Point Taken

This time of year, hockey fans are obsessively checking the chances of making the playoffs for each team. An interesting quirk of the NHL is that it awards two points for a victory and one point for a loss in overtime or a shootout (and zero points for a regulation loss). This is a throwback to the previous system, in which games could end in a tie if the score was deadlocked at the end of regulation, with each team picking up a point. So in a sense, the overtime/shootout system is kind of a hybrid… once 60 minutes are over and the score is tied, both teams are guaranteed one point, as in the old system. But now, they keep playing until a winner is decided, who still picks up the maximum two points possible for the game. This creates an interesting “non-fixed sum game” in which teams not playing in the game, but watching the standings, might root for an outcome in which they don’t care who wins, as long as it is decided in regulation (avoiding a so called “three-point game”)!  Also, there is a strong incentive to play conservatively late in the third period if tied, since you can lock down that sure point just by not giving up a goal. By the way, chess is a “fixed sum” system, since there is 1 point for a win, 0 for a loss, and 1/2 to each player for a draw – so the sum is always 1.

A strange effect is the different value of goals depending on whether your team is tied or behind at the end of the game. Consider the “point value” of a goal in a fixed sum system [two points for a win, one for a tie] during the final second of regulation. If you are tied, before the goal your expectation was to tie (1 point) and now you will get the win (2 points), netting a 1 point increase for your team. The same will be the case if you are behind by one, and score the tying goal in the last second (1-0 = 1). However, in the NHL, not all last-second goals are worth the same. If you are tied at 59:59 of game time and net the game-winner, your expectation goes up to 2 from 1.5 (one for the sure point for making it to overtime, plus 1/2 for the 50% chance of getting the additional point in extra time). But, if your team is down by one (with your goalie pulled, presumably, in desperation) and you get the equalizer, in addition to being a hero, you will add 1.5 points to the teams expectation value, from zero to 1.5, as explained before… Three times more than a game winner! Getting a point and the chance to play on for the second is quite a prize when the threat of a regulation defeat, a zero points, was looming.

In major league soccer, there is also a non-fixed-sum system [3 points for a win, 1 for a tie, to encourage playing for the win], but the value of goals is somewhat more even, but now it is more valuable to get the go ahead goal, which is worth 2, twice as much as the equalizer, worth just 1.

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Bracketology

In grade school, we were very into the mathematics of the NCAA men’s basketball tournament. This year, Warren Buffet has raised the stakes, by participating in a Billion Dollar Prize for a perfect bracket. What is interesting, beyond the fact that Warren’s Berkshire Hathaway is writing the contingency insurance (which is totally a thing) in case someone wins, is the difference in your change of winning between guessing randomly and having some knowledge about the games – although is is still vanishingly small. Picking all 63 games correctly assuming nothing about the teams has a probablity of 2^63 = 9.22 x 10^18. However, knowing the seeding and, for example, that 1 and 2 seeds almost always win their first-round games, you can improve your odds substatinally. Estimates vary, but some think your real chances are more like one in 10^11, which is a lot better, but I’m sure Warren is not losing any sleep. This site summarizes the difference:

“If all seven billion people on Earth filled out a somewhat informed bracket with these odds, over the course of 13 years, chances would be greater than not (51 percent) that someone would nail it. If everyone filled out a coin-flip bracket, that break-even would come over the course of 911 million years.”

The reason it is still so unlikely to win, even with the collective basketball acumen of all the experts, is that there is only one way for a bracket to be perfect (ie.  it has the lowest possible entropy), and a LOT of ways to be wrong.

Bracket

Dispatches from Denver – Day 2

Physicists have an interesting view of cancer. During the past few March Meetings, a challenging idea has been put forth: that cancer represents a atavism back towards an ancestral state. That is, before single cells groups together to make multicellular organisms, rapid division was the name of the game. But now, as in our modern, specialized society, cells need to act for the greater good of the whole organism, and reproduction had been confined to the germ cells. In fact, to build complicated organisms, some cells must commit suicide (apoptosis). Paul Davies explained cancer using the analogy of a genie in a bottle. Inside all cells is the ancestral program to multiply like crazy, which has been reined in by more recent adaptations. He says that certain mutations “break the bottle” and release the genie. (I sometimes think about some of the early versions of the Windows Operating system, which, were built upon the even older MS-DOS framework). Therefore, there is no point in trying to examine the shards of the bottle to understand why cells turned cancerous, they are just defaulting to their original pre-programmed state. He said that the reason evolution hasn’t eliminated these old subroutines is that they are used in some very central functions, like embryogenesis and would healing. This theory predicts some ways to combat cancer – according to this, cancer cells are most comfortable in environments similar to those of protozoic oceans from 1.5 billion years ago and it is already known that cancer cells prefer low oxygen situations. Charles Lineweaver suggests using biological warfare against cancer, which cannot muster an immune response, since this requires specialization of cells. One idea is to intentionally infect the patient with a pathogen that has a vaccine, so the cancer cells would be vulnerable, but the healthy cells would have the protection of the adaptive immune system.

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Dispatches from Denver – The 2014 APS March Meeting, Day 1

I’m in Denver for the 2014 March Meeting of the American Physical Society. It’s the biggest annual gathering of physicists in the US.

As a researcher in biophysics, I’m excited every year to see more and biological physics talks. The biggest theme I saw from these talks was the use of physics equations from completely different situations (eg. percolation phase transitions, information theory) applied in interesting ways to biological systems. Here are some highlights from the talks I attended on the first day:

Session A12: Phase Transitions in Biology

A12.1

The session started right at 8 am, and the presenter remarked somewhat amusingly that it might be “the first phase transition of the meeting.”  The irony is that the concept of a phase transition is so common in physics, and he was applying to a model of epidemiology. In fact, the main idea of his talk was the use of percolation theory to explain the spread of disease through a network of acquaintances.

A12.3

This talk elaborated on an idea I am using in my own research, that there can be hysteresis in the population dynamics of a species (like pack hunters) in which the probability of each individual to survive is better when there is at least a minimum number present. Below this threshold, they are doomed to collapse. There are some signals that a collapse is near – when fluctuations become bigger and take longer to recover from. This is a prediction of dynamical systems, a fold bifurcation.

B11.1

Physical Biology of the Cell

I’m a big fan of the biophysics textbook The Physical Biology of the Cell, which just came out with a second edition. The author, Robert Phillips, gave an amazing talk about the classes he teaches at Caltech for mostly non-biology science majors. He contents that science majors are looking for testable hypotheses and organizing frameworks, not just a collection of facts. He had a list of “big ideas” for biology:

  • The cell as the fundamental unit of life
  • The gene as the unit of heredity
  • Evolution over time by natural selection
  • The universality of biochemistry in living things

He talked about having his students cross-breed mutant fruit-flies and then sequence their DNA. Overall, a very interesting approach towards making biology “harder” as a hard science.

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