FORUMula1.com

[spankyham]

Very interesting; never going to happen in a million years; frankly Massa is not that good a driver, making up 100 points in four races!

Not that I wouldn't love to see it happen; I suspect that Ferrari have an emergency remote cut off switch in Massa's car if he refuses to yield to Alonso!

Dang, we've been discovered. Perhaps he used these to work out what's really happening

[Fred_C_Dobbs]

how about making a spread sheet for your daily medication

A bit harsh

Reality often is.

And I'm talking that real reality, not that medication-induced stuff.

[IceManpjn]

Law of probability does catch up with everyone.

You're doing it wrong.

As a simple example, if we do a basic coin toss (heads or tails) and if there's nothing artificial going on with the coin or with me in any way manipulating the outcome of the coin toss, then probability would put the results of the coin toss at 50-50; 50% chance of heads and 50% chance of tails. What needs to be understood is that the outcome of the second coin toss isn't influenced by the results of the first. The results of a tenth coin toss isn't impacted by the results of the previous nine. It's important to understand that just because there's a 50-50 chance doesn't mean that if the first toss came up heads that the second must come up tails to balance it out at 50-50. The fact remains that even if heads came up on the first toss there's still only a 50% chance of tails on the second, and nothing higher. If seven of the first nine tosses were heads, on the tenth there would still only be a 50% chance of it coming out tails. Unless I artificially manipulate the results, tails will never have more than a 50% chance no matter how often heads comes up on previous tosses, even though probability suggests they should average 50-50.

[JamesToohey]

Law of probability does catch up with everyone.

You're doing it wrong.

As a simple example, if we do a basic coin toss (heads or tails) and if there's nothing artificial going on with the coin or with me in any way manipulating the outcome of the coin toss, then probability would put the results of the coin toss at 50-50; 50% chance of heads and 50% chance of tails. What needs to be understood is that the outcome of the second coin toss isn't influenced by the results of the first. The results of a tenth coin toss isn't impacted by the results of the previous nine. It's important to understand that just because there's a 50-50 chance doesn't mean that if the first toss came up heads that the second must come up tails to balance it out at 50-50. The fact remains that even if heads came up on the first toss there's still only a 50% chance of tails on the second, and nothing higher. If seven of the first nine tosses were heads, on the tenth there would still only be a 50% chance of it coming out tails. Unless I artificially manipulate the results, tails will never have more than a 50% chance no matter how often heads comes up on previous tosses, even though probability suggests they should average 50-50.

Although you are entirely correct in one way, if we look at it in another it's a little different... lets say Webber's non-points finish was in the first race.

Therefore he would have had 14 points finishes in a row.

Now let's say, his chances of being in the points are 50-50, same as the coin. For the first race, the odds would be 1/2. Now for him to finish in the points for two races in a row, the odds would be 1/2 * 1/2, 1/4. The odds of three in a row is 1/2 * 1/2 * 1/2, 1/8.

Although the odds for points finishes for Webber are much higher and you have to take motivation and all sorts of variables into account.

So although the chances for each race are 50-50, the laws of probability DO in fact catch up with you if you look at the season as a whole.

[What's Burning?]

I can't believe this wasn't factored in... the next race being Japan after all.

[spankyham]

Law of probability does catch up with everyone.

You're doing it wrong.

As a simple example, if we do a basic coin toss (heads or tails) and if there's nothing artificial going on with the coin or with me in any way manipulating the outcome of the coin toss, then probability would put the results of the coin toss at 50-50; 50% chance of heads and 50% chance of tails. What needs to be understood is that the outcome of the second coin toss isn't influenced by the results of the first. The results of a tenth coin toss isn't impacted by the results of the previous nine. It's important to understand that just because there's a 50-50 chance doesn't mean that if the first toss came up heads that the second must come up tails to balance it out at 50-50. The fact remains that even if heads came up on the first toss there's still only a 50% chance of tails on the second, and nothing higher. If seven of the first nine tosses were heads, on the tenth there would still only be a 50% chance of it coming out tails. Unless I artificially manipulate the results, tails will never have more than a 50% chance no matter how often heads comes up on previous tosses, even though probability suggests they should average 50-50.

