eric.
00:51:58
Well done. Okay. Let's do one last one. And this is more involved. And this is the paper, y'all saw
00:52:04
that Dylan Weawad. Dylan Weawad is with Slack. He's a quantitative researcher with Slack.
00:52:09
He is a social psychologist out of Simon Fraser, making him Canadian. And he did, Northwestern has had, Northwestern, Kellogg's
00:52:19
Graduate School of Business at Northwestern, as Eric knows anyway, has had postdocs for years.
00:52:24
Great postdoc program. He did that. And then he's moved on to Slack. But he's rediscovering his love of hockey and
00:52:30
is running some quantitative analysis. And so I wanna ask y'all. So he sent us this paper and he's
00:52:34
a published academic. And so when he writes a paper, he's gonna write it soundly like an academic.
00:52:39
So it's this impressive, only 15 pages, but very strong methodologically. I wanna ask y'all, because he takes
00:52:45
on an interesting challenge. He goes to measure depth in hockey. And one of the reasons he sent it
00:52:52
to us was that we talked to Eric Tolsky a few weeks ago, the general manager of the Carolina Hurricanes.
00:52:58
And Tolsky's whole thing is basically depth. They've built their whole roster to be deep,
00:53:04
like less top-heavy and just deep. All four front lines, all three back lines, whatever.
00:53:09
They're gonna have guys that can play all the way. Is there an agreed upon measure?
00:53:12
Like you can imagine like entropy of skillset. You can imagine max minus min. You can imagine taking lines and looking at
00:53:19
the summation of some metric and looking at lowering the variance. Is there a well, I'm saying, is there
00:53:25
a, no, okay. But you mean something like this. But no, but you mean something like this
00:53:29
when you say depth. If we take Dylan to have done a thorough lit review, and I don't know that
00:53:35
that was his objective, so we don't know, but he's acting as if he's creating this.
00:53:39
I suspect teams, some teams have this. Some teams, certainly Tolsky has done this.
00:53:43
But as far as we know, there's no accepted measure. So I'm asking y'all how you go
00:53:48
about doing it. Just a neat little paper about Dylan. I just came up with three measures right
00:53:53
there. I just, so you have some strength parameter for a player. And so depth would be, well, I mean,
00:54:01
it depends on meaning across the whole team, or you could mean across lines. You could, matter of fact, around the team.
00:54:08
Well, you know, there's classic measures of, you know, variance is one. You could have some sort of- Just
00:54:14
look at the difference. How much, what's the rate of scoring per minute among each line and look at the,
00:54:21
how that erodes from, look for big drop in three and four in some way. So you want to use scoring, Adi, as
00:54:27
opposed to like some sort of strength measure. Well, you can make a composite measure because
00:54:31
there's obviously offense and defense. But I think the lines are different. I mean, they're misaligned, right?
00:54:36
You're out of my pen here, folks. No, no, no, but let's- No, no, let's- But isn't there offensive players and
00:54:42
defensive players- No, no, but this- But no, you're asking a good question. Suppose- Let's say, let's, straight offense.
00:54:46
We're going to play- Yeah, so I want to look at your rate of scoring and then compare that across the lines, either
00:54:53
per possession per minute, probably per minute. Okay. And then there's also a power play issue
00:54:57
because I think you bring in your top line. You could do that, yes. You could do power plays, sure.
00:55:02
Okay, so let me just walk you through a few of the steps that he does because I think it's thoughtful and interesting.
00:55:07
Let me say it's relevant also because he ran the numbers on this year's NHL and
00:55:12
Carolina is like a standard deviation beyond everybody else in this measure. And in his analysis, it shows that it's
00:55:19
predictive. It makes contribution above baselines on the likelihood of a team winning.
00:55:26
Okay, so that's how you're controlling for a bunch of other things that you'd expect.
00:55:30
It's there's incremental contribution. That's right. Can I just shout out to, yeah, go
00:55:35
ahead, finish. Well, I'm going to give you a little bit of a, I'm going to give you
00:55:37
a couple of steps on methodology because I thought they were nice. First, it's at the player level as opposed
00:55:42
to the line level. So he'll take a stat like ice time or closer to what you might care about,
