Toward the title 2013

[Schummy]

I'll try to put here graphs and calculations about the "title race".

Firstly a strange graph. Score positions of the current six first drivers (VET, RAI, HAM, ALO, WEB, MAS) using different score systems. I have used 5 systems that resemble some usual (or theoretical) systems. Each one is represented by a gray vertical line. In that vertical line appears the ordering with that system.

Climbing lines represent the drivers, with colors according to their teams.

Num. Wins: Number of wins and fall back to num of seconds and so on.
Aggressive: A system rewarding half points for one worse position.
Classic(al): F1 classic score system 9-6-4-3-2-1.
Conservative: System rewarding wins more than current F1 but less than the classical one.
Very conservative: Similar to current F1 system or MotoGP system. Rewards consistency over wins.



Not great changes across different score systems. The only detail is Alonso would be above Hamilton in any system less conservative (consistency oriented) than current system.

[Schummy]

I have done some WDC simulations (about 40000). Well, the calculations have been done by the computer, not me, of course

Probability of Title:
VET 44% |||||||||||||||
RAI 27% |||||||||
HAM 10% |||
ALO  8% |||
WEB  3% |
MAS  2% |
GRO  2% |
DIR  1%
ROS  1%
BUT  1%

The assumption for those simulations are all drivers will perform from now on with the same level of performance and consistency. Otherwise, if we suppose a level of performance like in these 4 races, Vettel jumps at about >80% and below Raikkonen they get a minimal probability.

If, however, we suppose a level of consistency (but equal performance level) like in these 4 races, Hamilton gets a low probability because ironically he has been very "consistent" and consistency is a bad thing when you are the dark horse. If you have to recover the gap with the leader, you need brilliant results.

So, assumptions are generous for Vettel's chasers but even so, their probabilities begin to look thin. Below the four firsts, probability of title is already below the likely status; they are basically team mates of the big four, or leaders of high middle class teams (Button, Di Resta).

Currently there would be aprox 90% probability that one of the big four gets the title. Half of that probability is for Vettel.

Alonso has a relatively low probability (8%), but let's remember that we are assuming an equal future performance for all of them. I we introduce an advantage performance for Alonso/Ferrari, the estimations would change, of course. The thing is, what level of performance advantage?, and is it probable?

The probabilities depend on two factors: (1) current gaps, (2) observed current common consistency in the championship. If consistency evolves to a lesser level, the chances of contenders will raise. If consistency become greater, Vettel's probabilities will increase. Intuitively, if races are more unpredictable, the probabilities for title are wider. For reference, in 2012 it had a lesser consistency than currently, but in 2011 it was similar.

[Schummy]

Just to put things in context, this is the probability of title evo across the 2012 season, following the same technique used in the former post.


(Line color and pattern are the expected for Vettel, Alonso, Raikkonen, Hamilton, Button and Webber)

• The first 5 races were chaotic, tittle wise.
• In 6th (Monaco) Button and Raikkonen began to lose the grip for the title.
• Valencia was the first turning point of the season: the title probabilities became centered on Alonso.
• Spa Alonso's disaster (almost fatally) didn't affect much his probabilities.
• Japan was the second turning point of the season. Alonso lost almost all his advantage; Vettel raised as a likely candidate. Before the race was 85%-10%, after the race was 55%-45%. Huge difference, the title race had started again from zero.
• The steamrolling sucession of wins for Vettel, put Alonso almost in a technical KO (25%-75%). He never would recover from that.
• Before the last race chances were 90%-10% for Vettel.
• In the 16th race (Korea) everybody, except Alonso and Vettel, dropped the title fight.
• Interestingly, during 2/3 of the season Webber's probabilities were very comparable to Vettel's (but the team apparently didn't give him equal support).

The highest probabilities of title reached during the season by the main drivers were:
Vettel: 90% (19th race)
Alonso: 86% (14th)
Webber: 27% (9th)
Hamilton: 26% (7th)
Button: 18% (1st race!)
Raikkonen: 10% (5th)
Rosberg: 9% (6th)
Pérez: 8% (2nd)

The lowest probabilities of title during the season:
Alonso: 7% (1st race!)
Vettel: 5% (13th race!)
Others: 0%

I find interesting those numbers... but I am a freaky.

[Razzzor]

That last graph is very interesting isn't it.

The first one not so much because I guess it's not taking into account the DNF and technical issues Alonso has had at the last race, his probability would otherwise be much higher.

[Schummy]

Reliability problems could be a sign of future weakness (let's think about last season's McLaren), so current sample of Ferrari's race performance is not very good. If it has been a bad fluke then probabilities will raise progressively in future races..