Although you are entirely correct in one way, if we look at it in another it's a little different... lets say Webber's non-points finish was in the first race.

Therefore he would have had 14 points finishes in a row.

Now let's say, his chances of being in the points are 50-50, same as the coin. For the first race, the odds would be 1/2. Now for him to finish in the points for two races in a row, the odds would be 1/2 * 1/2, 1/4. The odds of three in a row is 1/2 * 1/2 * 1/2, 1/8.

Although the odds for points finishes for Webber are much higher and you have to take motivation and all sorts of variables into account.

So although the chances for each race are 50-50, the laws of probability DO in fact catch up with you if you look at the season as a whole.

For starters, F1 isn't coin-tossing - it's nowhere near that reliable
But in this case, Ice is right, assuming the supposition is that he has a 50-50 chance at each race, then no matter how many times he ends up with points, his next probability is still 50-50.
It's somewhat like asking people if in a 7/45 lottery would they ever pick the number 1,2,3,4,5,6 & 7 and most would say "no way", then try and explain to them that those numbers (1-7) have exactly the same chance of coming up as whatever the winning 7 numbers might end up actually being.

[Fred_C_Dobbs]

I can't believe this wasn't factored in... the next race being Japan after all.

History shows
again and again
How nature points out
the folly of men ....

[Hexagram]

how about making a spread sheet for your daily medication

[JamesToohey]

Law of probability does catch up with everyone.

You're doing it wrong.

As a simple example, if we do a basic coin toss (heads or tails) and if there's nothing artificial going on with the coin or with me in any way manipulating the outcome of the coin toss, then probability would put the results of the coin toss at 50-50; 50% chance of heads and 50% chance of tails. What needs to be understood is that the outcome of the second coin toss isn't influenced by the results of the first. The results of a tenth coin toss isn't impacted by the results of the previous nine. It's important to understand that just because there's a 50-50 chance doesn't mean that if the first toss came up heads that the second must come up tails to balance it out at 50-50. The fact remains that even if heads came up on the first toss there's still only a 50% chance of tails on the second, and nothing higher. If seven of the first nine tosses were heads, on the tenth there would still only be a 50% chance of it coming out tails. Unless I artificially manipulate the results, tails will never have more than a 50% chance no matter how often heads comes up on previous tosses, even though probability suggests they should average 50-50.

Although you are entirely correct in one way, if we look at it in another it's a little different... lets say Webber's non-points finish was in the first race.

Therefore he would have had 14 points finishes in a row.

Now let's say, his chances of being in the points are 50-50, same as the coin. For the first race, the odds would be 1/2. Now for him to finish in the points for two races in a row, the odds would be 1/2 * 1/2, 1/4. The odds of three in a row is 1/2 * 1/2 * 1/2, 1/8.

Although the odds for points finishes for Webber are much higher and you have to take motivation and all sorts of variables into account.

So although the chances for each race are 50-50, the laws of probability DO in fact catch up with you if you look at the season as a whole.

For starters, F1 isn't coin-tossing - it's nowhere near that reliable
But in this case, Ice is right, assuming the supposition is that he has a 50-50 chance at each race, then no matter how many times he ends up with points, his next probability is still 50-50.
It's somewhat like asking people if in a 7/45 lottery would they ever pick the number 1,2,3,4,5,6 & 7 and most would say "no way", then try and explain to them that those numbers (1-7) have exactly the same chance of coming up as whatever the winning 7 numbers might end up actually being.

As I said, I know it isn't 50-50.

As I said, for each race the chance that he finishes in the points is, lets say 50-50 (I understand that it isn't), no matter what.

