Game Theory Of The Breakaway

If you have seen the film 'A Beautiful Mind' or you have done a bit of industrial economics, or even gambling, then you might have heard of Game Theory. It is a science that tries to make sense of the decision choices made by individuals, when they are faced with one-shot simultaneous move situations.

The application of game theory has found its way into topics from penalty shoot-out decisions, to how easy it is for two firms to collude to raise prices in an industrial market. In this blog, I try to show how game theory can be applied to a breakaway situation in a road race.

The classic example of game theory is the 'Prisoner's Dilemma': consider two gang members, stuck in two separate cells at a police station; both prisoners were arrested at the scene of a crime, and had no chance to discuss their alibi with the other.

Simultaneously, both prisoners are taken from their cells to separate interview rooms and told:
  • If you confess and your partner does too, then you will get 10 years in prison each
  • If you confess and your partner denies his involvement, you will walk away, but your partner will get 20 years in prison
  • If you stay quiet, and your partner stays quiet, then we have little to charge you on, and you walk away with just 2 years in prison
  • If you stay quiet, but your partner grasses on you, then he walks away and you get 20 years
Clearly the best outcome for the pair of criminals is to co-operate and stay quiet. But, because they don't know what the other one is going to do, they must work out the optimal strategy...

If your partner stays quiet, it is optimal for you to confess; if your partner confesses, it is optimal for you to confess. Therefore you always confess! This is the Nash Equilibrium, demonstrated by John Nash (Russell Crowe in 'A Beautiful Mind').

How is this like a breakaway situation?

Well... you get in a break from the peloton with another rider; you have got two options: "Work your socks off and make the break successful" or "Sit-in and free-ride to the finish line".

The outcomes are predictable:
  • You both work like crazy to make the break a success, and as a result you have got either a chance of getting 1st or 2nd place, so a minimum of 20 points for second at the finish line
  • You work your socks off, and keep the break away; but then because you are the only one working, you blow up... you get swallowed up by the bunch and watch your "mate" solo away to victory and get 30 points
  • Or alternatively, if they are doing the work, then reverse the above, and you could get 30 points!
  • Finally, you could both just sit in, wait for the bunch sprint and hopefully get 5 points at most
So, what is the outcome? Clearly the best option for the two as a pair is to work well together, and get at least 20 points each; but this rarely happens... The optimal strategy if your partner is working their socks off, is to sit in and claim 30. The optimal strategy if your partner is sitting in and refusing to work, is for you to do the same. Therefore, the Nash Equilibrium is to both sit in, and not work... No breakaway, and at best 5 points in the bunch sprint.

So there you have it, my understanding of why so many breaks don't work in road racing, especially it seems in lower category races. Get a bit higher up and some riders learn the tactics and game theory and realise that if they are not a sprinter either, then you do far better to work together tirelessly and try and get a good set of results.

Labels:


Comments

Post a Comment

Popular posts from this blog

SwissStop Disc Brake Pads Comparison Test Review – Are All Disc Brake Pads Made Equal?

Image
The market for disc brake pads for gravel bikes, mountain bikes and road bikes is saturated; there are hundreds of different brands producing disc brake pads claiming to last longer and perform better than the competition. So, what is the difference between a set of low cost disc brake pads from eBay/Amazon versus the high-end pads from SwissStop? Are SwissStop disc brake pads worth the extra money? To find out, I have been doing some extensive disc brake pad testing over the last few months. October to February is obviously a period of wet winter riding, and I have been testing the following list of brake pads on road, gravel and mountain bikes—to create the ultimate test for any disc brake set-up. The disc brake pads on test:  SwissStop Disc 34 RS (Shimano Road/Gravel)  SwissStop Disc 32 RS (SRAM Road/Gravel)  SwissStop Disc 31 E (MTB SRAM Avid)  Superstar Sintered Shimano Road Disc Brake Pads (Shimano Road/Gravel)  SOMMET Resin and Semi-Metallic Disc Brake Pads (SRAM Road/Gravel
Keep reading

