Monday MotoGP Mathematics: The Permutations For The MotoGP And Moto3 Titles At Valencia

For the first time in a long time, the MotoGP circus heads to the final race of the year at Valencia with not one, but two championships still undecided (and if there hadn't been that first-lap incident in the Moto2 race at Motegi, it could even have been three). The title is still to be decided in both the MotoGP and Moto3 championships, and the possible mathematical permutations are having race fans and followers racking  their brains trying to work out who needs to finish where for either Marc Marquez or Jorge Lorenzo to win the MotoGP title, or Luis Salom, Maverick Viñales or Alex Rins to lift the Moto3 crown.

To assist with this computation, we have drawn up two tables with all of the possible permutations, one for the MotoGP class, and one for the Moto3 class. Using the tables below, you can see all of the possibilities the two MotoGP men and three Moto3 riders have to win the title in their respective classes.

In the MotoGP class, Marc Marquez is the hot favorite to take the title, leading Jorge Lorenzo by 13 points. That is enough of a cushion for the Repsol Honda rookie to finish anywhere in the top 4 if he is to wrap up the title. Given that Marquez has only finished off the podium twice this year - once when he crashed at Mugello, washing out the front at Savelli, and once at Phillip Island, when he was black-flagged when his team left him out for one lap too many - the odds of Marquez not taking the title at Valencia are small.

Jorge Lorenzo will need help from at least three other riders if he is to be champion: first and foremost, he must win the race, something which, given his current form, he has a good chance of managing. However, he will need three other men to get between him and Marc Marquez, and that seems much more unlikely. Marquez' Repsol Honda teammate Dani Pedrosa has proven capable of beating Marquez regularly this year, and given both Honda's stated aversion to team orders (other than "whatever you do, don't take your teammate out"), and the open dislike there is between Pedrosa and Marquez, the senior member of the team is unlikely to go out of his way to help Marquez. If Dani Pedrosa can get on the podium, then he will surely try. He can always claim he was trying to beat Lorenzo, and take points off him that way.

Finding two other riders capable of getting between Lorenzo and Marquez will be difficult. Valentino Rossi has beaten Marquez twice, once at the first race in Qatar, and once at Assen, but has not shown the ability to match the pace of the youngster since then. Cal Crutchlow, Stefan Bradl and Alvaro Bautista have all shown pace this year, though Crutchlow has only beaten Marquez once, at Le Mans, in Marc Marquez' first ever wet MotoGP race. The other two Honda men have not been able to finish ahead of the youngster, and so Lorenzo cannot count on them doing so at Valencia.

But Lorenzo is not completely without hope. The 2006 championship is still fresh in everyone's minds, when Valentino Rossi came into the final race at Valencia leading Nicky Hayden by 8 points, yet lost the title by crashing early on, remounting, but not making up enough places to prevent Nicky Hayden from taking the title, after having led it for much of the season. This has been the aim of Lorenzo and his team since after the summer break, when Marquez was racking up the points: try to take the title chase to Valencia, and hope that the pressure will get to the Honda rookie. The title is not over by a long way.

So to the table below. The permutations should be self-explanatory. The lower section of the table sets out where the two riders must finish relative to each other if one or the other is to be champion. The finishing positions have been calculated for both Marquez and Lorenzo. The bottom line is that Jorge Lorenzo has to finish in the top 4, and Marc Marquez has to just follow his tailpipe to bring it home. The same calculation for the Moto3 championship follows below the MotoGP table.

Permutations for the MotoGP championship:

  Marc Marquez Jorge Lorenzo
Points 318   305  
Wins 6   7  
2nd 6   1  
3rd 3   5  
  Marquez is champion if Lorenzo is champion if
  Marquez finishes Lorenzo finishes Lorenzo finishes Marquez finishes
  1st to 4th Marquez is automatically champion 1st 5th or worse
  5th-8th 2nd or worse 2nd 9th or worse
  9th-12th 3rd or worse 3rd 13th or worse
  13th-15th 4th or worse 4th Marquez does not score
  Scores no points 5th or worse    


The situation in the Moto3 title chase is a little more complicated, with the three front runners separated by just 5 points. Between them, Luis Salom, Maverick Viñales and Alex Rins have taken 39 of the 48 possible podium positions, and so the championship looks like being a simple winner-takes-all equation. If any of the top three wins the race, they win the championship. Though a Rins win with Salom second would put the two men both on equal points and an equal number of wins, the title would go to Rins as he would have scored more second places.

