What’s more improbable: OSU/Florida or Oster/Levin?

It is a strange coincidence that Ohio State and Florida played for the national championship in both college football and basketball this year. What are the odds of something like this happening in the two premier sports? Let’s assume (1) there are 50 universities that have a shot at winning each of these national titles, (2) all 50 of these universities have an equal chance of making it to the final game.

I’m not trying to compute the odds that these two particular universities make it to the finals of both events — just that the same two teams make it. So any two teams can make the final game in football, I just need to figure out what the chances are they also make it in basketball. The odds that the first team will make it are 1 in 25 — there are two slots and 50 teams competing for the slots. But if Ohio State makes it, then there is only one slot left for Florida (with 49 teams competing for the spot), so the chances for Florida conditional on Ohio State already making it are 1 in 49. So the likelihood of the same two teams making it in both sports under my set of stylized assumptions (assuming I did the statistics right which is no doubt the biggest assumption of all in this calculation!) is about 1 in 1,225. So this sort of thing happening is a once-a-millennium kind of event if my assumptions are realistic.

That coincidence, however, is nothing compared to the next one. My favorite source of interesting facts has recently become the Everit St. Weekly. Last week I learned from this reliable source that Emily Oster is a liar. Now, reading further, I discover that two of the best young economists in the entire world, Emily Oster and Jon Levin, grew up on the same block. Now what are the odds of that?

Levin and Oster are easily among the 50 best young economists in the world. I don’t know exactly how many blocks there are in the United States. There are about 10,000 in Chicago. Chicago has about 1 percent of the U.S. population. So if Chicago blocks have an average number of people per block, then that would mean there are about 1 million blocks in the United States. My guess is there are more people per block in Chicago than for the country on average, so let’s say 2 million blocks in America. (That works out to 150 people per block, which doesn’t seem crazy.)

So under the extreme assumptions that (1) all blocks have 150 people, and (2) all blocks have an equal probability of producing a top economist, the odds that you pick a random block and it turns out that two kids growing up on Everit St. would become top economists is about 1.6 billion to 1. Under these assumptions, the chance of any block in America yielding two top economists would be roughly 40,000 to 1.

Was it something in the water on Everit Street? Probably not. By far the strongest predictor of getting a Ph.D. in economics these days is having a parent who is a professional economist. This is just a partial list, but off the top of my head I can think of the following economists whose children got/will get a Ph.D within a five year period: George Akerlof/ Janet Yellen, Ben Friedman, Richard Levin, Rob Townsend, Francine Blau/Lawrence Kahn, and Lawrence Ianoconne. That is just the tip of the iceberg — I know there are many others as well. So if you start with a block that has three families headed by economists (as Everit Street had since Bob Shiller’s family lived on that block as well), the odds start looking a lot more like Ohio State vs. Florida.

Be sure to stay tuned for the next gripping installment of my analysis of the Everit St. Weekly.


prosa

The number of universities with even remotely reasonable shot at winning each of the national titles is well under 50. Quite possibly only half that number in each sport.

egretman

...all blocks have an equal probability of producing a top economist

That assumption must be really wrong. Don't you think? There are whole neighborhoods, lots of them, where parents don't even expect their kids to go to college. Such parents can't even begin to guide their kids to economics. Where would these kids expect to get the mentors necessary to steer them to become "great young economists"?

egretman

Having said that. I'm amazed that you got the odds down to just 40,000 to 1. If I'm right, it's really probably below 10,000 to 1.

But really, these amazing odd things are bogus events. If you had called it ahead of time, I would be impressed. But if you just sit and wait and are willing to take "amazing odd coincedences" anywhere they occur in your field of economics, or any field really, then the odds that something amazing happens everday is probably close to a certainty.

Try to get that point across to your undergraduate students, please!

jonathank

I think Enrico Fermi would use an example of piano tuners - estimate the number of pianos, figure out how many could be tuned by a tuner, how often they might be tuned, etc. and you could derive the number of piano turners in Chicago. But this is different because, as noted in the comment above, you're trying to analyze the odds of coincidence. That's easy if you constrain the problem to things like birthdays but I'm not aware of a good way to analyze a problem like this, where there are no natural constraints on the coincidence, without teasing out specific factors. What if the people both attended the same school with a great economics program? What if they knew each other because the families were in academia? Those what if's constrain the possibilities. Without those constraints, I'm not sure what the meaning of a coincidence really is other than that it's a coincidence. A raw comparison of all the people on all the blocks or all the team with basketball and football programs isn't worth much.

