# Armstrong fast on his bike, but not great at probability theory.

Discussion in 'Road Cycling' started by Andrew Albright, Jun 30, 2003.

Not open for further replies.
1. ### Andrew Albright Guest

So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.

In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
odds will tell you the chances decrease the more you go along". [The author of the article, Bob
Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
with anyone'].

Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16, less
than 10%; the chance of getting 5 heads in a row is 1 in 32.

However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
getting a head when he flips the coin the fifth time is 1 in 2.

It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.

Now I know that this is probably over the heads of most of you, but I thought that I would try to
educate you all anyway.

Tags:

2. ### Tritonrider Guest

>[email protected] (Andrew Albright)

>So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
>In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
>odds will tell you the chances decrease the more you go along". [The author of the article, Bob
>Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
>with anyone'].
>
>Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
>about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
>The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16, less
>than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
>However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
>getting a head when he flips the coin the fifth time is 1 in 2.
>
>It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
>Now I know that this is probably over the heads of most of you, but I thought that I would try to
>educate you all anyway.
>

Missionary work to enlighten the heathen by internet? "1,2,3, lots" I got skoolin in
ciphers. Bill C

3. ### Tom Kunich Guest

"Andrew Albright" <[email protected]> wrote in message
news:[email protected]...
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics
get
> tricky with any streak. The odds will tell you the chances decrease the more you go along". [The
> author of the article, Bob Ford, compounds the error with his analysis of Armstrong as being a
> person who can 'crunch numbers with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads
in
> a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but
I
> thought that I would try to educate you all anyway.

We don't have your PhD, but then most of us ARE bright enough to know that ignorant rant is so far
off base as to show your own weaknesses.

Flipping a coin gives equal chances of coming up heads or tails. A bicycle race includes chance only
as a side issue.

4. ### Mark Janeba Guest

Andrew Albright wrote:
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

Lance's math sounds like BS, but your coin flipping analogy is too. yes, when you flip a coin
repeatedly, the odds don't change from one flip to the next. I've given that lecture many times.

But the trouble is, when you win the tour repeatedly, ... you get OLDER and the odds (if there are
such a thing) DO change from one win to the next. Age, being marked by the peloton, etc - all change
the odds from one year to the next for serial winners.

Truth is, there's really NO way to figure odds for this sort of thing, just lots of educated
guessing and gambling.

5. ### Boyd Speerschne Guest

[email protected] (Andrew Albright) wrote in
news:[email protected]:

> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

Andrew, Winning the tour is not as cut and dry as flipping a coin. When flipping a coin the odds
stay the same. When riding the tour the opposing teams get reshuffled every year, younger guys get
stronger and faster, and Armstrong doesn't get any younger. So, relative to last year, what he said
is a true statement. This also holds true when you take into account the odds of the streak
continuing given past history. This is probably more along the lines of what LA was referring to; as
opposed to the literal probablity of himself actually acheiving the streak.

ie.,

2 TDFs in a row... Bobet, Anquetil, Merckx, Hinault, Indurain, Lemond, Armstrong, Hinault, and maybe
more back in the day. 3 TDFs in a row... Bobet, Anquetil, Merckx, Hinault, Indurain, Lemond,
Armstrong 4 TDFs in a row... Anquetil, Merxkx, Indurain, Armstrong 5 TDFs in a row... Indurain

In this case the odds go from 7/8+ to 4/7 to 1/4.

Since LA has a strong respect for the history of the tour, I think he was probably just trying
to point out that its very hard to win five in row. So hard, in fact, that only one man has done
it so far.

- Boyd S. minor in mathematics, class of 1998

6. ### Urhome Guest

Chances are, even your interpretation is a bit odd. What I think he's getting at is that there's a
very low probability that, by now, all of the other riders and team strategists don't know all about
LA's strengths and weaknesses. There now will be more than a little desperation in the planning
rooms of the other teams. So, the probability is now much higher that competitors' will employ game
theory to achieve their goals and that can spoil the chances of a "favorite" in any race, since
their major objective is not winning the race but beating the leader so that there's at least a
chance for themselves.

"Andrew Albright" <[email protected]> wrote in message
news:[email protected]...
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

7. ### Dan Guest

[email protected] (Andrew Albright) wrote in message
news:<[email protected]>...
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

Yo, WTF does this have to do with riding a bike, dude?

8. ### David Ryan Guest

Andrew Albright wrote:
>
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

Looks like most people here don't give a flip

9. ### Dick Durbin Guest

[email protected] (TritonRider) wrote in message
news:<2[email protected]>...
> Missionary work to enlighten the heathen by internet? "1,2,3, lots" I got skoolin in ciphers.

