Statistics, Coin-flips & one reason for racing

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Jim Watt
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Statistics, Coin-flips & one reason for racing

Post by Jim Watt » Fri Mar 31, 2006 6:04 am

:D :shock: 8) Greetings to the Odd person and Oddsmaker who shows up to the lecture. We want to talk today about why [1] gathering information, (which for purposes of this post we'll define as (a) honest and (b) definite) is hard and why [2] extrapolating or predicting from it drives men mad.

In the first place, let's take the simple coin flip: we assign a committee to collect outcomes (that takes care of honesty) and define those outcomes as, and only as, one of 2 possible outcomes (heads/tails).

If, after what seems a reasonable number (and we'll agree that this can be --and will be-- argued about!) of trials we come up with the following: 342 tails; 12 heads, can we conclude anything?

Those who raised their hands and said "It's Bernie Ecclestone's coin!" may go to the head of the class :D

Because that's merely saying that the coin is not perfectly balanced.

Because if it were, every single trial would have a 50% chance of being heads or tails. And, now here comes the tricky part, so pay attention --especially if you think you know this!

IF THE COIN IS PERFECTLY BALANCED , AS THE NUMBER OF FLIPS INCREASES, THE RESULTS OF THE SERIES ARE INCREASINGLY LIKELY TO SHOW A SMALLER AND SMALLER DEVIATION FROM THE PERFECT 50:50 RATIO.

But, even in this crazily precise world of coin flips (that is only two possible outcomes) it is ONLY LIKELY. It is not required. The reason casinos stay in business is because ordinary saps cannot HELP themselves and if they're wrong about the coin, which is always possible, and even though it is Bernie's coin, it COULD be perfectly balanced, so on the next toss, if it is, it really COULD come up tails as easily as heads.

Of course, if it isn't balanced, the statistics you have gathered on it will show, if you continue to gather them a greater and greater liklihood to arrive at a measurable probablity on any given throw of tails showing up.

All this means, in layman's racing terms, is that when you examine an argument based on the collection of some data you have to know what is being measured and how it is being recorded.

Remember a couple of seasons ago in Brazil when Fisi won his first GP? Or was it Kimi? Or was it neither? Or was it both? The problem is that there are always (in a GP) several possible outcomes -- and by the time we have enough data to make reasonably accurate predictions, the season is over.

That's why we race. To find out, really, who won -- and then to argue about whether or not he (or she) should have or would have or could have if if if

Still. It's fun to collect data and part of the excitement of this season, for us, at least, if not for him, is how long J.B. can go before he busts the nut. Given the complexities he could be the best driver in the history of the world and retire as the best one never to win a race.


:roll: :roll: :roll: :lol: :roll: :lol: :roll: Jim
My Racing Gods: Fangio, Vukovich; Senna & Mears --all racers all the time; graceful winners & generous in defeat, but never giving up!!

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Post by JayVee » Fri Mar 31, 2006 11:01 am

:good: :good:

I did the stats on the World Champions on another thread but here is a summary:

46% of World Champions win their title within 4 seasons of their debut
71% of World Champions win their title within 5 seasons of their debut

Only 29% of World Champions took more than 5 seasons to win the title and only 14% of World Champions take more than 7 seasons to win the title

As for the driver with the most races without a win, that goes to Andrea De Cesaris with 208 followed by our favourite commentator Martin Brundle :shock: :shock: at 158 (how can he describe the feeling of winning a Formula 1 race when he has never won one - let alone explaining what happens to a driver after their first win :shock: :shock: :shock: :shock: )
Button is 10th with the highly rated Heidfeld right behind :shock: :shock: :up: :cheers:
I'm back and yes supporting Alonso "The Cute" in the Ferrari!

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Post by schmorbraten » Sun Apr 02, 2006 1:04 pm

i'm a fan of statistics. i haven't found a software or website yet which answers all my (statistical) questions 8) . Statistics can be very interesting in their own right as well as very revealing. But they're utterly useless when discussing whether a particular driver is capable of winning a wc or not, or whether he's now less likely to do so now that he's already done x gps. Statistics also teach us this: everything is possible. If 14% of the champions won their first wc after more than seven years, then almost everyone on the grid right now could well still be up to becoming a wc. And even Ralf, Rubens and David could take consolation from that. See?