But if you look at the season as a whole, before it began, the odds are different. Think about a tree diagram and then you'll understand:


The chances of the ball being red are 1/3 in three for the first pick and, similarly, 1/3 for the second pick. However, if you look at the two picks as a whole - the chances are 1/9 that you will get two reds in a row.

I hope you understand now.

[The Immortal Dragon]

Law of probability does catch up with everyone.

You're doing it wrong.

As a simple example, if we do a basic coin toss (heads or tails) and if there's nothing artificial going on with the coin or with me in any way manipulating the outcome of the coin toss, then probability would put the results of the coin toss at 50-50; 50% chance of heads and 50% chance of tails. What needs to be understood is that the outcome of the second coin toss isn't influenced by the results of the first. The results of a tenth coin toss isn't impacted by the results of the previous nine. It's important to understand that just because there's a 50-50 chance doesn't mean that if the first toss came up heads that the second must come up tails to balance it out at 50-50. The fact remains that even if heads came up on the first toss there's still only a 50% chance of tails on the second, and nothing higher. If seven of the first nine tosses were heads, on the tenth there would still only be a 50% chance of it coming out tails. Unless I artificially manipulate the results, tails will never have more than a 50% chance no matter how often heads comes up on previous tosses, even though probability suggests they should average 50-50.

Although you are entirely correct in one way, if we look at it in another it's a little different... lets say Webber's non-points finish was in the first race.

Therefore he would have had 14 points finishes in a row.

Now let's say, his chances of being in the points are 50-50, same as the coin. For the first race, the odds would be 1/2. Now for him to finish in the points for two races in a row, the odds would be 1/2 * 1/2, 1/4. The odds of three in a row is 1/2 * 1/2 * 1/2, 1/8.

Although the odds for points finishes for Webber are much higher and you have to take motivation and all sorts of variables into account.

So although the chances for each race are 50-50, the laws of probability DO in fact catch up with you if you look at the season as a whole.

You are both right, you are just facing the problem in two different ways. But you are saying the very same thing!

[racechick]

My head hurts!!
But if lewis doesnt win Massa would be an ACE champion

[Jabberwocky]

I think if you look at what statistician Persi Diaconis says you will notice that Alonso will win.

http://www.npr.org/templates/story/stor ... Id=1697475" onclick="window.open(this.href);return false;

Flipping a coin may not be the fairest way to settle disputes. About a decade ago, statistician Persi Diaconis started to wonder if the outcome of a coin flip really is just a matter of chance. He had Harvard University engineers build him a mechanical coin flipper. Diaconis, now at Stanford University, found that if a coin is launched exactly the same way, it lands exactly the same way.

The randomness in a coin toss, it appears, is introduced by sloppy humans. Each human-generated flip has a different height and speed, and is caught at a different angle, giving different outcomes.

But using high speed cameras and equations, Diaconis and colleagues have now found that even though humans are largely unpredictable coin flippers, there's still a bias built in: If a coin starts out heads, it ends up heads when caught more often than it does tails. NPR's David Kestenbaum reports.

*Note: In football's inaugural kickoff coin toss, the coin is not caught but allowed to bounce on the ground. That introduces an extra complication, one mathematicians have yet to sort out.

[Mr.Conte]

Actually Massa can mess it up for lots of people.
Lets say he lights a fire under his butt for the last 4 races.
Lets say Alonso wins two of the last 4 races and takes 2nd's in the other.
Massa takes 3rds for the last 4 races.
Ferrari would win the MFG championship and Alonso would be WDC.
It could happen?

[Hexagram]

My head hurts!!
But if Alonso doesnt win Webber would be an ACE champion

Fixed!

[racechick]

My head hurts!!
But if Alonso doesnt win Webber would be an ACE champion

Fixed!

He would be a reasonable choice (gone off him a little bit after Singapore ) But this is Massa's thread, and he'd be good too.