More about fastest laps

[Schummy]

More info about fast laptimes in Indy. In this thread I'm going to put a sort of "average fast lap" for every driver (who did some laps!). It is the average of the 25% fastest laps they did (i.e. in this case, the 18 fastest laps they did in the race).

Pure fastest lap is interesting as a measure of raw pace a driver is able to extract from his car in the best conditions. But it is a little bit "flukey" as sometimes it is not consistent with the 2nd , 3rd,... fastest lap he did. I particular, KR's fastest lap was better than LH's, but looking the 2nd, 3rd, etc fastest laps shows LH was usually faster than KR even in top laps. Everyone who has tried a F1 sim knows sometimes one does a fluke time

Another reason to do this stat is... I like to do calculations

Well, here it goes:

DRV  TEAM GAP  NL
-----------------
HAM  MCL 0.00  73
RAI  FER 0.03  73
ALO  MCL 0.08  73
MAS  FER 0.20  73
HEI  BMW 0.46  55
KOV  REN 0.62  73
VET  BMW 0.82  73
WEB  RBL 0.83  73
TRU  TOY 0.93  73
ROS  WIL 1.03  68
FIS  REN 1.07  72
DAV  SAG 1.11  72
WUR  WIL 1.61  72
SUT  SPY 1.72  71
BUT  HON 1.83  72
SPE  STR 2.06  71
LIU  STR 2.27  68
ALB  SPY 2.83  70
SAT  SAG    _  13

I have included the number of laps done because if a driver does less laps he has some disadvantage. The reason is I have put his missing laps as worse laps. In this case, only Heidfeld can suffer this effect.

Team mates gaps were:

HAM-ALO 0.08
RAI-MAS 0.17
HEI-VET 0.36
KOV-FIS 0.45
WEB-COU ----
TRU-SCH ----
ROS-WUR 0.58
DAV-SAT ----
SUT-ALB 1.11
BUT-BAR ----
SPE-LIU 0.21

Finally I have tabled the gaps (using this particular stat) between FA and LH and between FM and KR so far in the season:

GP  FA/LH  FM/KR
---------------- 
AUS  0.08  -0.94
MAL  0.47  -0.30
BAH -0.20   0.10
SPA  0.09   Inft*
MON  0.11   0.76
CAN -0.58*  0.10
USA -0.08  -0.17
----------------
Avg  0.00   0.10

An asterisk signals any datum considered statistically "anomalous" in comparison with the rest of values. It can be seen that Alonso's Canada and Kimi's Spain are anomalous gaps (obvious in case of Kimi).

The average gap is done discounting the anomalies (normal procedure to get a robust estimation). The average gap is negligible in FA-LH and very small in FM-KR. I have to say this average is slightly incorrect as I would have to compensate the difference in lap length among the circuits (laziness ). But, anyway, the results are surely very approximate.

Alonso and Massa "wins" 4-3 to his team mates in this kind of fast laps, so of course things are very equilibrate.

[Dutton]

Ah, lovely. I have often thought about this, and implied related things, but been too lazy to sit down and work it through (would've in my past).

It is clearly better to look at a larger base than one lap.

I will now read and reflect the data.

As I posted in another thread earlier today:

Originally Posted by Dutton

I guess we would need to look at the consistency of the various drivers'/teams' times.

It is always possible that a driver/team has a brief period when, for whatever reason, they run a lot quicker than normal. The truly good will consistently churn out high-end times.

Thus, over a race as a whole, the consistent quicker times of the better team will translate into a larger gap than may be apparent from qualifying/FL-list.

I was actually quite surprised about how close Ferrari managed to run to the Mclarens in the race (put another way, I was surprised at how consistently the Ferrari's were at a reasonably quick pace).

Clearly, this principle can be applied to all teams regardless of whether they are fast or not. I think to substitute "high-end" with "target" should suffice. Or, to put it another way, locally fast (as opposed to globally fast - although to two can coincide).

[Schummy]

Thanks, mate!

[Sev]

The stand out statistic on that was how much Albers sucks :P Or at the very least, how much better Sutil is.