[Schummy]

Graph showing the gap situation respecting a future title.



The main feature, IMO, is Hamilton is already entering a difficult situation. It is unrelated to his car, it is just according to the gap with Vettel and the number of races to go.

By now, title race centers around Vettel, Kimi and Alonso.

Now a bit of numbers:

    GAP    EG   P%  Btr Dif 
VET   0  
RAI   4   1.1  60%  +1       Comfortable
ALO  17   4.5  40%  +1  -19  Comfortable
HAM  39  10.4   0%  +2   +3 (Difficult)
MAS  44  11.8   0%  +2   +8  Difficult
WEB  47  12.6   0%  +2  +11  Difficult

GAP = errrr... the gap
EG = Equivalent Gap.
P% = Probability of overcoming the gap (naive calculation)
Btr = amount of points they have to be above Vettel in Monaco to improve their gap situation.
Dif = amount of points they have to be above/below Vettel to NOT enter the Difficult Zone.

Equivalent Gap is the equivalent gap if only there had one race to go.

So, if Alonso loses more than 19 points in Monaco, he would have a difficult gap to overcome. I.e., if Vettel wins he would need to be 7th or better at very least. Any other worse position would make the title an uphill battle.

If Hamilton wants to have good chances in the championship, he needs to recover at very least 3 points with Vettel in Monaco.

[Bononi]

Kimi looking good !

[Schummy]

Originally Posted by Bononi

Kimi looking good !

Of course! he is a magnet for women!

[Schummy]

Updating the gap analysis after Monaco.



Only Kimi and Alonso are in a comfortable distance from Vettel. Hamilton is a bit further in the Difficult zone after Monaco.

Rosberg, Webber(lol) and Massa are "comfortably" in the Difficult zone, and probably, sooner or later most of them will walk into the dreadful Unlikely zone.

"Strategic" goals for Canada are:
- Kimi has to avoid losing more than 13 points to Vettel to not be in the Difficult zone.
- Idem for Fernando losing more than 5 points to Vettel (if Vettel wins in Montreal, FA will be automatically in a difficult position).
- Hamilton needs to recover more than 10 points from Vettel in order to come back out of the Difficult zone. It is not easy, except if he wins the race.
- Mark needs more than 16 points over Seb in Montreal to not be in a difficult position. Basically he needs Vettel to retire in order to be allow to do something about it.
- Rosberg will be *almost* out of difficulties if he wins and Vettel does a zero. Ouch!
- Massa has not hope, in the short term, of having a reasonable shoot at the title, no matter what he does in Canada.

[Schummy]

Gap analysis in numerical form.

 ------------------------------------------------------ 
|     | GAP|  EGAP  Prb | >=  Prb | Cmf  Prb | Ulk Prb |
| VET |    |            |         |          |         |
| ALO | 36 | 10.39  10% | +2  34% |  +3  34% |         |
| RAI | 44 | 12.70   5% | +2  30% | +11   5% |         |
| HAM | 55 | 15.88      | +3  14% | +22   0% |         |
| WEB | 63 | 18.19      | +3  11% |          |-19  19% |
| ROS | 75 | 21.65      | +4   9% |          | -7  69% |
| MAS | 83 | 23.96      | +4   4% |          | +1  81% |
 ------------------------------------------------------

GAP = Current gap versus leader.
EGAP = Equivalent gap if there was only one race to go.
Prb = Probability of overcome that gap.
>= = Points over Vettel in next race to better the current options of title.
Prb = Probability of achieve that.
Cmf = Points over Vettel in next race to be in the Comfortable zone (reasonable title options).
Prb = Probability to achieve that goal.
Ulk = Points over Vettel to got to the Unlikely zone (i.e. the zone with very unlikely title options).
Prb : Probability to achieve that.

What is EGAP? For example, Alonso's current gap against Vettel is "probabilistically" equivalent to Vettel having a 10.39 points advantage in the last race. It gives a better intuitive view of current gaps.

Main themes:

• Alonso and Kimi have a low probability to overcome Vettel (10% and 5%), but it is still feasible. This is the main conclusion of the whole table.
• Alonso has some probabilities to go back to be in a Comfortable candidate position in next race. Kimi has few possibilities and for the rest it is almost impossible.
• Rosberg and Massa have a big risk of go to the Unlikely zone in next race. Massa's case is not a surprise, but Nico is in the edge of being discarded for the title.

[Adam43]

Again that feels right
Alonso and Raikonen really need to start turning it around. Trouble is Silverstone should suit the Red Bull, unless *whisper it* the tyres are pants.

[Schummy]

Now in a graphic view:



Basically, Vettel's streak of good results is ejecting everyone out of the Comfortable zone. Now every contender has a difficult task to catch Vettel.