We all know that many wcs haven't been decided by driver talent or overtaking spirit or whatever the driver in question could be lauded for, but by superior tyres, a superior car, a superior race strategy, a superior cheating talent within the engineering departments ... statistics are not only influenced by driver skill, but by many many other factors.

And when i, for example, think: 'jenson has all it takes but the car to do it up till now' or 'alonso only won last year because kimis car broke down all the time', then statistics are pointless. they don't change anything, they don't prove i'm right and everyone is (sadly ;-) ) still very well entitled to have a different view.

i don't want to say anything against statistics, but the thing which catches my eye is that they're always dragged into the arena at the wrong moment: when people are exchanging their (very interesting and revealing) views about the ifs and woulds and coulds and so on. they tend to heat things up and provoke even more usage of statistics by the ones who don't agree with the opinion in question, which doesn't lead to anything useful.

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Post by Jim Watt » Tue Apr 04, 2006 11:55 pm

:good: :coool:

thanks Jay Vee for the numbers & schmorbraten for the observation on the (emotional) use of statistics.

probably the reason the percentages slump so rapidly is not so hard to find; it's just hard (for fans) to accept:

the owners (makers) of the fastest machines like to turn them over to those winning races or, in their opinion, likely to do so.

everyone wants to get a fast driver under contract for as little money as possible (anyone can pay a fortune for a fast driver [Toyota anyone?], but the goal is to pay as little as possible)

hence fast drivers (or those perceived to be fast) more quickly get a shot at fast cars (Michael; Ayrton, Juan Manuel; Kimi; Fernando; --and now, Nico)

Jenson was perceived as fast, but you want to make any bets about Honda's plans for next year? I know they make fast cars and they want a WC before Toyota. So I expect them to rush Nico big time. bye bye Rubino, we hardly knew ye... And how about that Heidfeld lad?

All I'm saying is, especially after Melborne, I'd not like to be representing Jenson before the Honda board of trustees.

for the immediate future, of course, Kimi and Fernando will have fast cars; the question is whether that will be enough.

I love racing.

Jim
My Racing Gods: Fangio, Vukovich; Senna & Mears --all racers all the time; graceful winners & generous in defeat, but never giving up!!

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Post by JayVee » Wed Apr 05, 2006 5:02 pm

schmorbraten wrote:But they're utterly useless when discussing whether a particular driver is capable of winning a wc or not, or whether he's now less likely to do so now that he's already done x gps. Statistics also teach us this: everything is possible. If 14% of the champions won their first wc after more than seven years, then almost everyone on the grid right now could well still be up to becoming a wc. And even Ralf, Rubens and David could take consolation from that. See?
I fully agree! The reason for my post was a result from another discussion in another thread where I said that an exceptionally good driver would either jump straight into a competitive car or move into one a year or two into his F1 career, then of course it is up to him and his team (and a bit of luck to win the championship) and so I decided to look up the number of seasons it took (and the number of races) for all the world champions and the stats showed that nearly half of them have won within 4 years of their debut.
Does this stat mean that Webber, Button or even Barrichello will never be world champions, absolutely not but what the stats say is that historical data shows it will be harder for them.
I'm back and yes supporting Alonso "The Cute" in the Ferrari!

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Post by Julian Mayo » Sun Apr 23, 2006 1:50 am

Beware the Heffalump 8)
The Mountain is a savage Mistress.

Jim Watt
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Post by Jim Watt » Wed May 17, 2006 1:33 am

:D

I'll bite Julien. Who's the heffalump? I'd make Kimi the BanderSnatch and probably Fernando is a good candidate for Jube Jube bird. But who's the heffalump? Ralph?

jim
My Racing Gods: Fangio, Vukovich; Senna & Mears --all racers all the time; graceful winners & generous in defeat, but never giving up!!

Julian Mayo
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Post by Julian Mayo » Wed May 17, 2006 8:10 am

Jim Watt wrote::D

I'll bite Julien. Who's the heffalump? I'd make Kimi the BanderSnatch and probably Fernando is a good candidate for Jube Jube bird. But who's the heffalump? Ralph?

jim
:shock: got it in one :shock: :lol: :wink:
The Mountain is a savage Mistress.

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