Sports: January 2007 Archives

 

January 21, 2007

Gizmodo points to this site advertising the hyperbike, a new kind of human powered vehicle:

The designer makes a number of claims, including that:

  • It's safer than conventional bikes because it has three points of contact and so is more stable.
  • It's more efficient because of the large wheels, high gearing and because of whole body involvement rather than legs.

I'm quite prepared to believe that it's safer, not because it's more stable—bicycles are actually extremely stable at speed once you know how to balance them—but because the user is in a protective cage. It wouldn't be that hard to build a recumbent bike with similar properties if you wanted to.

I'm a lot more skeptical of the performance claims. I wonder if anybody has actually ridden this than that fast. Here's what the site says:

The Hyperbike will be the fastest & safest human powered vehicle on the road.

The circumference of an eight foot diameter wheel is roughly twenty-five feet and cadence, or the rate at which a person pedals, is most comfortable at a rate of 13 beats every 15 seconds. Gearing that allows an operator to rotate the wheels four times each pedal cycle, or at a 1:4 ratio while at the comfortable cadence rate will produce a speed upwards of 50mph.

Using the whole upper body, an operator, unobstructed by a seat and able to "throw" weight into each pedal thrust bouncing each stroke, like hill climbing on a conventional bike, will move the Hyperbike fast and effectively on all grades.

This is simply confused. The limiting factors in bicycle top speed have nothing whatsoever to do with the gearing of the bike. This is easy to see by doing some simple math.

Your average reasonable road bike has something like a 53/42 chainring combination on the front. That means that it's got 53 teeth on the big ring. It probably has an 11 or 12 tooth smallest cog on the back. For convenience, let's say it has a 52/13 for a 4:1 maximum gear ratio. The wheel itself is approximately 700mm in diameter, or 2.2 meters in circumference. So, every pedal revolution at the highest gear ratio moves you forward about 9 meters. A typical amateur cycling cadence is 80-100 rpm, which maps to 720-900 meters/minute or 27-34 mph. By the simple expedient of putting a readily available 11 tooth cog on the back and 55-tooth chainring on the front you can get to 41 mph at 100 rpm.

But these limits are purely theoretical because what's really important is power. Plugging these speeds into Analytic Cycling we can compute the power required to go at these speeds, which is 300, 561, and 947 watts respectively. For reference, few untrained cyclists can maintain 300 watts for more than a minute or two. Even elite cyclists have trouble maintaining 500+ watts for any length of time. To put this in miles per hour terms, maintaining 25 mph for an hour is doable by amateurs but quite hard. The hour record stands at around 31 miles.

At this point it should be obvious that the gearing isn't the limiting factor in the performance of a bicycle. But a bicycle only works the lower body whereas the hypercycle lets you recruit your upper body muscles as well, so maybe that helps. First, this isn't as big an advantage as you think. The upper body muscles are comparatively weaker than the lower body muscles, which is why racing wheelchairs are somewhat slower than standard bicycles despite having superior aerodynamics. So, all other things being equal, you might get 30-50% more power with the hyperbike but you'd be unlikely to get twice as much. Because the power/speed curve is cubic this might get you a speed improvement of 20%, but nowhere near doubling the speed.

But of course, all other things aren't equal because the vast majority of the energetic cost of riding a bicycle is wind resistance. The completely upright position of the hyperbike is vastly aerodynamically inferior to the partly upright position of a typical road bike (let alone a recumbent bike, which is why land speed records are always set on fully faired recumbent bikes). I would imagine that this increases the surface area by 50-100%, which would more than compensate for the somewhat increased power of recruiting the upper body muscles.

Just as a final check, if you plug 50 mph into Analytic Cycling's model, you come away with a required power output of 1695 watts, even with normal bicycle aerodynamics. If you can put out 1695 watts for more than a few seconds I'm pretty sure there are some people on the Olympic team who would like to talk to you.

UPDATE: The power/speed relationship is cubic, not quadratic. The air resistance/speed relationship is quadratic, but then you multiply by speed again.

 

January 19, 2007

A perennial problem with any athletic event is designing a fair reward structure. Say you're organizing an amateur mass-market athetic event like a road race. What divisions can people win in? The obvious and natural thing to do is to simply have everyone in the same division; the first X people across the line are winners and everyone else.... isn't. The problem here is that this restricts the pool of potential winners to a fairly small group, say men between 20 and 40. There's practically no athletic event at which even the best women are competitive with the top rank of men and there's a fairly sharp performance peak around 30-35 (depending a bit on what the sport is).

Now there's nothing necessarily wrong with just giving awards to those people but it's clearly a turnoff for people to be "competing" against others whom they have no actual chance at beating. And turning competitors off isn't a good way to get more people to enter your event. So, there's a lot of incentive to find some reward structure that gives a broader class of people a chance to win something. This even crosses over into professional sports where it feels unfair to force people to compete against others who are clearly qualitatively different—though it's worth noting that within gender (the most common division) variation greatly exceeds between gender variation and yet nobody thinks it unfair that I have to compete against men with 2:30 marathon times.

The three most common divisions that are used to partition up contestants are gender, age, and weight. All of these have the advantage that they seem superficially fair because they're either uncontrollable (age and except for edge-cases gender) or only marginally controllable (weight), which gives the appearance of fairness. In my experience the next most common division is "local contestants", which is also not really controllable and clearly arbitrary.1 All of these divisions also have the advantage of being (mostly) readily verifiable.