Or, as we teach in NASCAR country, "One, two, Earnhardt...."

Dick Durbin

11. ### Tom Schulenburg Guest

"Andrew Albright" <[email protected]> wrote in message
news:[email protected]...
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].
>
> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.

Apples and Oranges - No comparrison

The
> chance of flipping a coin four times in a row and getting heads all four times is 1 in 16, less
> than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
> However, if someone has flipped a coin and already has flipped four heads in a row, the chance of
> getting a head when he flips the coin the fifth time is 1 in 2.
>
> It is basic probability theory that each test (flip of the coin) is indepedent of previous tests.
>
> Now I know that this is probably over the heads of most of you, but I thought that I would try to
> educate you all anyway.

So, by this reasoning, anyone who wins a race has a 50% chance of winning the next one? You would be
correct in your statement if winning the race was a "random" result without influence. I think Lance
is correct in stating that the probability goes down, but not necessarily as a result of winning 4
in a row, but more of a result of being another year older. I think the mathematics get tricky
because it's hard to factor in the luck involved (crashes, sickness, etc), the fact that younger
riders are gunning for him, etc. Because the influences do change from one year to the next, It
would seem to me that Lance was correct.

-T

12. ### Ronaldo Jeremia Guest

Boyd Speerschneider <[email protected]> wrote in message
news:<[email protected]>...
> [email protected] (Andrew Albright) wrote in
> news:[email protected]:
>
> > So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
> >
> > In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak.
> > The odds will tell you the chances decrease the more you go along". [The author of the article,
> > Bob Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch
> > numbers with anyone'].
> >
> > Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> > about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads'
> > going. The chance of flipping a coin four times in a row and getting heads all four times is 1
> > in 16, less than 10%; the chance of getting 5 heads in a row is 1 in 32.
> >
> > However, if someone has flipped a coin and already has flipped four heads in a row, the chance
> > of getting a head when he flips the coin the fifth time is 1 in 2.
> >
> > It is basic probability theory that each test (flip of the coin) is indepedent of previous
> > tests.
> >
> > Now I know that this is probably over the heads of most of you, but I thought that I would try
> > to educate you all anyway.
>
> Andrew, Winning the tour is not as cut and dry as flipping a coin. When flipping a coin the odds
> stay the same. When riding the tour the opposing teams get reshuffled every year, younger guys get
> stronger and faster, and Armstrong doesn't get any younger. So, relative to last year, what he
> said is a true statement. This also holds true when you take into account the odds of the streak
> continuing given past history. This is probably more along the lines of what LA was referring to;
> as opposed to the literal probablity of himself actually acheiving the streak.
>
> ie.,
>
> 2 TDFs in a row... Bobet, Anquetil, Merckx, Hinault, Indurain, Lemond, Armstrong, Hinault, and
> maybe more back in the day. 3 TDFs in a row... Bobet, Anquetil, Merckx, Hinault, Indurain, Lemond,
> Armstrong 4 TDFs in a row... Anquetil, Merxkx, Indurain, Armstrong 5 TDFs in a row... Indurain
>
> In this case the odds go from 7/8+ to 4/7 to 1/4.
>
> Since LA has a strong respect for the history of the tour, I think he was probably just trying
> to point out that its very hard to win five in row. So hard, in fact, that only one man has done
> it so far.
>
> - Boyd S. minor in mathematics, class of 1998

Assorted r.b.r. dumbasses:

Reread this portion and then reconsider AA's remarks:

In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
odds will tell you the chances decrease the more you go along". [The author of the article, Bob
Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
with anyone'].

Albright's right - Armstrong is talkin' some voodoo math here.

-RJ

13. ### K. J. Papai Guest

[email protected] (Andrew Albright) wrote in message
news:<[email protected]>...
> So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
>
> In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak. The
> odds will tell you the chances decrease the more you go along". [The author of the article, Bob
> Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch numbers
> with anyone'].

Albright, you're being schooled big time. Since when does racing the Tour come down to pure chance?

> Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads' going.
> The chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> less than 10%; the chance of getting 5 heads in a row is 1 in 32.
>
Duhh... Most people with even half a brain know this by the time they're 17 years old.