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RandyfromCanada

why only 50 with a chance ? in Basketball there are 64 teams in the final tournament and 200 who could have gotten in but didn't , any of these could win , please note l said could may not be realistic but still could happen ,,,
same in football before season starts 200 plus teams could win COULD be the key word so when computing all this question it is what is chances of one school winning both , is way more than your calculations .........

Keegan

In the NCAA basketball tournament, the two teams must also be seeded on opposite sides of the bracket. Otherwise they would be forced to meet prior to the championship.

KTROB

Not only did FLA meet OSU in the NCAA championships but they also met Arkansas in the SEC Championship game in both football and basketball before going on to meet OSU. Not only that but both games were played in the Georgia Dome.

fkaJames

Ok, let's be really honest here. There's a lot more at work here than growing up on the same block. Oster and Levin came from families that had highly educated parents, wealth, educational encouragement, and many other amenities that most people don't have. It isn't particularly extraordinary that children of professors become professors. It might be quite extraordinary if, say, Oster and Levin had both chosen to be dairy farmers or over-the-road truckers.

I would venture to guess, further, that if you were to survey their elementary school classmates, you'd find few fast food workers, janitors and hotel housekeepers, and a higher than average percentage of Yale graduates. Just as, if you surveyed Levitt's St. Paul Academy classmates, you'd find the same kinds of accomplishment, and it wouldn't look anything like the cohort at, say, Minneapolis North High School from the same period.

The point is, Levitt is leaving out most of the important vectors and focusing on one that is likely to be trivial in the exercise.

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snubgodtoh

Egretman's right, you must consider block effects-->
the P of 95% of blocks producing two economists is very low. The P of one of those trendy older neighborhoods near urban universities that seem to supply 90% of academics with housing is probably just under the average %age of economists relative total faculty in the avg. university. The P that two would come from the same academic block would be slightly lower, the P that both would be down-right brilliant is infinitesimal.

As for the championships: I would hypothesize that Florida and OSU are #2 and #1, respectively, regarding spending on athletics. These are mini professional teams, I bet either one would have handed to my beloved Rams last season.

pglaskowsky

I was a little disappointed by this piece-- assumptions as wrong as these aren't even good enough to use for argument's sake.

My own alma mater, the University of Miami, took home championships in both football and baseball in 2001, and there were several years in the 1990s when the school took one title or the other. For about ten years, the odds that UM would take both in the same year were only about one in ten.

Salviati

Hi,

Could you give a bit more information about the way you evaluate the odds for having 2 economists in the same block ?

It is an approximation, but in my estimation there is about 1 chance in 125 million to have 2 economists grown up in a chosen block (p = 1-((2*10^6-1)^50+50*(2*10^6-1)^49)/((2*10^6)^50))),
and about 1 chance in 1,600 to have 2 economists in any block (p=1-((50!*C(2*10^6,50))/((2*10^6)^50)))

My formulas are not right because they wrongly assume the same probability for each block to have an additional economist even when some blocks have already economists (and therefore less room to have a new one).

However, I think this is a good first approximation. Are you sure that you did not forget that having 2 economists grown up in the same block means having at least 2 economists (possibly more)?.

Thanks a lot.

saturninesylph26

I just have to say that the Everitt St. Weekly is absolutely adorable and anyone who hasn't checked out the link yet should do so, if only for the gardening tips and sports reviews. One of the boys (now a man, I guess) who wrote for it seemed to have a slight obsession with rocks. I wonder what he does for a living (if Oster was already talking about missing women back then).

egretman

By far the strongest predictor of getting a Ph.D. in economics these days is having a parent who is a professional economist.

I know it doesn't prove anything. But anecdotally, that seems to be my impression of almost every career that a kid chooses nowadays. Engineer's kids pick engineering. Doctor's kids become doctors. Teacher's kids become teachers.

This seems more so than in the 60's or 70's. I guess most mentoring is done by parents now. Go figure.

Jim Johnson

prosa is right. the number of 50 universities having the chance to win both titles is a stretch.

Some basketball schools, Georgetown for example, don't play I-A football. Or their football teams are not among the elite (North Carolina, Connecticut, Duke)

Moreover, the number of elite football programs is really about 30. These are the programs that tend to populate preseason Top 25 polls in football. Of them, maybe 20 also have elite basketball programs.

So the odds are not 1 in 1,225 ... but a more realistic 1 in 190.

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Here are the 2007 Sweet 16 and their respective finishes in the final 2006 CBS Sportsline poll of all 119 teams

Florida (1)
Ohio State (2)
Southern Cal (6)
Tennessee (26)
Texas A&M (32)
UCLA (43)
Oregon (53)
Kansas (62)
Pittsburgh (68)
Vanderbilt (76)
North Carolina (91)
Memphis (110)
Butler (I-AA)
UNLV (I-AA)
Southern Illinois (I-AA)
Georgetown (I-AA)

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twobitsprite

You're assuming that all American's live on a city block. A large enough portion live off of rural roads, which can hardly be characterized as a "block".