00:55:49
like XG, expected goals. He looked at also things like assist and shots on goal, but it ends up with
00:55:55
a suite of these statistics. And in each case, he asked, he asked what's the compliment of the Gini coefficient.
00:56:02
So y'all know the Gini coefficient is this IO kind of, it's a concentration measure.
00:56:08
And so he's asking how concentrated is the ice time or shots on goal or expected
00:56:13
goals among the players or the offensive player or the skaters. It's all obviously defensive players can have XG
00:56:20
as well. And so that's one, that's the basic measure, but then he models the whole thing as
00:56:27
a latent variable. And so I think this is something that we ought to listen to. I think there's a nice contribution because he's
00:56:32
saying, look, it's not one thing. XG, like the compliment of the Gini coefficient
00:56:37
of XG for a team is an imperfect measure of depth. But if we get three or four of
00:56:43
these things and ask, is there a latent variable? I'd say this is basic measurement science.
00:56:49
You don't measure a construct with one thing. You use a bunch of manifest variables that
00:56:54
represent some underlying basic concept, which is why I was thinking of some sort of strength
00:57:00
model. You could call that latent thing a strength thing, which is manifested itself in different observables.
00:57:09
I'm excited to look at his paper, Cade. Thanks for bringing it to our attention.
00:57:13
I will just point out that that was the qualitative or quantitative or qualitative question that
00:57:18
we asked our high school students in our competition. Is that right? They were asked to essentially evaluate whether depth,
00:57:24
we didn't call it that, we call it line variance, how that affected winning.
00:57:29
And that was the final question for their high school students. And we didn't- Maybe I should just
00:57:35
say a few words, what you're talking, I mean, I obviously know what you're talking about.
00:57:39
You should just say a few words. What is the Wharton High School Data Science Competition?
00:57:42
So Wharton Analytics and AI at Wharton, we sponsored a major competition for high school students
00:57:48
and we created a fake hockey league. They played each other all season. And then we asked the students to forecast
00:57:55
the outcomes of the playoffs. And that was all very forecasty and very rigorous and qualitative.
00:58:03
But then we had them ask an open -ended question, like a hockey question, which is,
00:58:07
what is the relationship between having a depth, which is the right word for it, and
00:58:14
winning? And we asked them to study that. And it was actually very hard because there
00:58:20
was a very strong confounder, which is the top lines also play against the top defenses.
00:58:27
And so you have to control for the quality of the defense that they play against
00:58:32
to measure the quality of your top line. And if you didn't do that, you thought
00:58:36
that your underlying, your lower lines were better than they were because they were playing against
00:58:42
weaker defenses. And I will tell you that one team managed to do that out of the 700
00:58:49
submissions. Well, I know who it was because they presented actually at the Wharton AI and Analytics
00:58:54
Board Meeting. I assume you mean the Pingree team. Is that the team that won? They were the team that won.
00:58:58
I'm not sure they're the team that figured that out because it was so esoteric that
00:59:03
there were so many components to the program. All right, guys. So we'll let that one go.
00:59:07
If anyone's interested in chasing it down, Dylan's website is hockeydecoded.com, hockeydecoded.com.
00:59:15
Thanks, Dylan, for sending that to us. And listen, guys, we're always interested in the
00:59:19
work. And to be fair, the more put together the work is when you send it to us, the better, but we'll take work in
00:59:25
progress. We'll take data. We'll take websites. And Dylan, maybe he got lucky.
00:59:30
He got me in a moment where I could pause and read the paper, but we love that you guys send us stuff on
00:59:35
occasion and we learn from it. So please keep it up. Fellas, what else around the world of sports
00:59:42
right now before we have to run? Well, just one thing for me. I always love talking about tennis, but Yannick
00:59:49
Sinner has done something no one's ever done. He's won five straight Masters 1000 titles.
00:59:55
And no, not Federer, not Djokovic, not Nadal has ever done that. And my prediction is, I don't think, unless