-Ken

14. ### Dashi Toshii Guest

"Tom Schulenburg" <[email protected]> wrote in message
news:[email protected]...
>
> "Andrew Albright" <[email protected]> wrote in message
> news:[email protected]...
> > So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row.
> >
> > In a recent article in the Inqy, Armstrong said, "The mathematics get tricky with any streak.
> > The odds will tell you the chances decrease the more you go along". [The author of the article,
> > Bob Ford, compounds the error with his analysis of Armstrong as being a person who can 'crunch
> > numbers with anyone'].
> >
> > Most of you reading this probably aren't all that smart, so let's pretend that we aren't talking
> > about Tour of France wins, but rather flipping a coin and trying to get a streak of 'heads'
> > going.
>
> Apples and Oranges - No comparrison
>
> The
> > chance of flipping a coin four times in a row and getting heads all four times is 1 in 16, less
> > than 10%; the chance of getting 5 heads in a row is 1 in 32.
> >
> > However, if someone has flipped a coin and already has flipped four heads in a row, the chance
> > of getting a head when he flips the coin the fifth time is 1 in 2.
> >
> > It is basic probability theory that each test (flip of the coin) is indepedent of previous
> > tests.
> >
> > Now I know that this is probably over the heads of most of you, but I thought that I would try
> > to educate you all anyway.
>
> So, by this reasoning, anyone who wins a race has a 50% chance of winning the next one? You would
> be correct in your statement if winning the race
was
> a "random" result without influence. I think Lance is correct in stating that the probability goes
> down, but not necessarily as a result of winning
4
> in a row, but more of a result of being another year older. I think the mathematics get tricky
> because it's hard to factor in the luck involved (crashes, sickness, etc), the fact that younger
> riders are gunning for
him,
> etc. Because the influences do change from one year to the next, It would seem to me that Lance
> was correct.
>
> -T

Yes you are correct, Albright (oxymoron) is wrong.

Dashii

15. ### Dan Guest

Fred Marx <[email protected]> wrote in message news:<[email protected]>...
>
> Heads I ride Tails I drink Beer?

Why do they have to be mutually exclusive? I used to enjoy riding in central park on lazy sundays.
Do a few loops, buy a few bottles (with paper bag) from the homeless guys selling beer from a
backpack on the Sheep Meadow while soaking up the late afternoon rays.

16. ### Donald Munro Guest

urhome wrote:
> ... So, the probability is now much higher that competitors' will employ game theory to achieve
> their goals and that can spoil the chances of a "favorite" in any race, since their major
> objective is not winning the race but beating the leader so that there's at least a chance for
> themselves.

Cycling team managers/pros conversant with game theory ? That's like George Bush understanding the
theory of relativity.

17. ### Dashi Toshii Guest

"Donald Munro" <[email protected]> wrote in message
news:[email protected]...
> urhome wrote:
> > ... So, the probability is now much higher that competitors' will employ game theory to achieve
> > their goals and that can spoil the chances of a "favorite" in any race, since their major
objective
> > is not winning the race but beating the leader so that there's at least
a
> > chance for themselves.
>
> Cycling team managers/pros conversant with game theory ? That's like George Bush understanding the
> theory of relativity.

That sounds about right. Apparently Bush was a beneficiate of the Affirmative Actions program to get
into Yale. He scored 180 points below the median on the admission exam for his entering class at

university.

That's Affirmative Action at work!

Dashii

19. ### Dick Durbin Guest

Boyd Speerschneider <[email protected]> wrote in message
news:<[email protected]>...
> > Or, as we teach in NASCAR country, "One, two, Earnhardt...."
> >
> > Dick Durbin
>
> Who?

Kinda like Eddy Merckx on four wheels....except he's dead.

20. ### K. J. Papai Guest

"Dashi Toshii" <[email protected]> wrote in message news:<[email protected]>...
> "Tom Schulenburg" <[email protected]> wrote in message
> news:[email protected]...
> >
> > "Andrew Albright" <[email protected]> wrote in message
> > news:[email protected]...
> > > So everyone knows that Lance Armstrong is trying to win his 5th Tour of France in a row...
> > > Most of you reading this probably aren't all that smart, so let's pretend that we aren't
> > > talking about Tour of France wins, but rather flipping a coin and trying to get a streak of
> >
> > Apples and Oranges - No comparrison
> >
> > The
> > > chance of flipping a coin four times in a row and getting heads all four times is 1 in 16,
> > > less than 10%; the chance of getting 5 heads in a row is 1 in 32.
> >
> > So, by this reasoning, anyone who wins a race has a 50% chance of winning the next one? You
> > would be correct in your statement if winning the race
> was
> > a "random" result without influence. I think Lance is correct in stating that the probability
> > goes down, but not necessarily as a result of winning
> 4
> > in a row, but more of a result of being another year older. I think the mathematics get tricky
> > because it's hard to factor in the luck involved (crashes, sickness, etc), the fact that younger
> > riders are gunning for
> him,
> > etc. Because the influences do change from one year to the next, It would seem to me that Lance
> > was correct.
> >
> > -T
>
> Yes you are correct, Albright (oxymoron) is wrong.

What are the odds of A. V. AlBright accepting defeat here?