37 replies to this topic

[Sancho Panza]

A remark in another thread that Alonso is 70 points ahead of Fisicella leads me to ask what are the largest points gaps on record between team mates? How did Schumi's or Senna's teammates fare?

[Schu]

it might be Schumi against his main teammate in 94 eventhough he only race 3/4 of that season.

[BorderReiver]

Originally posted by Sancho Panza
A remark in another thread that Alonso is 70 points ahead of Fisicella leads me to ask what are the largest points gaps on record between team mates? How did Schumi's or Senna's teammates fare?

Nevermind that . . .

WHAT HAVE YOU DONE WITH THE GREAT ELMYRA?!?! AND FOR THAT MATTER DEAR OLD LENIN??!!

WELL???

(I really hope you get this reference, or else the above will look a bit mad and scary).

[Sancho Panza]

WHAT HAVE YOU DONE WITH THE GREAT ELMYRA?!?! AND FOR THAT MATTER DEAR OLD LENIN??!!

The heros are not all dead!

The Man from La Mancha lives on!

[BorderReiver]

Originally posted by Sancho Panza


The heros are not all dead!

The Man from La Mancha lives on!

Welcome to the BB.

[Sancho Panza]

Welcome to the BB.

[Milt]

Originally posted by Sancho Panza
A remark in another thread that Alonso is 70 points ahead of Fisicella leads me to ask what are the largest points gaps on record between team mates? How did Schumi's or Senna's teammates fare?

If you'll settle for a 'percentage gap', rather than an actual 'points gap', then look no further than Button / Sato
Button is exactly 3500% ahead of his teammate.
Why am I NOT surprised?

[wawawa]

Originally posted by Milt
If you'll settle for a 'percentage gap', rather than an actual 'points gap', then look no further than Button / Sato
Button is exactly 3500% ahead of his teammate.

How about Fittipaldi who won the 1972 WDC with 61 points vs ZERO for all his team-mates put together! Those 61 points also won Lotus the WCC!

[Pilla]

Originally posted by Milt
If you'll settle for a 'percentage gap', rather than an actual 'points gap', then look no further than Button / Sato
Button is exactly 3500% ahead of his teammate.
Why am I NOT surprised?

Im sure there are countless examples of a team like Minardi or Jordan having one driver score 1 or 2 points and the other drivers scoring nothing therefore percentage does not work.

[Milt]

Originally posted by Pilla


Im sure there are countless examples of a team like Minardi or Jordan having one driver score 1 or 2 points and the other drivers scoring nothing therefore percentage does not work.

I have to agree!
I never did figure out how to divide by ZERO
But, in Sato's case he has earned at least one point, plus the ones that were taken away from him, early in the season, (even though his fuel tank was never even looked at, by anyone)

[Pilla]

Originally posted by Milt
I have to agree!
I never did figure out how to divide by ZERO
But, in Sato's case he has earned at least one point, plus the ones that were taken away from him, early in the season, (even though his fuel tank was never even looked at, by anyone)

Exactly you cant do percentages because not everyone scores points.

[Milt]

Originally posted by Pilla


Exactly you can do percentages because not everyone scores points.

I think that it would be more accurate to say that you CAN'T do percentages because you CAN'T DIVIDE BY ZERO.

The standard way to find the percentage difference between any two numbers is to divide the larger number by the smaller one, then subtract 1 from the result, and multiply that result by 100.

The problem is that '0' (Zero) will divide into ANY number, an infinite number of times.
This was a problem, and a joke, with very early computers.
If somebody foolishly, or intentionally, told an early computer to divide by zero, the computer went totally nuts, and burned itself out!

[kismet]

Incidentally, attempts to divide by zero tend to make math teachers go totally nuts even today. If repeated often enough, this can also lead to burn-out.

Anyway, I'm sure this is all too obvious for everyone but I'll point it out anyway. The better the car relative to the competition, the more difficult it should be for a driver to accumulate significantly more points than his teammate, in percentage terms (assuming equal reliability/"luck").

[Sean L]

Since zero divides into any number an infinite amount of times, we can say that 1 team mate (who scores at least a point) is infinitely better than the other if said team mate has zero points.