On a side note; how come you counted Alonso's Canadian performance as anomolous? Because of the safety car interfering? Because in size alone, it doesn't seem anomolous.

[johnh875]

Interesting analysis Schummy, thanks for putting the data up.

[Schummy]

Originally Posted by Sev

On a side note; how come you counted Alonso's Canadian performance as anomolous? Because of the safety car interfering? Because in size alone, it doesn't seem anomolous.

Anomalous numbers have been signaled using median and semi-interquartie range SIQR = (Q3 - Q1) / 2. In a sort of "robust" standardization each value x is mapped to (x - Me) / SIQR . If the absolute value of it is greater than 4 it is signaled as "anomalous".

To calculate the average without anomalous values, in an unbiased way, anomalous are dropped but also the "opposite" values are dropped. In case of FA/LH, -0.58 is dropped (the smallest value), but +0.47 is dropped as well (the greatest value).

[Dani Filth]

have I told you before you're a sick man Schummy?? .. yeah . I think I did

[Schummy]

Dani, the last time you said it to me was last week when we were playing roulettes in Las Vegas

[Schummy]

More data.

Firstly, the six best drivers in this particular "fast laps" stat in each GP so far:

RAI  0.00  58
ALO  0.13  58
HAM  0.21  58
KUB  0.55  36
MAS  0.94  58
HEI  1.13  58

ALO  0.00  56
RAI  0.46  56
HAM  0.47  56
MAS  0.76  56
HEI  0.79  56
ROS  0.89  42

HAM  0.00  57
MAS  0.09  57
RAI  0.19  57
ALO  0.20  57
HEI  0.23  57
KUB  0.70  57

MAS  0.00  65
ALO  0.20  65
HAM  0.31  65
KOV  0.39  65
RAI  0.54   9
KUB  0.60  65

ALO  0.00  78
HAM  0.11  78
MAS  0.73  78
KUB  0.99  77
FIS  1.20  77
BUT  1.46  77

HAM  0.00  70
HEI  0.35  70
ALO  0.58  70
MAS  0.80  51
ROS  0.84  70
KUB  0.97  26

HAM  0.00  73
RAI  0.03  73
ALO  0.08  73
MAS  0.20  73
HEI  0.39  55
KOV  0.62  73

I have done a little retouch in the way I get the mean of the best 25% of driver's laps. Formerly I completed missing laps with "infinites" ( a lap done at 0 mph have a laptime of "infinite"). Now I just calculate the 25% of the existing laps. I find this is a better procedure, the former penalized too much those drivers who have retired from race. This is the reason there are some little differences respect the first post in this thread; no big deal, anyway.

Secondly, I have done a sort of WDC classification table counting those average best laps instead of race results. So we get something like a WDC classification in terms of race pace. I'm fond of the "classic" scoring system 9-6-4-3-2-1, so I have used it in this calculation:

     A  M  B  S  M  C  U
HAM  4  4  9  4  6  9  9 = 45
ALO  6  9  3  6  9  4  4 = 41
MAS  2  3  6  9  4  3  3 = 30
RAI  9  6  4  2  0  0  6 = 27
HEI  1  2  2  0  0  6  2 = 13
KUB  3  0  1  1  3  1  0 =  9
KOV  0  0  0  3  0  0  1 =  4
ROS  0  1  0  0  0  2  0 =  3
FIS  0  0  0  0  2  0  0 =  2
BUT  0  0  0  0  1  0  0 =  1

McLaren drivers lead clearly, Raikko is near Massa. KubiK defends well (3 to 4) against Heidi , Kovalainen is doing well against Fishy. Button has done a surprising appearance (in the chaotic Montreal race).

Thirdly, team mates comparisons. Here some minor differences can be seen respect the first post (because of the change of method).

ALO-HAM  0.01
MAS-RAI  0.02
HEI-KUB  0.36
FIS-KOV  0.16
ROS-WUR  0.75
WEB-COU -0.28 
TRU-RSC  0.26
BUT-BAR -0.17
SAT-DAV  0.12
LIU-SPE  0.46
SUT-ALB  0.33

In general terms, those are close gaps, extremely close in Mac and Ferrari in fact (interesting in the case of the last mentioned team). Exception is Rosberg against "poor" Wurz. Coulthard leads Webber, but their results have been a bit unstable at the moment, with some "rare" races. Let's see how it goes, though. More or less the same about Barry leading Button.

