[Speaker] Riders ready, watch the gate.
This is BMX bicycle racing. It's basically an
acceleration contest, if not endurance,
and so the whole thing is it's like hard
drag racing, you know, it's get going really
fast, hold the lead and then carry it on
through to the end. So what you
do is you get three opportunities to
advance. They're called motos:
moto1, moto2, moto3. Some other
organizations have different rules, but
I'm talking about ABA; American bicycle
Association. You have eight lanes on a
track and to advance into the next round
you had to win one of the motos, okay?
That means- so you get into the first
moto, and usually a very good rider would
win it, he or she would sit down and then
the other seven riders would go into
the second moto;
then whoever won that would sit down.
Then there'd be a third moto for the
third rider. Then those three riders
would advance into the next level of
competition; at a big meet it could be
eighth finals, quarterfinals, semifinals;
but you're advanced, okay? So the big issue
is to get out of the first round, it's
like in basketball getting past the
first round of the playoffs.
Well there's eight riders and so you
have eight lanes. And lane 8 is
always called the one that is farthest
from where you turn. So if you turn left
this would be lane 8, if you turn
right this would be lane 8. - (Brady: The outside lane?)
It's the outside lane; you have to travel
further. If all riders were equally
talented you wouldn't win out of lane
8. I mean, if they all fell down or if
something happened, somebody nearly- but
in general, assuming that all riders are
equally talented, the chances of winning
out of lane 8 are very slim. - (Brady: A lot of people)
(watching might have seen the Olympic)
(Games or running races where we see)
(staggered lanes or we could have a tilted)
(start line; like an angled start line.)
(BMX racing doesn't compensate in this way?)
No. If you could keep people in
their lanes, you know, like you do
in track - you say you have to stay for
the first lap in your lane. But of course you don't;
and what happens- if you ever try to do
that these really aggressive riders, okay,
would just- in other words if somebody was
in front and they saw somebody starting
to pass him they would just move in
front of them and knock them down. So you
can't give someone an opportunity to be
in front of somebody else because
they'll move it out and it's gone. So
that doesn't work.
Years and years ago, when my son started
racing, everybody just rushed the gate
and just-- now notice that Lane 8
outside is no good, and lane 1 inside
it's too easy to get- for somebody to cut you
off or somebody to get you boxed in. So the
good lanes are usually 2, 3, 4;
maybe in an extreme case 5, but but
let's say 3 and 4. In the early
days people would rush to the track when
they said we're going to- okay let's
start the racing, and they'd run and get
into 3 or 4. So then they said, no
that's not fair. So then they decided,
okay what we're going to do is we're gonna call
these at random. Sometimes you'd
have a deck of cards, okay, and they'd
have 8 and you just pull the card
and that was your lane; or they have
an urn with balls in it and you pull one
and stuff. And at least that was fair, in
the sense that, you know, you had equally
likely chance to get any one of the
lanes. So that's how it went on for
years and years and years. At the start
of each moto - remember we have three
motos, so you have a random draw at the
start of moto 1, random draw at the
start of moto 2, random draw at the start of moto 3.
Now the problem was, that with that
random draw, there's a reasonably likely
chance that you could pull three 8s. And if
you are off somewhere, like my son once
was, we were in Shreveport Louisiana, and
he drew three 8s. Well, he'd rode gallantly, okay,
but he still didn't qualify into the
next round. - (Brady: So he got- he was unlucky?)
The curse of lane 8, the curse of lane 8.
So I said we need a better system. We
need one where my son can't get three
8s; or two 8s and a 7. A
colleague of mine who's a statistician;
we just started talking, and said let's
fix this.
Okay, we're mathematicians, we're hotshots;
let's fix this system. There were two
breakthroughs, okay two breakthroughs. The
first breakthrough was
let's not assign a lane independently
three times. Let's instead give you a
triple, and your triple would have three
numbers. An example, let's say it had
1, 5, 8 - that means you get Lane 1
in in the first moto, Lane 5 in the
second, and 8. And here's another major
breakthrough: instead of working
mathematically with the numbers of the
lanes like 1 and 2 and 3, we
decided to work with the priorities, okay?