[Henri Greuter]

Originally posted by wawawa
How about Fittipaldi who won the 1972 WDC with 61 points vs ZERO for all his team-mates put together! Those 61 points also won Lotus the WCC!

Ralf against Zanardi at Williams in '99 comes to mind as a vaguely similar achievement.

And in '89 far the first 75 5 of the season Mansell had scored all points for Ferrari with Berger down at 0.


Henri

[mikedeering]

In terms of points, MS scored 92 in 1994. He had various teammates during that season (Lehto, Verstappen and Herbert). Combined, his teammates scored 11 points. Incidently, MS only counted 12 races that season due to DQ and bans. Points difference of 81. I can't think of a bigger gap in terms of points.

In many ways though Alonso's achievement is greater - Fisichella would rate higher than the teammates MS had in 1994. Lehto was injured, Verstappen and rookie and Herbert only got 2 races. To outscore Fisichella by 70 points when the Italian has such an excellent record against other teammates is impressive.

You might think the best season for Senna against a teammate would be 1986 or 1987 versus Dumfries and Nakajima. 1986 55-3 in Senna's favour for 52 point lead, in 1987 57-7 for a 50 point lead. However, in 1991 he actually outscored Berger 96-43 for a 53 point lead.

[Pilla]

Originally posted by Milt
I think that it would be more accurate to say that you CAN'T do percentages because you CAN'T DIVIDE BY ZERO.

The standard way to find the percentage difference between any two numbers is to divide the larger number by the smaller one, then subtract 1 from the result, and multiply that result by 100.

The problem is that '0' (Zero) will divide into ANY number, an infinite number of times.
This was a problem, and a joke, with very early computers.
If somebody foolishly, or intentionally, told an early computer to divide by zero, the computer went totally nuts, and burned itself out!

I meant cant obviously

[Frank Tuesday]

Originally posted by mikedeering
In terms of points, MS scored 92 in 1994. He had various teammates during that season (Lehto, Verstappen and Herbert). Combined, his teammates scored 11 points. Incidently, MS only counted 12 races that season due to DQ and bans. Points difference of 81. I can't think of a bigger gap in terms of points.

In many ways though Alonso's achievement is greater - Fisichella would rate higher than the teammates MS had in 1994. Lehto was injured, Verstappen and rookie and Herbert only got 2 races. To outscore Fisichella by 70 points when the Italian has such an excellent record against other teammates is impressive.

You might think the best season for Senna against a teammate would be 1986 or 1987 versus Dumfries and Nakajima. 1986 55-3 in Senna's favour for 52 point lead, in 1987 57-7 for a 50 point lead. However, in 1991 he actually outscored Berger 96-43 for a 53 point lead.

Actually, I would suspect that his gap over andretti in '93 was his biggest. I think he scored in the 60's and Andretti was in single digits(?).

[Don Speekingleesh]

In 1993 Senna had 73 points and Andretti had 7, but Hakkinen also scored 4.

[jimm]

Originally posted by Henri Greuter



Ralf against Zanardi at Williams in '99 comes to mind as a vaguely similar achievement.

And in '89 far the first 75 5 of the season Mansell had scored all points for Ferrari with Berger down at 0.


Henri

IF you mean the whole season this is absolutely incorrect. Berger won Portugal and finished 2nd at Spain and Monza. Berger: 21 pts, Mansell 38

[John B]

Originally posted by mikedeering


In many ways though Alonso's achievement is greater - Fisichella would rate higher than the teammates MS had in 1994. Lehto was injured, Verstappen and rookie and Herbert only got 2 races. To outscore Fisichella by 70 points when the Italian has such an excellent record against other teammates is impressive.

I agree, adding the points changes recently seem to favor closer gaps - more cars score at a higher % of the winner, and there are fewer on the grid to compete with.

Given other changes like # of races the percentage method is probably the most realistic - just disregard those tailenders

[thanos]

Originally posted by Milt
The problem is that '0' (Zero) will divide into ANY number, an infinite number of times.

Division by zero yields a undefined result, not an infinite one.

[Dmitriy_Guller]

Originally posted by thanos

Division by zero yields a undefined result, not an infinite one.

What's the difference?