Well, ok, I'm going again into my tomb because the Moon is rising quickly.

[Sev]

That last stat is fairly interesting, because in absolute fastest lap times Rosberg and Wurz are fairly close together. I guess Wurz just can't run them together.

Also, what's with the huge change in gap between for initial set of data and this one with respect to Sutil vs Albers? Is that just because Albers crashes out the whole time?

[Red Bulldog]

Originally Posted by Schummy

Anomalous numbers have been signaled using median and semi-interquartie range SIQR = (Q3 - Q1) / 2. In a sort of "robust" standardization each value x is mapped to (x - Me) / SIQR . If the absolute value of it is greater than 4 it is signaled as "anomalous".

To calculate the average without anomalous values, in an unbiased way, anomalous are dropped but also the "opposite" values are dropped. In case of FA/LH, -0.58 is dropped (the smallest value), but +0.47 is dropped as well (the greatest value).

Well yeah

[Schummy]

Originally Posted by Sev

Also, what's with the huge change in gap between for initial set of data and this one with respect to Sutil vs Albers? Is that just because Albers crashes out the whole time?

The initial post was about GP USA (only), but the later post was comparisons between team mates in the season. So the big gap was for Indy.

I'll try to post details about Rosberg-Wurz and Sutil-Albers, along the 7 GPs, a bit later. So we could see how it has behaved.

[Mr V]

Originally Posted by Schummy

More data.

( a lap done at 0 mph have a laptime of "infinite").

Don't mean to be pedantic, but a lap done at 0 MPH wouldn't be a lap done at all - surely a lap "undone"

Great work though, even if it does confuse the hell out of me at times

[Schummy]

Well, I'm confused everyday

[Schummy]

As promised , here are the differences along the 7 GPs between those two pairs. "Infty" means the second mentioned driver cannot do a minimum of valid laps. "-Infty" means the same for the first mentioned driver.

ROS-WUR:
1.04 0.37 0.41 Infty -0.02 1.33 0.60

SUT-ALB:
1.60 -Infty 0.61 0.14 -0.20 0.04 1.08

Very clear advantage for Rosberg, as the only GP where Wurz was faster than him was Monaco with just a negligible 0"02 gap.

Albers has "beaten" Sutil two times (MAL and MON), but in Malaysia Sutil didn't do enough laps. In Monaco the gap was small. Sutil has been faster 5 times, with two big gaps, one pretty biggy and two very small. In short there were three races with similar pace and three races with a very clear aadvantage for Sutil.

[Schummy]

Data about that statistic (average of the 25% best laps) in GP FRANCE. Expressed as gaps respect the best driver.

GP FRANCE
DRV  GAP  LAPS
--------------
MAS  0.00  70
RAI  0.02  70
HAM  0.35  70
FIS  0.64  70
HEI  0.66  70
ALO  0.69  70
BUT  0.73  70
RSC  0.74  69
KUB  0.86  70
ROS  0.95  70
KOV  1.04  69
BAR  1.35  69
WEB  1.35  69
WUR  1.40  69
COU  1.45  69
SPE  1.72  55
SAT  1.91  68
SUT  2.06  68
ALB  2.75  28
DAV     _   1
TRU     _   1
--------------

Updating of the "points table" of 25% fastest laps (scoring: 9-6-4-3-2-1)

     A  M  B  S  M  C  U  F
HAM  4  4  9  4  6  9  9  4 = 49
ALO  6  9  3  6  9  4  4  1 = 42
MAS  2  3  6  9  4  3  3  9 = 39
RAI  9  6  4  2  0  0  6  6 = 33
HEI  1  2  2  0  0  6  2  2 = 15
KUB  3  0  1  1  3  1  0  0 =  9
FIS  0  0  0  0  2  0  0  3 =  5
KOV  0  0  0  3  0  0  1  0 =  4
ROS  0  1  0  0  0  2  0  0 =  3
BUT  0  0  0  0  1  0  0  0 =  1

Team mates average gap along the season. Averages exclude "anomalous data" as explained in former posts. Column "VOL" is an indicator of "volatility" of results. Smaller values mean greater confidence in the average. Greater values mean that pair of driver have had big variations among the races (so the average is less meaningful).

