Sports

Sport Science: Human vs. Bow

Super Bowl Sunday is, of course, the great American holiday. Past years have seen inspirational performances by Joe Namath, Joe Montana, and Janet Jackson. This year pits the New Orleans Saints against the Indianapolis Colts. New Orleans, of course, is known as a city of saintly behavior, while Indianapolis’s claim to fame involves horsepower in some tangential way.

When faced with contests of ritualized violence, we like to look for the science. So check out this video of Saints quarterback Drew Brees participating in a rigorous laboratory experiment by throwing the ol’ pigskin at an archery target. Joking aside, that is some pretty sick accuracy there.

Impressive that a human arm beats a bow and arrow for accuracy (although it’s not completely clear that the distances and conditions were perfectly analogous). All in the wobble, apparently. But if I were defending my castle from the barbarian hordes or something, I’d still prefer archers over some guys throwing footballs.

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The Category Mistake at the Heart of College Football

Too many things I would blog about, if only I could slip into an extra timelike dimension and experience several weeks in just a few of your Earth minutes. Between now and New Year’s I’m going to clean out my collection of blog-worthy things; if you’ve read enough of Cosmic Variance in the past, you should be able to extrapolate to a full post.

Today: “Top Ten Stupidest Arguments in College Football,” which is itself so full of stupid arguments one suspects one is being punk’d. College football is the only major sport that decides who plays in the championship game on the basis of a vote, rather than by a playoff. One can debate the merits vis-a-vis excitement and revenues, but the whole operation is based on an epistemological blunder: the idea that there is something called the “best” team. The point of sports is not that there are better teams and worse teams, it’s that some teams win and some teams lose. Winning and losing is not some approximation to the true measure of excellence that we are forced to put up with; it’s what the games are all about. A sensible world would have a playoff, and let the teams play. (I’ve actually heard people argue that a playoff would be bad idea because the “best” team might not win.)

(If I could just train myself to make posts that are that short all the time, I’d blog twice as often. Maybe five times as often. Are more/shorter posts better?)

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arxiv Find: Star Clusters and Usain Bolt

From the “physics answers the questions you really care about” file, some friends have treated the Olympic 100-meter dash as an astrophysics problem, and figured out how fast Usain Bolt could have run had he really tried:

Velocity dispersions in a cluster of stars: How fast could Usain Bolt have run?
Authors: H. K. Eriksen, J. R. Kristiansen, O. Langangen, I. K. Wehus

Abstract: Since that very memorable day at the Beijing 2008 Olympics, a big question on every sports commentator’s mind has been “What would the 100 meter dash world record have been, had Usain Bolt not celebrated at the end of his race?” Glen Mills, Bolt’s coach suggested at a recent press conference that the time could have been 9.52 seconds or better. We revisit this question by measuring Bolt’s position as a function of time using footage of the run, and then extrapolate into the last two seconds based on two different assumptions. First, we conservatively assume that Bolt could have maintained Richard Thompson’s, the runner-up, acceleration during the end of the race. Second, based on the race development prior to the celebration, we assume that he could also have kept an acceleration of 0.5 m/s^2 higher than Thompson. In these two cases, we find that the new world record would have been 9.61 +/- 0.04 and 9.55 +/- 0.04 seconds, respectively, where the uncertainties denote 95% statistical errors.

Complete with this interesting photo reconstruction:

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The Hidden Complexity of the Olympics

Chad laments that we don’t hear that much about the decathlon any more, because Americans aren’t really competitive. I also think it’s a shame, because any sport in which your score can be a complex number deserves more attention.

Yes, it’s true. The decathlon combines ten different track and field events, so to come up with a final score we need some way to tally up all of the individual scores so that each event is of approximately equal importance. You know what that means: an equation. Let’s imagine that you finish the 100 meter dash in 9.9 seconds. Then your score in that event, call it x, is x = 9.9. This corresponds to a number of points, calculated according to the following formulas:

points = α(x0x)β   for track events,

points = α(xx0)β   for field events.