[Henri Greuter]

Originally posted by jimm


IF you mean the whole season this is absolutely incorrect. Berger won Portugal and finished 2nd at Spain and Monza. Berger: 21 pts, Mansell 38

You are indeed right. It was a typo error within my original message instead of 75 5 it should read 75 %, But obviously I forgot to press the shift button as well or not deep enough.
Sorry.

Henri

[thanos]

Originally posted by Dmitriy_Guller

What's the difference?

Without going too much into mathematics, an undefined result is meaningless while an infinite result (unbounded limit) is not. Arithmetic operations involving infinity may be performed - this is not true with undefined numbers.

Division by zero is generally a sign that the problem is not properly set up or is being applied to a nonsensical situation. For example, when calculating per capita income (total income / size of population), it would be nonsensical to apply this formula to a group with a population of 0, which would yield a divide by zero situation.

In any event, this reveals the problem with comparing totals with ratios on the very low ends. It wouldn't make much practical sense to contend that a person who made only $1 their whole life had infinitely more financial success than a person who made $0.

[Youichi]

Originally posted by BorderReiver


Nevermind that . . .

WHAT HAVE YOU DONE WITH THE GREAT ELMYRA?!?! AND FOR THAT MATTER DEAR OLD LENIN??!!

WELL???

(I really hope you get this reference, or else the above will look a bit mad and scary).

BorderReiver, you've got to face it, there are no more heroes any more.

[armonico]

Originally posted by Milt

I never did figure out how to divide by ZERO

It is a mathematical feature.

Any figure divided by zero gives (or approximate to) infinite.

Then, you can even approximate towards - infinte, if the fugure is negative or + infinite, ifthe figure is positive. It si use to see the tendency of mathematical functions.

It is also use with mathematical limits in equations and functions.

Zero divided by any figure gives (or approximate to) zero.

[943yt8d]

You can use an approximate (a+1)/(b+1) or whatnot to avoid dividing by zero but it still doesn't make any sense to compare them generally. It's best to restrict the comparison to champions with a team member with the same amount of races or to look how big percentage of the total points did the champion bring in.

[Dmitriy_Guller]

Originally posted by thanos

Without going too much into mathematics, an undefined result is meaningless while an infinite result (unbounded limit) is not. Arithmetic operations involving infinity may be performed - this is not true with undefined numbers.

Division by zero is generally a sign that the problem is not properly set up or is being applied to a nonsensical situation. For example, when calculating per capita income (total income / size of population), it would be nonsensical to apply this formula to a group with a population of 0, which would yield a divide by zero situation.

In any event, this reveals the problem with comparing totals with ratios on the very low ends. It wouldn't make much practical sense to contend that a person who made only $1 their whole life had infinitely more financial success than a person who made $0.

Arithmetic operations involving infinity are so restricted that using 1/0 as infinity would not create any paradoxes. Both 1/0 and infinity are equally meangingless if thought of outside the context of implied limits. The higher the level of math I took, the less distinction I saw between 1/0 and infinity.

But, coming back to comparison, it's indeed a good point that proportions tend to become very unstable and meangless near the lower (or negative) ranges, while absolute differences become meaningless near the high ranges. The compromise metric that I can think of is computing the percentage of total team points that the driver earned. No matter the situation, the difference between drivers cannot be more than 100%.

[ensign14]

How about when Robb Gravett had points deducted in the BTCC one year? He ended the year on something like minus 2. So I beat him. If his team mate was on 10 points, his team mate was minus five times better than him. Which is really shite. Or good.

[Milt]

Originally posted by 943yt8d
You can use an approximate (a+1)/(b+1) or whatnot to avoid dividing by zero but it still doesn't make any sense to compare them generally. It's best to restrict the comparison to champions with a team member with the same amount of races or to look how big percentage of the total points did the champion bring in.

I think you've nailed it, but the formula for computing that percentage gets a little more complicated.

Using my original example of Button and Sato, so far this year....
Button has scored 36 points.
Takumo has scored 1 point.
So "total points" are 37

Now, from my second post in this thread...
"The standard way to find the percentage difference between any two numbers is to divide the larger number by the smaller one, then subtract 1 from the result, and multiply that result by 100"
So... 37, divide by 36 = 1.02777`
Subtract 1 = .02777`
Multiply by 100 = 2.777`
Now, this is where it gets a little tricky...
Subtract that 2.777` from 100 to get 97.222`

The 'result' is that Button has scored 97.2%, out of all the BAR Honda's team points, so far this year.