This sort of division works well for some sports but not as well for others. In martial arts, for instance, weight matters and there are often weight classes, but there's enormous skill variation between athletes. If you let white belts compete against black belts what you get is less a match than a rout. In martial arts with strict ranking systems you can just pair up people of the same rank (or maybe one-up or one down) against each other. 2. In less formal sports, sometimes how long you've been training is used as a proxy. Since most dojos don't keep particularly good records of when people have trained or what rank they have attained, and those records aren't centralized, it's pretty easy to sandbag. The theory here is that it's better to be a winner in the beginner's division than be a loser in the advanced division, so you claim you're a beginner.

One way of countering sandbagging is to turn it into a repeated game. Bicycle racing is divided into 5 "categories". The way you move up from one category to another is by winning races. If you're too dominating in a category you get promoted to the next one. What makes this work is that people tend to race each other repeatedly, so they tend to find their own level. Obviously you can sandbag a little bit, but you can't win very often because you'll eventually get moved up.

This doesn't work as well in non-iterated situations. An interesting case I ran into recently is rock climbing. A typical bouldering competition involves a bunch of problems of various difficulties, with harder problems being worth more points. Because climbing is so skill-based, it makes sense to have divisions, but it's so hard to compare people's skills that the competitions I've heard of (note: I've never done one but I've spoken to people who have worked them) have competitors self-sort into divisions. Obviously, this is incredibly susceptible to sandbagging. Competitions deal with this by promoting people who look too good into the next division.

Unfortunately, this strategy is inherently unstable because it's precisely the people you would expect to win (the best people in the division) who are most likely to get bumped out for being too good. A related problem is that there's a lot of variation in experienced difficulty for problems that are nominally the same grade, so it's precisely when you're having a good day and the problems seem to be easy for you that you have to worry about being declared too good. And of course you can still sandbag some by figuring out where the line is and climbing right up to it. What mostly seems to suppress this sort of thing is that it's considered unsporting. This works in a small community, but in my experience once the stakes get big (or even not so big) people seem to lose their sense of sportsmanship. Do any readers who've done comps have a read on how much people try to game the rules?

1. It's also interesting to look at the evolution of sports, which seem to accrete finer divisions. For example, the Ultimate Fighting Championship used to be totally open but later weight classes were added. A while back triathlon introduced the "clydesdale" division for heavier athletes (the female version is called Athena). Clearly, heavier athletes are at a disadvantage but it seems to me that this division is still regarded with a bit of suspicion.
2. A related problem in martial arts is that you need to keep the divisions fairly small because otherwise the tournament requires two many matches to converge on a single winner.

 

January 3, 2007

Ross Bernstein's The Code: The Unwritten Rules Of Fighting And Retaliation In The NHL provides these 10 reasons why hockey fights start:
  1. Retaliation and retribution.
  2. Swinging the momentum
  3. Intimidation
  4. Sending a message
  5. Trying to draw a reaction penalty
  6. Deterrence
  7. Job security
  8. Protection
  9. Prison justice
  10. Bad blood

There's a bit of redundancy here, but it's striking the extent to which fighting has been integrated into game strategy. For instance, here's reason 2:

The second reason for fighting is to provide a spark or catalyst to wake up your team. Fighters will challenge opponents when their team is down for the sole purpose of winning the fight and thus swinging the momentum of the game. If a player battles like a warrior and wins, the crowd gets pumped up and the players get a shot of adrenaline to inspire them to work harder. It is all about gaining a mental edge or psychological advantage in hockey and a good scrap can achieve that in a heartbeat.

Here's Marty McSorley:

The code can be completely different for guys when they are playing on a bad team. When you are an enforcer on a bad team it is your job to go out and try to turn the game around. A tough guy knows that he can swing the momentum 180 degrees from a dull, boring game to one the fans are totally into, and the players respond to that. That guys knows when he has to use his shift to try and stir it up out there in order to get his teammates and his fans back into it. That is a tough job, I have been there. It is particularly tough when you are playing on the road and an opposing team's home ice. It goes against who you are as a person and as a player to go out and start something when nothing is going on. But hey, it is the nature of the beast with this role.

I would also add that when that situation arises, it means even more to be able to do it with respect and honesty. What I mean by that is if it was my responsibility to go out and sti something up, then I would go up to their tough guy and bring it up with him directly. ... I would talk to him directly and put him in a position to address me out on the ice, with respect.

Now that tough guy knows the code and knows that he needs to match you, because that is your job. ... Even if he is tired or sore, he knows that he needs to face you and give you your shot to turn your team's momentum around that night. It is a battle, one on one, and we both know our roles. A victory will spark your team's emotions and foce them to play harder, while a loss can do just the opposite. It is a tough job, but a true fighter relishes that momentum out there and fights for his teammates.

Another notable point is that many of the former players interviewed by Bernstein (admittedly most of them enforcers) believe that fighting is a critical part of keeping the game orderly, because it gives players an informal way of keeping other players in line for behavior that the refs don't notice (or that might not be explicitly illegal). The "instigator rule" which gives extra penalty time to whoever starts a fight comes in for particular criticism on the theory that it interferes with informal dispute resolution resulting in more aggressive play, more injuries, and more heated fights when they happen. I don't know if it's true, but it seems clear that if the NHL really cracked down on fighting effectively, it would dramatically change the strategiy shape of the game.