That’s right — power laws! With rather finely-tuned coefficients, although it’s unclear whether they occur naturally in any compactification of string theory. The values of the parameters α, x0 and β are different for each of the ten events, as this helpful table lifted from Wikipedia shows:

Event α x0 β Units
100 m 25.437 18 1.81 seconds
Long Jump 0.14354 220 1.4 centimeters
Shot Put 51.39 1.5 1.05 meters
High Jump 0.8465 75 1.42 centimeters
400 m 1.53775 82 1.81 seconds
110 m Hurdles     5.74352    28.5    1.92    seconds
Discus Throw 12.91 4 1.1 meters
Pole Vault 0.2797 100 1.35 centimeters
Javelin Throw 10.14 7 1.08 meters
1500 m 0.03768 480 1.85 seconds

The goal, of course, is to get the most points. Note that for track events, your goal is to get a low score x (running fast), so the formula involves (x0x); in field events you want a high score (throwing far), so the formula is reversed, (xx0). Don’t ask me how they came up with those exponents β.

You might think the mathematics consultants at the International Olympic Committee could tidy things up by just using an absolute value, |xx0|β. But those athletes are no dummies. If you did that, you could start getting great scores by doing really badly! Running the 100 meter dash in 100 seconds would give you 74,000 points, which is kind of unfair. (The world record is 8847.)

However, there remains a lurking danger. What if I did run a 100-second 100 meter dash? Under the current system, my score would be an imaginary number! 61237.4 – 41616.9i, to be precise. I could then argue with perfect justification that the magnitude of my score, |61237.4 – 41616.9i |, is 74,000, and I should win. Even if we just took the real part, I come out ahead. And if those arguments didn’t fly, I could fall back on the perfectly true claim that the complex plane is not uniquely ordered, and I at least deserve a tie.

Don’t be surprised if you see this strategy deployed, if not now, then certainly in 2012.

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Who To Hate?

We have been remiss in not addressing the major event going on right before our eyes: the NBA Finals. In my case, it’s literally before my eyes, as I live just a couple of blocks from the Staples Center in LA, where action resumes tonight. I fully expect to run into Jack Nicholson drinking himself into a stupor at a local bar later this evening.

Now, every year the NBA Finals are a momentous event, but this year is especially noteworthy, as the teams involved are the LA Lakers and the Boston Celtics — a remarkable 11th Finals rematch between these two franchises. However, to a Philadelphia 76ers fan such as myself, one needs to say “the Hated Lakers” and “the Hated Celtics.” One or the other of these evil organizations has been responsible for bouncing my beloved Sixers out of the playoffs on countless occasions, most recently in 2001 when a Lakers juggernaut led by Shaquille O’Neal made short work of a plucky Philadelphia squad led by Allen Iverson — a David vs. Goliath matchup in which Goliath won fairly easily, as seems to usually happen in the real world.

So the question of “who to root for?” becomes one of “who do you hate less?” A truly thorny issue. Points to be considered:

  • As much as the Lakers are historically annoying, there is no question that the Sixers-Celtics rivalry is the deeper and more passionate one. Two Eastern Seaboard metropolises with inferiority complexes regarding New York, this rivalry blossomed over the course of the famous Russell-Chamberlain duels, the like of which have never been repeated in NBA history. (I will just note that nobody would ever have asked Bill Russell to star in movie with Arnold Schwarzenegger.)
  • But then Wilt left the Sixers — to join the Lakers! One of an unending series of Philadelphia sports tragedies.
  • Overall, the Lakers are probably more deserving of our disdain. Boston fans, while notoriously parochial, are at least passionate about their team, while for Lakers fans basketball games are just another opportunity to appear on TV.
  • Both Larry Bird and Magic Johnson were really annoying, even if one must grudgingly admit that they were good at basketball. But only Bird got into a fight with Julius Erving on the court. So that’s a point against the Celtics.
  • The Lakers are coached by Phil Jackson, who is quite a good coach but an incredibly irritating human being. After Celtics forward Paul Pierce was injured in Game One and managed to return to the game, Jackson was mockingly dismissive, scoffing that angels must have visited him at halftime. Phil Jackson does not deserve to win anything ever again.
  • LA is led by Kobe Bryant, while Boston is led by Kevin Garnett. A complicated situation. Both very talented, obviously. Kobe is originally from the Philadelphia area, but has managed to alienate his hometown fans so thoroughly that he cannot play against the Sixers without hearing a constant barrage of boos. More importantly, Garnett has always been intensely dedicated to the game and a consummate team player who struggled with inferior teammates and accordingly received all sorts of undeserved media criticism; Kobe, meanwhile, has always been a selfish and petulant media darling who undermined the Lakers franchise for a number of years by pushing Shaquille O’Neal out of town.