01:00:02
he gets injured, I don't think he's going to lose unless, until Alcaraz comes back.
01:00:09
I mean, the gap between him and everybody else, look, he just played Zverev, who's number
01:00:15
three in the world. He beat him 6-1, 6-2. It's the fourth straight match. He hasn't given up more than six games
01:00:23
to Zverev. And that's the number three player in the world, okay? And Djokovic is injured right now.
01:00:28
Maybe Djokovic beats him on a bad day for Sinner, but the gap is so large that he may win every tournament he competes
01:00:37
in, assuming he stays healthy right now. I don't see any reason why he wouldn't
01:00:41
be. I have to start looking at the betting odds, but you have to put him at minus 400 minimum, minimum for any tournament he
01:00:49
plays right now. That takes the fun out of it, doesn't it? That's a little too heavy.
01:00:53
It does. How long is Alcaraz out, you said? It's hard to know. I mean, he's not playing the French, which
01:00:58
is upcoming. They're not at the French yet. They still have, I forget which one's next,
01:01:02
the Italian Masters or whatever. But there's one more tournament and then the
01:01:05
French, and Alcaraz is already saying, because of his wrist, he's not playing the French.
01:01:10
So, yeah. So that's what caught my eye. All right. We should note that two Philadelphia franchises are
01:01:19
in the second round of the playoffs. That's not nothing. How long has it been?
01:01:22
How long has it been since that happened? Both Flyers and the Sixers are into the
01:01:24
second round? That's pretty good. They're both getting whipped right now in that
01:01:29
second round, but presumably the Sixers will bounce back. I assume that that Knicks first game was
01:01:34
just because of how rough that Sixers- Well, the Knicks, by the way, have set up, I mean, whatever this is worth, it's
01:01:39
a small sample. The Knicks have now set a playoff record. They've won four, three straight, but they've won
01:01:44
four straight, I think, playoff games now by 25 points or more, which has never been
01:01:48
done before. So the Knicks are on a heater. They were down 2-1, just remember, mind
01:01:52
everyone, they were down 2-1 to the Hawks. They beat them three straight by plus 25.
01:01:57
They beat the Sixers by 39 last night. So whatever heater they're on, they're on a
01:02:03
wrecking crew mission right now. And you're right, the Sixers may bounce back
01:02:07
and lose by 15. Now, one trick, concern potentially, is that they were winning, and then the team starts to
01:02:14
try to get desperate, and then it ends up creating a gigantic margin if it doesn't
01:02:18
work out. They were beat pretty early on this game. Yeah, I have to tell you, I was
01:02:22
in- It cuts out pretty quick. I was in Penn Station when the Knicks were playing their last game of their first
01:02:26
series, and at the bar in Penn Station, they had the game going on, and I turned over and looked, and I saw the
01:02:32
score, and I'm like, that can't be real. Right, it was like 90 to 30 or something.
01:02:36
No, it was an unbelievably unreal score. But there's this thing in tennis that I
01:02:41
think is known, that tennis players, if they get behind in a set, sometimes just say,
01:02:47
I'm gonna lose this set, I'm gonna conserve energy. And I think this happens in basketball series
01:02:52
as well, that sometimes a team will get sufficiently behind, they're like, we're gonna conserve energy
01:02:56
this time, we're gonna come back- Well, Cade, I mean, let's remember, the Sixers played
01:03:00
seven games. They ended on Saturday. So they had to fly down from Boston. By the time they was blown out, I
01:03:08
know for a fact, Embiid, Paul George, Tyrese Maxey, they were all pulled in the early
01:03:12
to mid part of the third quarter, the third quarter, because they're playing again tomorrow.
01:03:17
There's no, I mean, I'm saying there's no rest. There's one day rest.
01:03:20
You obviously, the game's over. Tank this game and go for the next one. I'm worried about that in the Eastern NHL
01:03:28
playoffs, the Canes are up on the Flyers 2-0. They're big favorites anyway, they might sweep them.
01:03:33
The team I'm pulling for, the Sabres, haven't yet started their series against the Habs.
01:03:39
And so it could be that the Canes get out and have like a 10-day break before- Get rusty.
01:03:46
Then you hope for us, that's exactly right. All right. Let me give you one other thing, guys,
01:03:49
before we go. The NHL lottery, draft lottery is today. So there's a few wrinkles here that are
