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 On Wednesday
we ventured into Harvard’s science ghetto for a lecture titled, ”The
Mathematics of Games and Sports," by the eminent
mathematician and sports fan Joseph B. Keller.
We arrived at lecture hall G115 in the Maxwell
Dworkin Lab five minutes late, and the room was already packed, As we
wormed our way into the back, a courteous undergraduate handed us a folding
chair, which we promptly unfolded on some poor fellow’s foot.
Glancing around the lecture hall at the crowd of about 200, we immediately
noticed several things. First, the audience was at least 90% male, not
surprising considering that both math and sports obsessions
are, in our culture, considered mostly (although not exclusively) male
domains.
The other thing we saw was that the ages of the mostly males we saw
ranged in an almost smooth spectrum from little kids of 8 or 9 to septuagenarians,
graybeards and wizened cane-walkers.
Personally, we were there hoping for some tips or techniques to improve
our historically disastrous bottom line in the boisterous world of sports
betting. One of the things we most enjoy about living in or near Cambridge
are the constant opportunities to listen to really smart people talk
about the things that light them up. This really smart mathematician
who obsessively applies numbers to sports MUST have discovered how to
turn
a profit on his efforts.
The lecture started promisingly enough. After warming up the crowd with
some really lame intellectual jokes about inverse problems, where you
start with the answer ("If the answer is "Dr. Livingston I presume?"
what is the question? Punchline: "What is your full name, Dr. Presume?")
he segued into a theoretical way to make money betting on baseball, or
any sports with many teams in a division.
The idea is that at the end of the season, "mathematical elimination"
is a tricky term. Generally, the newspapers (and the bookies, Keller
implied) consider that a team isn’t eliminated until even if it won
all its remaining games, and the teams with which it is completing for
the
pennant
or a playoff spot lost all of theirs, it would still fall short. Keller
pointed out that it would be impossible for the competition to lose all
its games because a good number of those games were against each
other,
and somebody had to win. Therefore, mathematical elimination actually
takes place a few games earlier, and somehow (we’re not really clear
on this part) a savvy bettor could parlay that into a profit.
From there, however, things rapidly went downhill. As Keller became
increasingly enthusiastic about his topic, he started talking in a foreign
language – math. Terms
like "connected matrix" "unique vectors" and "all non-negative
registers" were flying around the room as he launched into an explanation
of why the conventional league standings, as seen everyday in the newspaper,
were inadequate and misleading because they didn’t take into account
strength of schedule.
Next, he computed the most efficient expenditure of energy for a world
class athlete running in 100, 200, 400, and 1600 meter races, factoring
in acceleration,
oxygen burn, acid buildup in muscles and other constraints on velocity,
and showed how the performances of real world athletes mirror his findings. Someone
asked if this also applied to race horses, and we grew momentarily hopeful
of gleaning a tip we could use. Unfortunately, Keller replied that although
his theory should apply to horses, the horses refused to listen.
At this point he unveiled his tour de force, a series of a dozen differential
equations to prove mathematically the obvious truism that a flipped coin
will land heads up exactly 50% of the time, representing with letters
and symbols the height of the toss, the rotational force, the movement
of the axis of rotation over time, the resistance of the air, etc.
Of course, we understood none of the math, and as we could see absolutely
no utility, let alone profitability, in the physics of tossing a coin,
we got up to leave. A marvelous invention, mathematics, but ultimately
little more than a toy with which to play with our senses. The seductive
illusion of numbers is that they really equal the physical reality they
are supposed to mirror, and within a fine-tuned human brain they can
reach a dizzying degree of internal cohesion and delicate complexity.
But in the final analysis, there are no zeros in nature, and an equals
sign is really just a pair of parallel lines.
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