Very soon, some theoretical contenders will be out of the realistic zone, i.e. they will be practically discarded for the title.

In a short term, only Alonso and Kimi could mount a reasonable challenge to SV's expectations. In mid term, perhaps Hamilton could do it (if Mercedes gets a string of great results and Red Bull fades out).

[Born Racer]

Thanks for the update. 10% doesn't feel realistic. Alonso always makes a bit more of a go of it in the end, but by his own high standards, he's not had a great start to the year.

[Catingaround]

[PepsiVodka]

Originally Posted by Schummy

Now in a graphic view:



Basically, Vettel's streak of good results is ejecting everyone out of the Comfortable zone. Now every contender has a difficult task to catch Vettel.

Very soon, some theoretical contenders will be out of the realistic zone, i.e. they will be practically discarded for the title.

In a short term, only Alonso and Kimi could mount a reasonable challenge to SV's expectations. In mid term, perhaps Hamilton could do it (if Mercedes gets a string of great results and Red Bull fades out).

Christian Horner is just too good at what he does. It's like he can get that extra 10% that no one can get out of the car and that's what makes RBR dominate also the amount of money they have.

[Schummy]

I have been so busy lately (-_-,) but I hope I can do more silly numbers soon.

[Schummy]

Updating after Monza.



Hamilton and Raikkonen have gone out of the Difficult region and entered the Unlikely zone. Basically they are out of the title race.

Alonso has lost even more terain and now he is well deep in the Difficult región. It means that title is still feasible but pretty difficult to achieve.

I estimate his options like 3%-5% approx, according to that graph. So, Vettel looks well in his way to a 4th title.

[Catingaround]

Thanks Schummy, these are fun.

[Bononi]

That's great Schummiy, and Seb is close to his 4th...

[Schummy]

Originally Posted by Catingaround

Thanks Schummy, these are fun.

I could not resist to your post in July

[Schummy]

Originally Posted by Bononi

That's great Schummiy, and Seb is close to his 4th...

Alonso has lost three WDC for just some minimal points. At least this year he is going to lose with a bigger margin, it hurts less

[Aysedasi]

All over and done bar the booing........

[Bononi]

Originally Posted by Schummy

Alonso has lost three WDC for just some minimal points. At least this year he is going to lose with a bigger margin, it hurts less

Is that would be enough to put Ferrari in alert ?

I guess not.

Now if Kimi goes to Ferrari things will get interesting...

[Aysedasi]

Yep, it'll be Kimi and not Fernando who wishes he was in a Red Bull.....

[Schummy]

Season is entering its final third, so it 's about time to put "strategic goals" for the main driver. (LOL, that is a pompous way to say I am going to post my usual stuff in this thread.)

For the next GP in Singapore, drivers have some goals respecting scores, that can be descripted as: (1) maintain chances for title, (2) entering/remaining in the "comfortable" title expectations, (3) entering/remaining in the "difficult but somehow likely" title expectations. For achieve those goals, they should get a score over Vettel such as writen in the following table.

 
  ----------------------------------
|      pts | gap | mtn | cmf | lik |
 ----------------------------------
| VET  222 |     |     |     |     |
| ALO  169 | -53 |  +4 |  NO |  -8 |
| HAM  141 | -81 |  +6 |  NO | +20 |
| RAI  134 | -88 |  +7 |  NO |  NO |
 ----------------------------------

(GOV: Gap over Vettel in Singapore)
mtn: GOV needed to maintain current chances; cmf: GOV to have comfortable chances for title; lik: GOV to have some likely chance for title.

• Alonso needs to over-score Vettel by 4 points to maintain the same chances for title. If he does not achieve it, he will have lower probabilities for the WDC; if he scores a gap bigger tan 4 points, he will increase his probabilities. Analogous reasoning for Hamilton and Raikkonen's cases.
• The NOes in cmf column mean ALO, HAM and RAI cannot be in a "comfortable" title option even if they win the race and Vettel DNFed it.
• Alonso "needs" to lose 8 points respect Vettel to be in a unlikely title position. It would be the realistic end of his chances for this season. Interestingly, Alonso has said that he think Songapore is his last opportunity to this title. One thing Fernando is not, is being a fool.
• Hamilton needs a massive 20 points outscore with Vettel in Singapore just to not be in an unlikely title position. So, there is still a little candle of hope in his season. Kimi is in a hopeless situation, because, no matter how well he does in Singapore, and how bad Vettel ends, he cannot go out of the "unlikely title" label. To achieve it, he would need a series of outstanding results and Vettel's apalling results in several GPs. In short, he is out.