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Mathematical Prediction of pecking order in Australia


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#1 mattferg

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Posted 25 February 2013 - 07:35

Note: I've already posted this in the guess the starting grid topic, but I felt users might want a seperate thread to discuss my findings and to not clog up the previous thread.

I averaged out the qualifying results for the top driver in Melbourne for the entire length of this set of regulations (the past four years, three for Caterham and Marussia), used this to rank the teams in each qualifying 1-11, averaged out the position over the years, and got the following pecking order:

1.75 RBR
3.25 McLaren
3.5 Mercedes
4.5 Ferrari
4.5 Lotus
5.75 Williams
6.75 Sauber
7.5 Force India
7.5 Toro Rosso
10 Caterham
11 Marussia

For teams that were tied (Such as Ferrari and Lotus, and Force India and Toro Rosso) I took the highest qualifying position to decide which team went ahead. In the case of Ferrari and Lotus, this was both third, and as such I took the highest average qualifying position for both drivers, which in this case was Alonso 3rd and Massa 5th in 2010. For Force India and Toro Rosso the highest was 9th, for Force India in 2012.

Admittedly these results can be interpreted in a variety of ways, with certain teams changing drivers over the years, and as the results only take in the top driver, this can also skew the results. It also doesn't take into account the posibility of a team having a really-off year (such as Ferrari last year). In such cases where the teams are very close on average, such as McLaren and Mercedes, where both teams have an entirely different driver line-up to 2009, these could swap, and this also includes Lotus and Ferrari, who have almost entirely different line ups, and are tied on points.

Now obviously many will complain that I didn't include second driver results, so as such I added together the team's qualifying positions (e.g. if a team had a front-row lockout they got 3 points, a 9th and 10th would be 19 points, etc.), and then I used those numbers to rank the teams per year 1-11. If a team was tied on points I used the highest qualifying position for that team in that year. I then averaged out each year as before:

1.75 RBR
2.5 Mercedes
3.5 McLaren
4.25 Ferrari
6 Lotus
6.25 Williams
6.5 Sauber
6.75 Toro Rosso
7.5 Force India
10 Caterham
11 Marussia

Overall not too many changes - McLaren and Mercedes have swapped, Ferrari is now clear of Lotus, and Toro Rosso and Force India have swapped.

Interpret how you will! And yes, I've counted Brawn as Mercedes. I will not be making a calculation based on driver performances (ie using Jenson's results from Brawn and McLaren, Alonso's from Renault and Ferrari etc.) and will not be doing pre-2009 estimates. The reason for this is that only 7 drivers have records for the past four years in Melbourne, and I don't think pre-2009 data is relevant for team predictions.

Edited by mattferg, 25 February 2013 - 08:15.


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#2 noikeee

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Posted 25 February 2013 - 09:49

That's not a prediction, that's an average of the past. Nice exercise in mathematical futility (I do often waste time in similar pointlessness), but doesn't really tell us anything other than Red Bull has been pretty quick the last few years (shock horror).

#3 mattferg

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Posted 25 February 2013 - 11:50

That's not a prediction, that's an average of the past. Nice exercise in mathematical futility (I do often waste time in similar pointlessness), but doesn't really tell us anything other than Red Bull has been pretty quick the last few years (shock horror).


I disagree - I think it demonstrates a team's ability to prepare for the coming season, and to a small extent driver performances in Australia, and who usually develops a car that's good there. It's interesting to compare it to WCC standings before, during, and after this season.

#4 boldhakka

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Posted 25 February 2013 - 11:53

So you have numbers for four years. Do the same averages for the first three years and see how well it predicts the fourth year. Then you'll also have some idea of how well these numbers work as representations of the future instead of simply a description of the past.

#5 mattferg

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Posted 25 February 2013 - 19:11

So you have numbers for four years. Do the same averages for the first three years and see how well it predicts the fourth year. Then you'll also have some idea of how well these numbers work as representations of the future instead of simply a description of the past.


Some things were off, others were correct!

1 RBR - McLaren
2 Mercedes - Mercedes
3 Ferrari - RBR
4 McLaren - Lotus
5 Sauber - Toro Rosso
6 Williams - Williams
7 Lotus - Force India
8 Toro Rosso - Ferrari
9 Force India - Sauber
10 Caterham - Caterham
11 Marussia - Marussia

Left is predicted, right is actual. This is using the second formula.

This is tricky because the McLaren results are skewed from 2009!

Edited by mattferg, 25 February 2013 - 19:15.


