For those of you who are not fortunate enough to be Pittsburgh born and bred, the above photo shows what greets your arrival at the Pittsburgh airport, right before you descend to baggage claim — side-by-side statues of George Washington and Franco Harris.

(If you’re unfamiliar with Franco, he’s probably best known for his “Immaculate Reception“.)

UPDATE: Note that this opinion is now officially endorsed by the current administration. Take that Arizona!

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?)

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:

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(x₀-x)^β   for track events,

points = α(x-x₀)^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 (x₀-x); in field events you want a high score (throwing far), so the formula is reversed, (x-x₀). 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, |x-x₀|^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.

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.

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.

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

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.

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:

1. Portland
2. Atlanta
3. NY Knicks
4. Boston
5. Charlotte
6. Minnesota
7. Seattle
8. Milwaukee
9. Memphis
10. Philadelphia
11. Toronto
12. Orlando
13. Indiana
14. Golden State

You can see each year’s records here. The three teams with the top picks in last year’s lottery were Toronto, New York (which they had traded), and Charlotte. So, if we began the system this year, using the actual 05/06 draft order to determine the previous year’s bottom finishers, the Knicks would get bumped down one spot, and this year’s draft order would look like this:

1. Portland
2. Atlanta
3. Boston
4. NY Knicks
5. Minnesota
6. Charlotte
7. Seattle
8. Milwaukee
9. Memphis
10. Philadelphia
11. Toronto
12. Orlando
13. Indiana
14. Golden State

And here’s how it actually will proceed under the current system, in the so-called “real world”:

1. Portland
2. Seattle
3. Atlanta
4. Memphis
5. Boston
6. Milwaukee
7. Minnesota
8. Charlotte
9. NY Knicks (traded to Chicago)
10. Sacramento
11. Indiana (traded to Atlanta)
12. Philadelphia
13. New Orleans
14. LA Clippers

This year, the teams with the worst records were Memphis, Boston, and Milwaukee; in an unlikely turn of events, they were each bounced out of the top three picks by the vagaries of the lottery balls.

Admittedly, no system is perfect, but I think mine is a substantial improvement. The present lottery system did dispense come cosmic justice by preventing Memphis from getting the first pick; they are actually a decent team, who like the Spurs ten years ago suffered an injury to their best player (Pau Gasol), and should be okay again next year without the benefit of the first pick. But the two-year rule also smoothed out their record to achieve a similar result. Portland gets the top pick either way. Atlanta, who have been pretty bad for a while, would get the second pick (in a draft where two players, Greg Oden and Kevin Durant, are rated much higher than anyone else), rather than Seattle who are actually a fairly decent team. The Knicks are a special case, as Isiah Thomas is bent on running them into the ground, and one part of his strategy is to trade away all of their draft picks, so who really cares?

Most importantly, the Boston Celtics are prevented from getting one of the top two picks, despite having the second-worst record this year. That also happened in the real world, but only through a fluke. This is important because (1) everyone hates the Celtics, and (2) they were the team that most obviously tanked at the end of the season in a desperate attempt to get a better draft pick. Now, one could argue that they could have tried even harder to lose games, perhaps by having Paul Pierce kidnapped by some guys from Southie. But really, it would have been hard to tank harder than they actually did.

It’s too late for this year, of course, but there are future drafts waiting to be salvaged. David Stern, call me! Together, we can fix this thing.

• All beer must be domestic and in cans.
• Empty cans are to be hurled at the TV at Suitable Moments.

The same people show up year after year, and now that we’ve aged to the point of spawning, our roaming, unsupervised pack of offspring has taken up the latter item with gusto. Overheard while they were hunting for empty cans: “I wish the grown-ups would drink more.”

Anyways, this year was particularly festive, given the amazing first return, the fabulously sloppy ball during the downpour in the first half, the glow-in-the-dark Tron marching band during the half-time show, Manning’s quick perky dance that he squeezes between yelling at his squad and the snap, and the deep pleasure of the announcers soberly discussing the fine work of the Colts’ defensive tackle Booger McFarland.

And any event where I can dust off the crockpot and whip up mexican velveeta dip is all right by me.