In the final calculation, and as painful as it is to say out loud — one has to root for the Celtics. Emotional attachment to a sports franchise is ultimately a completely irrational feeling, arising from unpredictable factors of geography and history rather than a sober contemplation of objective criteria. So you have to go with your gut, and my gut would very much like to see Kevin Garnett finally win the NBA Championship he so richly deserves. We’ll have to put aside the ugly reality that he’ll be wearing one of those horrible green uniforms when he does it.

And wait until next year.

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Sixers!!!!

My beloved Philadelphia Seventy-Sixers, under the coaching tutelage of local hero Maurice Cheeks, have returned to the playoffs after a two-year absence. It wasn’t easy; they started the season with an ugly 5-13 record, but turned it around late to slip into the seventh seed in the tepid Eastern Conference. Their efforts earned them a series with the Detroit Pistons, a perennial power who finished with the league’s second-best record. Pistons center Rasheed Wallace has played in more playoff games than all 15 members of the 76ers roster combined.

But this afternoon, the plucky Sixers came back from a 15-point third-quarter deficit to beat the Pistons in their first game. That’s why they play the games. In their honor, here is my favorite video of Mo Cheeks, back from when he was coaching Portland a few years ago: chokes me up every time I watch it.

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Any Given Sunday

As a native Philadelphian who spent many years in Boston, I can sincerely attest that New England has the most insufferable sports fans in the entire country. So I was kind of not looking forward to today’s Super Bowl coronation of the New England Patriots as the Best Football Team in All the Galaxy and Throughout Eternity. And then, against all the various odds I saw in Vegas last week, they lost! And I was happy.

Then it occurred to me that the winners were the New York Giants. Well, the happiness was brief.

40756669a22263dadc4c6d7c6211300c-getty-77331464mw093_super_bowl_xl.jpg

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Win the Smallest Trophy Ever!

Physics Central is sponsoring a contest with a Super Bowl tie-in — a prize for the best video “that demonstrates some aspect of physics in football.” (Is there such a thing? Need you even ask?) Just load it up to YouTube with the tag “nanobowl,” but hurry — the deadline is this Sunday, February 3rd.

trophy-thumb.jpg

The winner will receive (seriously) a nanoscale trophy, visible only with an electron microscope! Oh yes, and the winner will also receive $1,000. In normal-sized money.

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Fixing the Lottery

I’m back from dinosaur hunting, no worse for wear, save for the indignities suffered upon me by Delta Airlines on the trip home. A brief report will be forthcoming.

But a looming event demands our attention: tonight’s NBA draft, the process by which the world’s most promising young basketball talent is apportioned to the Association’s various teams. A process, which, by all accounts, is in serious need of fixing. But don’t worry, I have it figured out. (Hey, I was stuck in airports for over eight hours.)

The basic problem is one that is common to the draft process of most professional sports leagues: the draft rewards failure. The teams that finish at the bottom of the season’s standings get to choose first in the draft, funneling the best players to the worst teams. The motivation, of course, is fairness: the good teams have had their chance at success, let’s give the bad ones a fighting chance. The ultimate goal is to win, so the incentive to grab a better player should be offset by the incentive to win games.

In most other sports that idea basically works, but it fails drastically for basketball. The problem is that the difference in game-altering ability between the first one or two players and the next few can be huge. There are fewer players on court in hoops than in other sports, so one great player can wield a disproportionate influence. The incentive to get that very first pick can be tremendous, especially if it’s between a group of teams that aren’t good enough to make the playoffs anyway.

As a result, a straightforward worst-pick-first draft structure leads to a race to the bottom, where bad teams intentionally lose games to have a chance to make the first pick. Repulsed by the idea that teams would purposely tank, the NBA decided to alter the incentive structure by softening the reward for losing. In 1985 the NBA instituted the Lottery: all of the teams that had missed the playoffs (seven back then, fourteen today) would be entered into a random drawing for draft position, with equal chances of getting any of the first picks.