#6 Harry

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Posted 25 February 2013 - 19:28

1. Red Bull
2. McLaren
3. Lotus
4. Ferrari
5. Mercedes
6. Sauber
7. Williams
8. Force India
9. Torro Rosso
10. Marussia
11. Caterham

#7 Alolnso

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Posted 25 February 2013 - 20:43

Again, this is not a prediction. You need other tools (like regressions and time series analysis). It's difficult to do and it won't be much better than the general gut feeling.

Besides, I'm not sure whether using the past results in Melbourne is the right choice of data. I would go with preseason testing and the results from the three oversea races (from the past 3 years).

The reason why I would use the data from the preseason testing is very simple: it's the car they use in the actual races and the car doesn't change much in the first couple of races. The race results would then be used to determine if the testing form was genuine or not. That way you could have an idea what teams do during testing (some teams run with a lot of fuel, others will less fuel, etc).

So having used all of that data from the three previous years, you only need to see what happened during the 2013 preseason tests, and maybe you'll have a good idea of what's going to happen. However, there are a lot of unrealistic assumptions that you would need to do and it's not guaranteed that it will be better than what the drunk guy in your local pub said.

Edited by Alolnso, 25 February 2013 - 20:44.


#8 mattferg

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Posted 25 February 2013 - 21:51

Again, this is not a prediction. You need other tools (like regressions and time series analysis). It's difficult to do and it won't be much better than the general gut feeling.

Besides, I'm not sure whether using the past results in Melbourne is the right choice of data. I would go with preseason testing and the results from the three oversea races (from the past 3 years).

The reason why I would use the data from the preseason testing is very simple: it's the car they use in the actual races and the car doesn't change much in the first couple of races. The race results would then be used to determine if the testing form was genuine or not. That way you could have an idea what teams do during testing (some teams run with a lot of fuel, others will less fuel, etc).

So having used all of that data from the three previous years, you only need to see what happened during the 2013 preseason tests, and maybe you'll have a good idea of what's going to happen. However, there are a lot of unrealistic assumptions that you would need to do and it's not guaranteed that it will be better than what the drunk guy in your local pub said.


Unfortunately this is entirely wrong, because, as we know, preseason testing times mean little or nothing.

1. Red Bull
2. McLaren
3. Lotus
4. Ferrari
5. Mercedes
6. Sauber
7. Williams
8. Force India
9. Torro Rosso
10. Marussia
11. Caterham


This isn't the guess the grid thread.

Edited by mattferg, 25 February 2013 - 21:58.


#9 boldhakka

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Posted 26 February 2013 - 12:36

Some things were off, others were correct!

1 RBR - McLaren
2 Mercedes - Mercedes
3 Ferrari - RBR
4 McLaren - Lotus
5 Sauber - Toro Rosso
6 Williams - Williams
7 Lotus - Force India
8 Toro Rosso - Ferrari
9 Force India - Sauber
10 Caterham - Caterham
11 Marussia - Marussia

Left is predicted, right is actual. This is using the second formula.

This is tricky because the McLaren results are skewed from 2009!


Well, thanks for doing the numbers. So we notice that the standard deviation around the average is quite high, which means the average performance at Melbourne is not a good predictor or representation of any one specific race at Melbourne.

#10 wrcva

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Posted 26 February 2013 - 14:03

Again, this is not a prediction. You need other tools (like regressions and time series analysis). It's difficult to do and it won't be much better than the general gut feeling.
...


True. Time series will be too much hassle but cross-sectional will be interesting to try. How about something like this (as a theoretical framework). Not sure if there is data...

Prediction Equation (to express WDC points earned with respect to pre-season testing variables since that is the only thing available this year to date);

P = points earned in a season (dependent var to be predicted) is a function of;

TMiles = pre-season test miles completed
TireDeg = tire degregation differential on long runs (proxy for car's balance)
SpeedTrap = average speed for testing days (not sure if this would have prediction power)
Updates = number of major updates prior year (proxy of next yr, but not sure if such data available...)
Stint = Average test stint lap count > 3 laps
PitS = Average pit stop duration prior year
Temp = Average testing temperature (degrees)
...

Some dummy vars
WDC (yes/no): has the driver ever won WDC
WCC (yes/no): has the car ever won WCC
...

You train the model using last year's data to calc all coefficients (and see if the model has any prediction power). If yes, you plug in this year's data to have some fun...
Maybe there are better vars --- (this is after thinking about it for 5 mins after your regression statement).



#11 boldhakka

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Posted 26 February 2013 - 15:24

^^ Not enough training data for the number of degrees of freedoms (aka features, aka parameters) you have in your model!