01:03:57
just a little bit interesting. But by the way, the presumed number one pick, it's not 100% sure, but the
01:04:01
presumed number one pick is that kid that's at Penn State. He kind of unexpectedly went to Penn State
01:04:07
when Penn State was practically just an intramural team still, Gavin McKenna. And by the way, he's like six foot
01:04:13
170. It's just amazing to me that a guy on the hockey ice, six foot 170, which
01:04:18
is a very average size guy, could be that good. But setting that aside, the odds, the top
01:04:24
odds for the worst performing team last year, the Vancouver Canucks, it's 25 and a half
01:04:29
percent, 25% chance. It's pretty, pretty good. And then it drops to Blackhawks are 13,
01:04:34
Rangers are 11. And here's something for us to pull for tonight. In absentia, Shane Jensen's Calgary Flames are the
01:04:41
fourth highest probability of getting the number one pick, nine and a half percent.
01:04:44
So we should all be pulling for the Flames. They haven't done quite as much flattening as
01:04:50
like the NBA has done with the draft lottery, et cetera. Or where they haven't even, there's tiers.
01:04:56
Like bottom four in the NBA are all at the same percentage now, so in other words, you can tank, but there's no reason
01:05:02
to tank from third to second. They haven't, I don't think they've done that
01:05:06
yet, but they're talking about making that last change she just said. But there's another wrinkle in here that I've
01:05:10
never seen before. We talk about tournament design, but here's lottery design.
01:05:13
Of course, we're hearing a lot about it from the NBA, but I think this is just gonna exacerbate what you just said.
01:05:17
They have separate draws for the number one and the number two pick. I think that means in the NBA, they'll
01:05:25
count down like 10, nine, eight, seven to one. And so it's one draw all the way
01:05:30
through. I think that means they're gonna choose a ball for number one, and they're not just
01:05:36
gonna do a full, well, would it make any difference? And they're gonna, that team will obviously be
01:05:42
removed for the next draw. Why would it be any different? That team's probability should be, that probability, let's
01:05:50
say it's 25.5%, that probability should be distributed equally. In other words, it doesn't violate what we
01:05:56
call the IIA property, meaning the remaining 74 .5% probability still has the same ratio
01:06:03
amongst all the other teams. So there should be no impact. Yeah, so why would it matter?
01:06:09
Maybe I have it, maybe I get, so I don't know. I don't know what they're doing and what
01:06:13
they're doing wrong. That must not be what they're doing. Anyway, I would just wanna, something for a
01:06:16
future show, but I have a group of students from my Moneyball Academy over the summer.
01:06:20
They studied the rate at which value is lost as you go down the draft curve for all sports.
01:06:28
And hockey surprisingly gets the incredible amount of value from the top of the draft, and
01:06:33
it drops quickly, but way more than other sports. I was surprised. I didn't realize how predictable a top-ranked
01:06:41
hockey player is in terms of value. That's a lot. The difference in predictability is what you're talking
01:06:46
about, though, the drop. Yeah, but even, it starts high, and then it stays high and it goes down, but
01:06:52
it's amazing. So the metric they used was all-star appearances, and they are a lot at the
01:07:00
top of the draft. Interesting, and did you have any sense of where the other sports come in?
01:07:04
Yes, we have that. We'll have to talk about that at a later date, because it's a great little study.
01:07:10
Well, it's surprising given the long development time on most hockey players.
01:07:16
It's much more like, it's in the direction of baseball as opposed to like a football
01:07:19
or basketball. Okay, guys, that's a pretty solid show. Well, well over an hour here.
01:07:25
It feels like we haven't talked in a while, and we did some today. We'll let it go there.
01:07:30
For the whole team here, Eric Bradlow and Adi Weiner joining me, Shane Jensen in absentia,
01:07:35
Dion Simpkins, the big boss behind the scenes making this thing happen for more than 12
01:07:39
years now, Marissa Reyna, our producer, and Deep Patel, boss lady, keeping us all in line.
01:07:46
Thanks to that whole team. Thank you guys for listening. Come back and join us next time.
01:07:49
Between now and then, enjoy your sports.