If none of the top three win, the mathematics gets a lot more complicated. Rins, as the rider with the fewest points, must finish ahead of both Salom and Viñales, and he must finish in the top 10. Viñales must finish above 13th, and can allow Rins to finish one or two places ahead of him, as long as they are both well down the field. Salom can afford not to score any points, as long as both Viñales and Rins are well outside the top 10. But the most likely scenario is that all three will take it to the line, and the title will be decided on finishing order. Looking back at last year, Viñales finished 8th, Salom 10th and Rins 16th. If that were to be repeated again this year, then Salom would be champion.

The table below shows the mathematics of the championship. The column for each rider shows what must happen if that rider is to be champion and he finishes in the position shown on the left hand side. So for example, if Salom were to finish in 5th, then he is champion if Viñales finishes in 4th or lower, and Salom finishes in 3rd or lower. Likewise for Rins, if he finishes 10th, then he will only be champion if Viñales finishes 13th or lower, and Salom does not score. To help with calculations, the points scoring system is shown at the bottom of the page.

Permutations for the Moto3 championship:

  Luis Salom Maverick Viñales Alex Rins
Points 300 298 295
Wins 7 2 6
2nd 2 8 5
3rd 3 4 2
Finishing Position Is champion if: Is champion if: Is champion if:
1st Champion Champion Champion
2nd Finishes ahead of Viñales & Rins Finishes ahead of Salom & Rins Viñales 3rd, Salom 4th
3rd Viñales 4th & Rins 3rd Finishes ahead of Salom & Rins Viñales 4th, Salom 6th
4th Viñales 5th & Rins 3rd Salom 6th, Rins 5th Viñales 6th, Salom 9th
5th Viñales 4th & Rins 3rd Salom 8th, Rins 4th Viñales 8th, Salom 10th
6th Viñales 5th, Rins 4th Salom 9th, Rins 5th Viñales 9th, Salom 12th
7th Viñales 5th, Rins 4th Salom 10th, Rins 5th Viñales 10th, Salom 13th
8th Viñales 6th, Rins 4th Salom 11th, Rins 6th Viñales 11th, Salom 14th
9th Viñales 7th, Rins 5th Salom 12th, Rins 7th Viñales 12th, Salom 15th
10th Viñales 8th, Rins 5th Salom 13th, Rins 8th Viñales 13th, Salom no score
11th Viñales 9th, Rins 6th Salom 14th, Rins 9th Rins cannot be champion
12th Viñales 10th, Rins 7th Salom 15th, Rins 10th  
13th Viñales 11th, Rins 8th Salom no score, Rins 11th  
14th Viñales 12th, Rins 9th Viñales cannot be champion  
15th Viñales 13th, Rins 10th    
No score Viñales 14th, Rins 11th    


Grand Prix motorcycle racing points scoring system:

Finishing position        Points scored
1   25
2   20
3   16
4   13
5   11
6   10
7   9
8   8
9   7
10   6
11   5
12   4
13   3
14   2
15   1


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I think the team order will be Dani either has to win the race or finish behind Marc, and Dani will do as told. How it plays out I'm not sure, but Lorenzo's super strong pace on the first lap means it will be very hard for Dani to escape in the early stages if the starts go the way they have recently. Lorenzo will attack hard and immediately because he has to, which will put Dani in the awkward position of not leading the race but not wanting to impede Marquez. I think in that scenario Dani will let Marquez past without any fight whatsoever and then follow at a safe distance from there on just as in Motegi.

Moto3 - I'm sure it's going to be a good race to watch if even only2 of the 3 of them are up front, especially the last few laps. but I want to see all 3 of them fighting for it. I'm so glasd I started following the lower classes last year - it's never dull.

MotoGP - I don't want to see either Lorenzo or Marquez repeat what happened to Rossi in '06. I want to see them fighting for the win.

I'm also looking forward to the post-race test - it will be interesting to see how the new riders moving up to Moto2 and MotoGP do, as well as the performance of the production Honda, Forward Yamaha and what Aprilla has on track.

I don't think we will be able to see much from Forward yet. The bike is going to be pretty much a slapped together thing given the little time FTR had to work with it. If they are half a second faster than their current bikes, I'll be optimistic about this project.

I thought they were using the Yamaha chassis and swingarm at first while FTR develops a chassis ?

My understanding was the team has to fit suspension, wheels, brakes to get it on the track.