Tmates   GAP   VOL
===================
ALO-HAM -0.05  0.16
RAI-MAS -0.02  0.30
HEI-KUB  0.20  0.43
FIS-KOV  0.19  0.32
ROS-WUR  0.70  0.34
WEB-COU -0.21  0.69
TRU-RSC -0.10  1.07
BUT-BAR -0.05  0.58
SPE-LIU -0.36  0.52
SAT-DAV  0.30  0.60
SUT-ALB  0.39  0.45
===================

• Extremely close gaps in McLaren and Ferrari.
• Big gap (disastrous?) in Williams.
• Surprises in Red Bull and in Toyota (but Toyota's volatility is too high to be trustable).
• Perhaps some surprises in Honda and Super Aguri.

[Schummy]

Matrix meaning how many times a driver has been faster than other:

     HAM  ALO  MAS  RAI
HAM  ---  4-4  6-2  5-3
ALO  4-4  ---  5-3  4-4
MAS  2-6  3-5  ---  5-3
RAI  3-5  4-4  3-5  ---

Hamilton beats everyone except Alonso. Alonso, in turn, doesn't beat Raikkonen. But Raikkonen is beaten by Massa (a good mess ).

[Schummy]

In this graph appear the laptimes of Hamilton (black, no pun intended) and Alonso (red, no pun neither) during GP FRANCE. At the left the fastest lap, then the second fastest lap, the third fastest lap, etc. At the right the slowest laps (except anomalous laps: first lap, in and out laps,...)

GP France, Hamilton-Alonso

Interestingly, only in his fastest lap Alonso is better than Hamilton. In the rest of laps Lewis is faster than Fernando. The gap is big: most of time is 0.5 secs or bigger. The datum about absolute fastest race lap is deceiving (or perhaps not, see below).

Only the best two or three FA's laps are comparable to LH's good laps. This has two sides:

• Alonso showed he had the ultimate pace if he had not been hindered by traffic.
• Alonso had more than 2 or 3 laps free of traffic, so he was most of time below LH's pace even with clear air. Moreover, in the last laps he didn't the pace to fight Fisichella.

[Schummy]

Now a graph (histogram-like) showing the (smoothed) frequency of lap times of Raikkonen (green), Massa (red) and Hamilton (black) in Magny-Cours. The first laps, and the in and out laps have been dropped in each case (two piststops for Ferraris, three for Hamilton), because they don't represent any significant lap time..

Comparison between KR, FM and LH

• LH's laps are more homogeneous or "stable" along the race (his "bell curve" is narrower).
• The ultimate fast pace of the Ferraris was faster than LH's in perhaps 0.2 secs (the left extreme of each curve).
• Hamilton had several slow laps (traffic, probably) as showed in the tail at the right. The two Ferraris didn't have any of this (I suppose it's the advantage of being at the front and exiting at the front in the pitstops).

[RotorFan]

Nice work.

Maybe its obvious, but I would say Hamiltons bell-curve is caused by an additional pit stop, so he never had as much fuel on board as the Ferraris or as big a variance in tyre wear.

[Schummy]

In fact the LH's stints 2 and 3 were very "narrows" in terms of lap time variations (in particular stint 2 was relatively "longish"). Stints 1 and 4 were more "normal", "wider" set of laps.

Interestingly, this season, lap times during a stint don't always follows a clear pattern according to the decreasing fuel weight. Tyre wear plays a role and sometimes lap times are pretty stable, sometimes the best laps are the first ones and the last ones, and sometimes the last laps are the best. Certainly with less fuel in pitstop the overall speed is faster along those patterns in the stint, but it is not being the major factor in homogeneity of laps.