1 meant the best lane, 2 meant the
second best and 8 meant the worst. That
has mathematical content. So we put
mathematical meaning into it by saying,
priorities. They're well ordered, they're
numbered, there's a 1 - it means
something, an 8 - it means something.
Those two breakthroughs: triples and
priorities. That's kind of subjective so
what you do is you ask a bunch of good
riders which one is their most desired,
and there's almost total agreement.
Almost- if you had to say anything it'd
almost always be lane 3. Sometimes
before, okay maybe, but it was almost the
same. Which was the worst? Everybody
would say 8. So maybe there's some
fuzziness in between, but almost all the
good riders would tell you the same
thing. So that- so that was not a problem.
(Brady: So did you do this? Was there some)
(kind of survey or poll?) - Yeah I did, every time.
I did it with my son and his friends. And
they thought that, you know, sometimes
there was a right answer and a wrong
answer; of course there wasn't. So now I
had to build a mathematical model that
says, how am I going to come up with the
very best set of eight triples that
will be the fairest? And then run it on
the computer, with an algorithm, to give
us the best. So we did. And what we did is,
we tried to say, look: everybody should have
the same. You know, if you if you summed
up priorities like maybe the priorities
like 1, 5, 8 as I said before; and
you sum them you know you're going to
get 14. Well maybe everybody should have
the same sum of priorities, that would be
a good fairness criteria; but you can't do
that. They're all going to be 13 or 14. So
you now you start playing mathematical
games about saying a model. So soon you
start to realize that the best solution
is going to have four 13s and four
14s. So that's already cutting
the data back a lot you see, it's already
saying oh now I don't have to search
everything. And so with that constraint,
that four are going to be 13 and four are
going to be 14 you start to do the search.
Out comes a situation where you get
these optimal eight triples. In less than
one second
we found 7,000 solutions, okay. So so yeah
but that's too many solutions, so-
(Brady: Doesn't that meant that's great? That you could just-)
No no no no. You say good things but look, in
in mathematics and physics, when you find
too many solutions that means you didn't
put enough information into your
mathematical model. The most beautiful
mathematics is there exists one solution,
see? And that's why in life we say, ah
there's one perfect marriage partner,
there's one perfect house, there's one
perfect- I'll grant you that there's
not but anyway we like that. So I spent
time with a student and we said, look: if
you're an average rider the third moto
is more important than the first and the
second, and I'm going to tell you why.
Because there's always some hotshot and
this hotshot is going to
win the first race. Then the second
hotshot will win the second. - (Brady: So they're not)
(in the third race?) - They're not in the
third race! So now you want to optimize
your chances in the third race. - (Brady: That's)
(when you want the prime lane?) - That's when
you want the prime lane. So I said let's
weight these sums so that they're not all
equal, and that a good lane in the third
moto is worth more than a good lane earlier.
And we put a little tiny bit of weighting on
there, and very simple; I mean like the
weighting was that maybe in the third
moto there's only six riders, so we
weighted it by maybe 8 over 6 or
something. That gave us the unique
solution. So we ended up with our optimal
solution. I say any reasonable
mathematician, or intelligent person, once
you told them, look think of priorities
and think of triples - they'd come up with
our system. That's what I say.
(Brady: Professor the only problem I see with your system is,)
(the priorities are very subjective and,)
(and Billy the BMXer might prefer lane 1 because)
(he's good on tight corners; and Sally)
(might like the outside lane because she)
(doesn't like crashes, and like different)
(riders might have different priorities)
(and not like your ball system.) - I mean of
course you're right, but you're really
fine-tuning at a level that doesn't
exist, okay? I mean the bulk of the riders-
so yeah so there's somebody who has some
particularly - well they're going to lose,
they're going to pay a price, okay. But you're
doing this for the bulk of the things.
And and granted there's always going to
be some kind of a - like that,
okay? And and and indeed you can say that.
But it's it's not a it's not a concern,
okay, and you just say we're going to do
this for the bulk of the riders, it's
going to take care of the bulk of the problems.
[Extras] In a certain sense, I wasn't trying to save the
world, I was trying to use mathematics in
something that would improve the quality
of my local life while my son was racing,
okay? And we did that, and and so to me it
was a validation of mathematics, okay, how
people go, oh mathematics is not useful.
Well mathematical thinking and the
mathematics allowed me to do something
very interesting.