But they also have to design the fuel tank and bodywork, not to mention coming to grips with the spec ECU and software. Probably lots of details to iron out on that bike.

Bike wise Aleix Espagaro I going to regret not sticking with Aspar. But he probably already made his choice before the deal with Honda was announced. I can understand he did not want another season on an ART.

Does anybody know what the weekend weather forecast is for Valencia??? I pray for a dry weekend so that weather does NOT play a role in deciding the MotoGP Championship! I am no JL99 fan but he's battled back very hard... impressive! However, I want to see the kid get the title! MM93's rookie MGP season... Most iMpressive! Go Marquez...

How's the Yamaha engine situation? Imagine all the buildup for this title finale only to have it ruined by JL having to start from pit lane? Someone would have to give MM another penalty point, for farting at the pre-event press conference or something, so that they both start from pit lane.

That's a good question. Is Lorenzo using a worn-out engine for this race?

There is no way HRC will allow Pedrosa to dice with Marquez let alone allow him to finish ahead of him despite the perceived "dislike" between the two. They will not risk a repeat of 2006, where Pedrosa took out Hayden in the next to the last race of the season thus allowing Rossi to take the points lead going into the last race. Unless he crashes out Marquez is a lock; he is on the best bike and consistently has shown the skill and maturity of a champion. He has been riding "safe" for the past couple of races knowing full well that the championship is a mere formality. you think HRC will be able to stop Pedrosa (and Puig) from doing whatever they choose. HRC I am sure would not 'allow' but they are not on track. The one on track is Pedrosa(with Puig on the back),

Marc could be a wild man in the past, barging past slower riders and making very bad choices that put his and others health at risk. In his first year in MotoGP however, he has not only surprised me with his speed and consistency (race finishes, not practice crashes)but his maturity to know when to reign in the competitive fire and finish 2nd or 3rd. Those days are also what put him in the best position to win the championship, not just the top step performances.

This is going to be an exiting weekend. A shame I have to miss it.

Not just the riders need a cool head. It's a team sport. One bone headed move from any of the team members can blow a sure thing. Pedrosa's tire warmers, running out of gas, cold tire crash. Unlikely. I expect MM will shake up modern history.

Kenney Robert's achievement may as well have been filmed in black & white. The bigger question to me is how has MM/MOTO2 riding style change MGP if he wins?

JL99 and VR46 have both voiced that they do not like this track. DP26 has said and shown that it suits him well in all classes and I believe he can play into upsetting JL99's hopes.
On an aside, while JL99 sure makes it hard to like and even at times respect him, I am REALLY impressed with what emerged from him on the track this season. I am not tempted to berate DP26 at all, more tempted to applaud JL99 even though I cringe at every one of his celebrations.

It's very hard to not think of 06 with this years last race circumstances.

Bottom line, like said before- Lorenzo has to win & MM93 has to bin it.

Lorenzo cannot afford to charge off into the distance. He does that and the title is gone. He has to slow down just enough to keep Pedrosa behind him and try to make Marquez crash or put Marquez into a position where someone else crashes him out. Marc has shown a remarkable consistency in races, crashing far less than most predicted he would. So, literally, Jorge has to do whatever is possible to make sure Marc winds up on the ground.

I suppose that's excitement for some.

Sadly, had we avoided the phiasco at Phillip Island, the title is settled, and Jorge, Dani and Marc all come to Valencia with nothing to lose, all eager to prove who really is fastest.

Now THAT would be a shootout. Unfortunate that it is not the case ...

I agree with you 100% that George has to get numbers between himself and Marc, but its a sort of PI situation Sete was faced with may years back against Valentino. No one could stay their pace. I'm sure Dani can and will be a boot in for the win. However,if the 3 of them stay out of trouble its tickets. The big one in terms of permutations and possibilities is indeed M3.

Jorge needs Marquez on the ground, end of story. The odds of Jorge winning and Marquez finishing fifth are very, very slim, based on the history of the season so far. Jorge is better off letting Pedrosa go and doing everything he can to punt Marc off the bike, or hold him up enough that Rossi can do the punting.

We'll know within two laps what is going on. If Jorge is anywhere near his qualifying times, he's going for the win and hoping for a miracle. If Dani fires into the distance and Jorge is cruising around, he's hoping to knock Marc off or force him into a crash.

Ironically, it is only after a championship is sealed that you actually see riders actually racing at 100 percent.

I stopped caring after Phillip Island, Dorna have ruined the season for me with their making up rules on the fly.

Valencia just reeks of media concoction.