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Old 4 May 2012, 21:06   #1
Schummy
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Monotonous or plural seasons?

Some seasons are dominated by one driver and become monotonous in the sense of the winner of every GP is very predictable. Even two dominant drivers (example: Prost-Senna) can be monotonous in this respect.

Other seasons are very entertaining because there are a lot of race winners, making unpredictable the outcome of future races.

So, I have tried to make a sort of "Contenders Index" showing how many race contenders there is regularly in a given season. In fact, I am sorry to say, I have done two Index, brightly named CIX1 and CIX2. A CIX values of 3, for example, would mean there are about 3 regular contenders for race wins. It is the equivalent to have three drivers who wins all the races, in the same proportion.

The minimum value is CIX = 1, and it means the terrible scenario where one driver wins every race. Maximum value is N = number of drivers competing in the season. LOL, this maximum value is just a theoretical possibility!

I have done the calculations for the last decade:

Year WC CIX1 CIX2 NW Wins
2011 VET 2.68m 3.35m 5 11,3,3,1,1
2010 VET 4.16p 4.75 5 5,5,4,3,2
2009 BUT 4.18p 5.10p 6 6,4,2,2,2,1
2008HAM 4.33p 5.43p 7 6,5,2,2,1,1,1
2007 RAI 3.47 3.88 4 6,4,4,3
2006 ALO 3.00 3.67 5 7,7,2,1,1
2005 ALO 3.11 3.81 5 7,7,3,1,1
2004 SCH 2.22m 2.61m 5 13,2,1,1,1
2003 SCH 5.25p 6.30p 8 6,2,2,2,1,1,1,1
2002 SCH 2.06m 2.60m 4 11,4,1,1

CIX1 = Index based in statistical properties.
CIX2 = Index based in entropy.
NW = Numbers of winners in the season.
Wins = Number of wins of each winner, in the season.

I have added "m" or "p" to some CIXs, "m" means a "monotonous" season and "p" a "plural" season. Those adjectives have been chosen according to CIX values, in a way more or less reasonable:

CIX1 < 3 : monotonous
CIX1 > 4 : plural

CIX2 < 3.5 : monotonous
CIX2 > 5 : plural

Monotonous seasons: 2002, 2004 and 2011 (in this decreasing order)
Plural season: 2003, 2008 and 2009 and perhaps 2010 (decreasing order)

2003 was the season with Williams's Montoya and Ralf getting very good results and having 8 race winners!

2008 was the Hamilton title and 2009 was the Button-Brawn season.

The simple "number of winners in a season" is not enough to characterize a season. For example, 2007 was the season with less winners (4), but those 4 drivers fought equally for race wins, however 2004 and 2011 had 5 race winners but were very monotonous because the dominant driver won a big part of races.

This season is heading in a good direction in this respect. Let's hope we will see a classic drama with many first actors.
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Old 5 May 2012, 01:05   #2
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Very interesting Schummi !
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Old 5 May 2012, 01:05   #3
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Nice one Schummy. Your mention of 2007 is interesting; I actually find seasons where there are just a few contenders throughout the year ratchet up the tension nicely because you are aware of the intensity and pressure on a few individuals (to speak of just the drivers rather than their teams). Seasons where you're not even sure who's in contention for much of it are great fun but not necessarily, for me, more exciting. 2010 was exciting in the way Seb appeared to 'steal' it at the last, with many of us having thought it was going a different way for much of the season. It was the reversal of form at the last moment that made that so striking. Had Seb been so obviously in a four-way battle all year, it wouldn't have been such a magnificent conclusion.
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Old 5 May 2012, 01:11   #4
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2003 now looks the most interesting season...
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Old 5 May 2012, 13:16   #5
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2003 now looks the most interesting season...
Which just goes to show how you can make statistics say anything you want.

Keep it up, Schummy.
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Old 5 May 2012, 14:07   #6
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More data. I have added the seasons back to the beginning of the post Senna-Prost era, i.e. from 1994.

I also have added some new columns.
Code:
Year WC   CIX1   CIX2  NW   %DW   SDIX  Wins 
2011 VET  2.68m  3.35m  5  58.9%  1.08  11,3,3,1,1
2010 VET  4.16p  4.75   5  26.3%  0.68  5,5,4,3,2
2009 BUT  4.18p  5.10p  6  35.3%  0.91  6,4,2,2,2,1
2008 HAM* 4.33p  5.43p  7  33.3%  0.89  6,5*,2,2,1,1,1
2007 RAI  3.47   3.88   4  35.3%  0.79  6,4,4,3
2006 ALO  3.00   3.67   5  38.9%  0.78  7,7,2,1,1
2005 ALO  3.11   3.81   5  36.8%  0.76  7,7,3,1,1
2004 SCH  2.22m  2.61m  5  72.2%  1.16  13,2,1,1,1
2003 SCH  5.25p  6.30p  8  37.5%  1.17  6,2,2,2,1,1,1,1
2002 SCH  2.06m  2.60m  4  64.7%  0.99  11,4,1,1
2001 SCH  3.00   3.72   5  52.9%  1.06  9,3,2,2,1
2000 SCH  2.53m  3.16m  4  52.9%  0.93  9,4,3,1
1999 HAK  4.38p  5.28p  6  31.3%  0.84  5,4,2,2,2,1
1998 HAK  2.38m  2.89m  4  50.0%  0.85  8,6,1,1
1997 VIL  3.47   4.38   6  41.2%  0.92  7,5,2,1,1,1
1996 HIL  2.63m  3.26m  4  50.0%  0.91  8,4,3,1
1995 SCH  2.76m  3.53   5  52.9%  0.99  9,4,2,1,1
1994 SCH  2.38m  2.89m  4  50.0%  0.85  8,6,1,1
New columns are:
%DW = percentage of wins for the dominant driver.
SDIX = SuperDominant Driver Index, LOL another bombastic name . It's an obscure index that I'll try to explain later. Basically, it tries to mean the drivers who won more races that were statistically expected. For the moment, let's consider it as a curiosity

The added seasons are mostly monotonous, 4 or 5 monotonous against just 1 plural season. It was probably the worst F1 epoch in terms of race predictability. LOL, the only "good" season was 1999... because poor Michael broke his leg, otherwise...

The only other "reasonably fought" season was 1997, when the dominant team (Williams) began to have opposition from other teams... and its drivers were not particularly dominant.

An interesting by-product of that table is to see how the more winning driver always won the title, except the (in)famous 2008. Even the three times that the WC tied his numbers of wins, he had won counting back 2nd, 3rd,..., positions. The funny thing about it is that the three times that there were a tie in numbers of wins, Alonso was involved in them! (his two titles and in 2010, where he lost to Vettel).

The %WD percentage is a certain measure of the predictability of race winners. For example, in 2011 Vettel won 58.9% of the races. It means that betting for him (that is the optimal betting) had won 58.9% of the bets. Thus 2011 winners have been predictable 58.9% of times. Obviously, the lower value for %WD, the more unpredictable are race winners.

As you can see %WD is pretty much correlated with "monotonous" or "plural" seasons. %WD > 50% results in a monotonous championship, while the cut point for a plural championship is about %WD < 35%. In short, years with predictability more than one half are monotonous, years with predictability lower than one third are plural.

Last edited by Schummy; 5 May 2012 at 14:13.
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Old 5 May 2012, 15:57   #7
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Originally Posted by Marbot View Post
Which just goes to show how you can make statistics say anything you want.

Keep it up, Schummy.
You tell me...
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