"Average" grid position

[Schummy]

I know Saturday qualify is not what it used to be with the different strategies, errors in that one lap, etc, but it is always a valid stuff to speculate.

It is calculated with the first THREE GPs: AUS, MAL and BRA (let´s see how it goes on in Imola). I have ordered drivers by the mediane of grid positions and I've added the usual average too.

   Name        Me  Av
 1.Barrichello  2  2.67
 2.M.Schumacher 3  3.67
 3.Coulthard    4  5.67
 4.Trulli       5  6.33
 5.Heidfeld     7  8.33
 6.Raikkonen    7  8.67
 7.Montoya      8  6.67
 8.Button       9  9.33
 9.R.Schumacher 9 10.67
10.Alonso      10  7   
11.Panis       10 10   
12.Villeneuve  12 10.33
13.Frentzen    13 10.33
14.Fisichella  13 11.67
15.Webber      14 11   
16.daMata      16 15   
17.Pizzonia    17 16.67
18.Firman      17 17.67
19.Verstappen  19 19
20.Wilson      19 19.33   

Ferrari   5
McLaren  11
Renault  15
Williams 17
Sauber   20
BAR      21
Toyota   26
Jordan   30
Jaguar   31
Minardi  38

Some comments come to my mind:
- Ferrari goes on the class of the field on Saturdays.
- Kimi clearly overcame by DC by now.
- Excellent Trulli (in qualif) as always, Alonso had one pole but otherwise clearly superated by Jarno. Excellent Renault.
- Ditto for Heidfeld and HHF (without pole ).
- Low Williams perfomance.
- Button steering Jax into retirement? .
- What happens with daMata on Saturdays?
- Surprising bad perfomance of Jordan in qualif. Firman looking pretty bad by now.
- Is Webber so good or is Pizzonia so bad adapted to F1? (I think MW probably is one of the revelations so far)
- Minardi... well, let´s them appart. Wilson must show he can outperform Jos if he wants to have a decent F1 career.

[Wrex]

Good stuff Shummy.

Tell me, can you give us the average's for Friday qualifying (when all are on light fuel)?

Would be interesting to see the average grid using last years rules.

[Mark Webber]

sorry what do you mean medaine ?

[Schummy]

I meant "median": the middle grid position discarding the best one and the worst one. It is useful to not be too much influenced by "fluke" circunstances. Anyway, it will be more useful when we get more GPs.

BTW, congratulations for your nice results so far

Wrex: You are right, good idea. If Friday is done with light fuel, it can be more representative of pure pace from drivers/cars (as in previous seasons). What I don't know is if are 100% commited, as it apparently is not as important as Saturday qualif. Next time I'll do the calculations with Friday data

[Adam43]

Great stuff Schummy.

I think it does show that Ferrari is the class of the field on Saturday. It is probably true, although perhaps not shown in the stats, that Ferrari is still teh class of the field on Sunday too.

[Peter Mallett]

But if you are using just the middle grid position and there's only been three GPs................... or should I just shut up at this point?

[BootsOntheSide]

He meant that the median only uses 3 races, so it's just their second-best position from the three races. The actual average is calculated form all 3.

[Maxmil]

Originally posted by Schummy
I meant "median": the middle grid position discarding the best one and the worst one. It is useful to not be too much influenced by "fluke" circunstances. Anyway, it will be more useful when we get more GPs.

Not to start a statistical argument - which I would surely lose - but do the "medians" really mean anything for such small samples? Here is the brief description of "median" from a Middle School mathematics website:

"By definition, a median is a statistical term identifying a piece of data (number) that divides numerically ordered data into two equal halves. In easier terms, the median is the middle piece of data when those data are placed in numerical order. Let's look at two examples. One example has an odd number of pieces of
data, and another has an even number of pieces.

45
46
46
47------> Median because there are 3 pieces above and 3 pieces below
50
57
60


45
46
46
47
50
--------> 53 is the median ***Explanation below***
56
60
61
62
62

The reason 53 is the median is because the median falls halfway
between the numbers 50 and 56."

Note there is no mention of discarding the high and low values, and this was not done when I took my stats courses several eons ago. The other problem, which you note, is that a sample of three races is too small to produce meaningful results. As seen below;

1 2 20 The Median is 2

1 2 3 The Median is 2

Which driver do you sign for the season?

More extreme cases:

For a sample size of 9,

2 3 4 6 8 20 20 20 20 The Median is 8

1 1 1 1 8 9 9 9 9 Yup, still 8

End of lecture.

[Schummy]

Ehemmm... discarding high and low values are exactly the same procedure you describe

With any number of values average and median (and any other location measure) give us some information. Obviously, with a shirt sample that info is small, but it is related to the "shortness" of sample not because of median.

What you are decribing about median behaviour is the well known characteristics and properties of it. Median is well established as a reasonable robust alternative for average, and then I'm not going to "defend" it at all

Anyway, for the sake of statistical info, my intention isn't to apply median during all the season, but calculate a "trimmed" mean: ideally I'll discard 25% of highest values and 25% of lowest values, and I'll average the resting 50%. It is to drop "anomalous", fluke, circumstancial, values that can happen with current qualify format.

In the next GP I'll discard the highest and lowest values and will average the three other values.

Thanks for the feedback! I hope you check future calculations about this issue :up:

[Maxmil]

Originally posted by Schummy
Anyway, for the sake of statistical info, my intention isn't to apply median during all the season, but calculate a "trimmed" mean: ideally I'll discard 25% of highest values and 25% of lowest values, and I'll average the resting 50%. It is to drop "anomalous", fluke, circumstancial, values that can happen with current qualify format.

Now that I can certainly agree with.

[Dutton]

The Friday Qual is clearly the most representative of pace. It is why it is of more interest to me than Sat Qual, but Sat Qual being the one I care most about results wise.