Craig

A better way to figure out the odds (without so many arbitrary assumptions) is to take the odds of a particular team winning the NCAA tournament and the odds for the same team winning the BCS from an online gaming site's futures betting. You can get similar odds from any betting site--they all use standardized handicapper companies.

Since these people actually make a living from predicting sports winners, you can assume they are good estimates.

Using the futures odds for Florida winning the 2008 BCS (8/1 on bodog.com)and the odds for Florida winning the 2008 NCAA tournament (not yet available, but I'm assuming it'll be about 12/1 since they will probably lose their best players), you get 96/1. Considering the NCAA has been around since 1910 and this feat has been accomplished once (1 time in 97 years), this number seems just about right.

As for why it was Ohio State both times, that's a little harder. Also, Arkansas was Florida's SEC championship opponent both times, too. The planets must have just aligned this year.

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Yaguar

I'm not at all certain about your math on the two economists. Even if we take all your assumptions to be true, I think the math itself might be faulty.

The easier way of thinking about the problem is "what is the probability that no two of the top fifty economists are on the same block?" rather than the probability that they are.

Take the first economist. He can live in any of the 2 million blocks. It doesn't matter. The second economist, however, can only live in 1,999,999 of the 2 million blocks. (The ones that aren't already taken.) So the probability of the top two economists not living on the same block is 1,999,999/2,000,000. Now add the third economist. He can live on any of 1,999,998 blocks to keep our condition true. So for three economists, it's 1,999,998/2,000,000 x 1,999,999/2,000,000 x 2,000,000/2,000,000. For four economists, it's 1,999,997/2,000,000 1,999,998/2,000,000 x 1,999,999/2,000,000 x 2,000,000/2,000,000.

You see the pattern. Now, before I get you my answer, I'd like to make the qualification that I ignored the effect of "occupied" blocks now having only 149 people instead of 150. However, that effect is so negligible that I omitted it for simplicity's sake. It could mess with the answer a little bit. Also, I haven't checked my work, so there's a chance I missed something big.

But I get a ~0.9939 probability that there aren't two top economists on the same block. Or a .00061 chance that there are.

That's about 1 in 1633. That's what the poster in post 11 got, too. When you take into account the obvious factors involved, that some blocks are much, much more likely to produce economists than others, the coincidence doesn't look nearly so impressive anymore.

This reminds me a lot of the famous probability problem about a group of a few dozen people in a room. It is extremely likely that at least two have the same birthday, much more than people believe. 365 seems like a whole lot of days, and surely a few dozen people isn't enough to create a shared birthday. You only have a 1/365 chance of sharing a birthday with each other person in the room. But what you don't realize is that there are so many different combinations of people who can share a birthday that there's a very good chance.

2 million seems like a lot of blocks, and given 50 people, it's hard to believe that any two share a block. But there are 1225 different pairings of those 50 people, so it's actually not so spectacularly unlikely that one of those different pairings shares a block.

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ManipulationNation

To maximize the chances of having two of the world's top 50 economists grow up on the same block, let's assume all economists come from parents of economists.

How many Ph.D. economists were there in the world one generation ago? I have no idea, but let's say 100,000. Then let's assume that 100 of them worked at each of 600 different locations and the rest were spread out elsewhere. Of the 100 at each location, economists already there help some of the newcomers find housing, so let's assume that two eonomists come to live on the same block in each of 600 locations.

Of the 600 opportunities for a match, we need for both families on the block to have kids (That may take us down to 400), we need for at least one kid in each family to get a Ph.D in Economics (That may bring us from 400 to 25), and we need for them to be amongst the best 50 young economists in the world (Let's say 50 chances left out of 50,000 "young" economists). So we have 25 opportunities x .001 x .001.

By those assumptions, I get this happening once every 20,000 generations.

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djfedder

please please please stop....my Texas instrument 64 calculator has melted on my desktop, my ears are bleeding and I swear I just saw a drone being piloted by two young economists

TheQuitter

the OSU/FL seems more improbable. like you said, one indicator of a child growing up to be a phd economist is based upon the parent.

soo.. i'm thinking it's more like, what are the odds that sons and daughters of economists become world class economists? b/c if you're an economist and you get a job at the u of chicago, then someone else wants to join. the new guy joining asks the veteran, "hey so where are some good neighborhoods to live around here?" you get the drift.