Recipe – The Ultimate High Energy Flapjacks

Image
This traditional flapjack recipe is packed full of energy for long days on the bike. The oats supply a great low-GI fuel source, while the dried fruit offers instant energy and sweetness. Whether on or off the bike, these flapjack bars are a great high-energy snack for cycling. You can adapt the recipe by adding in other dried fruit, seeds, nuts, and spices to make these even more varied and flavoursome. I particularly like pumpkin seeds and chopped crystallised ginger added to the mix. Ingredients 200g butter 100g brown sugar 1 tbsp golden syrup ½ tbsp black treacle 300g porridge oats 100g raisins 75g soft-dried figs 50g soft-dried apricots Method Set the oven to 150°C or 140°C for fan-assisted oven. Place the shelf in the middle Stick a big pan on the scales and measure in the butter and brown sugar Heat the pan on the hob until the butter and sugar are all melted Add a tablespoon of golden syrup and half a tablespoon of treacle to the mix Add the porridge oats and y
Keep reading

Review – Selle Italia SLR Boost Gravel Superflow Saddle S3

Image
The Selle Italia SLR Boost Gravel Superflow Saddle is designed for gravel bike riding. Featuring gel inserts to reduce vibration, titanium saddle rails to absorb trail buzz, and a sleek low-profile design to offer style and performance—this is a saddle made for adventure. The SLR Boost Gravel is Selle Italia's latest offering for the growing Gravel segment of the market; engineered specifically to enhance riding comfort on difficult terrain and during endurance gravel events. Available in two sizes, I opted for the smaller version (S3), and have been testing it out over the last month… I have become a great advocate of the cut-away design for saddles—it offers greater flexibility in the centre of the saddle and reduces pressure on the sensitive perineum region. The SLR Boost Gravel Superflow is a superb example of this kind of saddle design; with a cutaway section, short nose, and flared sides to effectively support your seat bones. To improve comfort on rough terrain, Selle
Keep reading

Review – TRP Spyre SLC Cable Disc Brakes

Image
Cable actuated disc brakes get a lot of bad press. There is some justification for that — most of the systems lack the modulation and performance of their hydraulic counterparts. There is however one set of cable disc brakes that shines above the rest: the TRP Spyre SLC Disc Brake. This lightweight and sleek cable disc caliper excels in both design and functionality. My Kona Private Jake arrived in 2016 with a set of TRP's Spyre-C disc brakes fitted as standard. Those brakes worked very well for over 25,000 kilometres of use and abuse; I rode the bike for daily commutes (including a salty daily ferry journey), and I rode the bike fully loaded over the highest cols in the Pyrenees on the #CoastsandCols tour. The Spyre-C took all this abuse in hand and always produced the stopping power I demanded. This year, with the Kona Private Jake hitting a 25,000 kilometre anniversary, I decided it was time to upgrade and replace a number of the parts. To be honest, most of the component
Keep reading

Review – SunRace CS MX80 (MX8) 11-46T Cassette for SRAM

Image
If you are running a SRAM Force or Rival 1X drivetrain set-up, then you may well find yourself wishing for a lower gear, especially on bikepacking adventures. The SunRace MX80 / MX8 11-46 tooth cassettes supply two additional low ratio gears than you get on the standard 11-42T SRAM cassette. That is an upgrade worth considering... On my Kona Sutra LTD build , I was concerned about a lack of low end gear spread for the Tour Divide . Whilst pure grunt will usually get you up most things on an 11-42T cassette, I thought with the cumulative fatigue and long climbs on this 21 day bikepacking route, I might need something lower... SRAM rate their SRAM Rival and Force 1X rear derailleurs as suitable for a maximum of a 42-tooth cassette—I was keen to see if the SunRace MX80 and MX8 cassette would work with the derailleurs and provide that sought-after lower gear possibility. You may well not have heard of the SunRace brand, but you likely have heard of Sturmey Archer—the iconic hub gea
Keep reading