The lottery removed the incentive for finishing with the worst record in the NBA, but introduced an even worse incentive: now a team that just missed the playoffs could possibly land a franchise-caliber player if the ping-pong balls bounced their way. The last thing the Association wants is to see teams trying to not make the playoffs, so they instituted a compromise: via an ungainly formula, each non-playoff team would have a weighted chance of getting a top pick, with better chances for the teams with the worse records. This year, for example, the 14th-worse team had a 0.5% chance of getting the #1 pick.

Which, of course, is the worst of all worlds! There is still some tempting incentive to miss the playoffs, but there is also incentive for non-playoff teams to lose more games. It is almost inevitable: the first pick, in the right year, can be enormously valuable, so any chance to get it will be highly sought-after, no matter how such chances are distributed.

Aside from all this, there is another nagging problem with the basic idea of worst-pick-first drafts: teams can be rewarded not only because they struggled valiantly but lost with inferior talent, but also because of sheer incompetence. Good players can be steered to teams that regularly suffer from bad decision-making at the level of coaching or management.

With all that in mind, here is my magic formula for fixing the NBA Lottery. (Unfortunately, I know of no way to prevent the crimes against fashion regularly committed by draft attendees.) Each year, the draft order will be chosen by the following two-step algorithm:

  • Order the teams by their record over the last two years. Break ties using this year’s record.
    In one simple stroke of genius, most of the draft’s problems are solved. A team’s two-year record is less affected by an individual loss than its one-year record is. The incentive for tanking games is correspondingly diminished. More importantly, it’s the teams that are consistently bad that really need the help, not one-year horrors. The obvious case in point is the San Antonio Spurs, who in the late 90’s were a very good team, led by David Robinson, who couldn’t quite get over the hump. Then Robinson was injured for most of the 96-97 season, the Spurs had the third-worst record in the league, and they won the lottery. They were able to choose Tim Duncan, with whom they have just won their fourth NBA championship. That’s just wrong.
  • Teams will choose in (reverse) order of their two-year records, except that a team cannot choose in the top 3 for two consecutive years. Those that would be in the top three are bumped down until they are not.
    We want to help truly bad teams, not one-year flukes, but we don’t want to reward consistent failure either. By preventing teams from choosing in the top 3 two years in a row, we let bad teams play their best basketball without feeling like they are costing the franchise a great draft pick. Note that there is no randomizing element at any step of the algorithm, but it manages to greatly reduce the incentive for bad teams to tank late-season games. Such an incentive will still exist whenever two teams are in close competition for a single once-a-decade talent, but those players have to go somewhere.

To see how this would work, here are the records of the bottom 14 teams for the combined 2005/2006 and 06/07 seasons, starting with the worst:

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The Gridiron, Distilled

The deciding game of college football’s Mythical National Championship, in which Northern power in the form of the Ohio State Buckeyes will put a serious hurt on Southern speed in the form of the Florida Gators, isn’t until next week. But yesterday we had the two important games of the season. One saw plucky Boise State finish an undefeated season by squeaking past perennial powerhouse Oklahoma, in a 43-42 overtime thriller that is guaranteed to go down as one of the best college football games of all time. 22 combined points in the last minute and a half of regulation, breathtaking trick-play laterals, gutsy two-point conversions, and a happy ending to boot. It’ll be hard to beat that.

The other important game was the Outback Bowl, since any game featuring Penn State is automatically important. The Nittany Lions smartly dispatched the favored Tennessee Volunteers, 20-10, adding to coach Joe Paterno’s all-time-best bowl victory total. But, as exciting as the game undoubtedly was (what would I know, I was on an airplane as usual), the only reason we mention it here on our ponderously serious blog is to point to this terrific animated summary of the game from Tennessee site Rocky Top Talk.

Outback Bowl Graphic

Click to get the full animation, which colorfully summarizes every drive of the game. (Dashed lines are punts, in case you were wondering.) Some day all sporting events will be virtual; those of us with basic subscriptions will only have access to animated summaries like this, while those who spring for the premium service will get to see artificial highlights generated by the best computer graphics available at the time.

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