Episode Highlights

  • Mark Brody Joins the Show
    Mark Brody, a pioneer in sports analytics, discusses his work in golf rankings.
    “Mark, thanks for making time for us.”
    @ 00m 59s
    May 07, 2026
  • The Concept of Strokes Gained
    Mark Brody invented the concept of strokes gained, revolutionizing golf analytics.
    “He flat out invented the concept of strokes gained, which is just kind of ridiculous.”
    @ 01m 25s
    May 07, 2026
  • College Golf Rankings Discussion
    Mark shares insights on the complexities of college golf rankings and their implications.
    “This sounds like a ball, frankly.”
    @ 04m 14s
    May 07, 2026
  • World Golf Rankings Explained
    Mark discusses the differences between predictive and performance-based rankings in golf.
    “The official World Golf Rankings objective is clearly not to be predictive.”
    @ 19m 25s
    May 07, 2026
  • The Principle of Ranking
    A principled way to rank golfers involves unbiased measures of skill, redistributing points based on performance.
    “It’s a standard of any ranking system ought to be that way.”
    @ 22m 15s
    May 07, 2026
  • Surprising Uses of Strokes Gained
    Mark Brody reflects on the unexpected impact of his strokes gained concept in golf and beyond.
    “I didn’t really anticipate that it would form the underpinnings of an official world golf ranking.”
    @ 29m 59s
    May 07, 2026
  • The Brewers' Surprising Success
    The Brewers have outperformed expectations significantly over the last 11 years, achieving 7.6 wins above expectation.
    “They’re ahead of the league on that.”
    @ 49m 10s
    May 07, 2026
  • Yannick Sinner's Historic Win
    Yannick Sinner has achieved an unprecedented five straight Masters 1000 titles, a feat unmatched by legends like Federer and Djokovic.
    “He’s won five straight Masters 1000 titles.”
    @ 59m 51s
    May 07, 2026
  • Knicks Set Playoff Record
    The Knicks have made history by winning four straight playoff games by 25 points or more, a record never before achieved.
    “The Knicks have now set a playoff record.”
    @ 01h 01m 49s
    May 07, 2026
  • NHL Draft Lottery Insights
    The NHL draft lottery is underway, with the Vancouver Canucks holding a 25.5% chance for the top pick.
    “The NHL lottery, draft lottery is today.”
    @ 01h 03m 50s
    May 07, 2026

Episode Quotes

  • You really need to go into the analysis to figure out...
    The Math Behind Sports Rankings and Golf Analytics
  • It’s a standard system.
    The Math Behind Sports Rankings and Golf Analytics
  • It doesn’t bother me at all.
    The Math Behind Sports Rankings and Golf Analytics
  • Just use the goddamn challenge.
    The Math Behind Sports Rankings and Golf Analytics
  • She had no errors, that’s amazing.
    The Math Behind Sports Rankings and Golf Analytics
  • The Knicks have now set a playoff record.
    The Math Behind Sports Rankings and Golf Analytics

Key Moments

  • Questioning the System20:14
  • Bias in Rankings21:12
  • Unexpected Impact29:25
  • Final Thoughts32:26
  • Umpire Accuracy46:24
  • Brewers' Performance47:29
  • Hockey Depth Analysis52:32
  • Sinner's Dominance59:51

Tension Over Time

Words per Minute Over Time

Vibes Breakdown