If anybody knows of an 'easier way' of accomplishing the above 'calculation', I'm all ears, because that's a lot of work!

[Dmitriy_Guller]

Originally posted by Milt
I think you've nailed it, but the formula for computing that percentage gets a little more complicated.

Using my original example of Button and Sato, so far this year....
Button has scored 36 points.
Takumo has scored 1 point.
So "total points" are 37

Now, from my second post in this thread...
"The standard way to find the percentage difference between any two numbers is to divide the larger number by the smaller one, then subtract 1 from the result, and multiply that result by 100"
So... 37, divide by 36 = 1.02777`
Subtract 1 = .02777`
Multiply by 100 = 2.777`
Now, this is where it gets a little tricky...
Subtract that 2.777` from 100 to get 97.222`

The 'result' is that Button has scored 97.2%, out of all the BAR Honda's team points, so far this year.

If anybody knows of an 'easier way' of accomplishing the above 'calculation', I'm all ears, because that's a lot of work!

Have you tried dividing 36 by 37? That would both be simpler and more correct.

[Clare]

Originally posted by Dmitriy_Guller

Have you tried dividing 36 by 37? That would both be simpler and more correct.

And so much easier

[Milt]

Originally posted by Dmitriy_Guller

Have you tried dividing 36 by 37? That would both be simpler and more correct.

Bingo! Thank you!
Much, MUCH, simpler way to arrive at almost the exact same number...
36/37 = .97297297 x 100 = 97.3 %

I wonder where/how that miniscule little difference 'creeps in'? Any clues on that one?

[Dmitriy_Guller]

Originally posted by Milt
Bingo! Thank you!
Much, MUCH, simpler way to arrive at almost the exact same number...
36/37 = .97297297 x 100 = 97.3 %

I wonder where/how that miniscule little difference 'creeps in'? Any clues on that one?

The difference is due to the fact that you calculated the ratio of lower scorer's points to higher scorer's points, a number which has some meaning, and then you subtracted it from 1 to get a number with no meaning. The difference is tiny in this case because Sato's point tally is, well, tiny. If you take two drivers with almost equal point tallies, you will quickly see the error in your calculations.

[Sancho Panza]

Actually I think it has some meaning. Milt seems to have calculated the score of the lower ranked driver as a % of the higher ranked driver's score - rather than the team total (the Dmitriy_Guller metric!).

I do agree that this metric is perhaps the best and simplest way to get a very rough evaluation.

[Milt]

Originally posted by Dmitriy_Guller

If you take two drivers with almost equal point tallies, you will quickly see the error in your calculations.

I see your point!
If I use Ralf Schumacher (39 points), and Jarno Trulli (43 points), the total for Toyota is 82 points, so far this season.
43/82 = .5243
Multiply .5243 by 100, to get the 'percentile value' of 52.43%
Out of all the points scored by Toyota this season, 52.43% were scored by Trulli.
He's underpaid, compared to Ralph, but I think we all knew that, before the season even started (my appologies to any Ralph fans out there)

If you do it the way I first suggested, (in post number 12 of this thread), it tells us that Trulli was 10.26% better than Ralph.
(43/39 = 1.10256, -1 = 0.10256 x 100 = 10.25, or 10.25%)
And, Ralph's 39 points, plus 10.25% = Trulli's 42.99` points, so either system is accurate.
So, another way to say all of the above is that Trulli scored 10% more points than Ralph, or 52% of Toyota's season's total, so far

But, my system does NOT work, if EITHER driver has scored '0' (zero) points.
And, the "Dmitriy_Guller metric" WILL!

[mikedeering]

If you are going to bring retainers into it, surely the only fair way to compare team mates is points scored per dollars earned. So Ralf starts to look really bad, where as Rubens might actual look a good value proposition compared to Michael...

Of course, this doesn't work at the opposite end of the grid, where pay drivers screw things up and you get points scored per dollars spent by them.