March 25, 2008

No End In Sight: The Clinton Machine Rumbles Onward

Since it is that time of year, perhaps a basketball analogy is in order. Hillary Clinton's campaign is the (once) heavily favored high-octane powerhouse whom analysts had predicted to win the game because of superior skills, experience and determination. For various reasons however, team Clinton finds itself down by 15 points in the closing seconds of the 4th quarter. They have given their best effort in a hard-fought and tightly contested game, but have come up short. They have lost the contest fair and square. Still, team Clinton is utilizing the final moments of the game to foul team Obama every 2 seconds, prolonging the inevitable while the crowd becomes restless and starts to boo while heading for the exits. Nothing short of a miraculous barrage of three-pointers and steals by team Clinton combined with some missed free-throws by team Obama could change the outcome. Unfazed by the scoreboard, team Clinton is going to fight to the death, lobbying the referees to change the rules, accusing the other team of cheating and calling the fans traitors.

In today's New York Times, conservative columnist David Brooks wrote an op-ed piece that I actually agree with. If you are not familiar with Mr. Brooks, he is a prominent commentator (frequently appearing on NPR, PBS and print media) who I generally disagree with because of his longstanding support of the Iraq war, Bush's tax cuts and a few other issues. (To his credit, it should be noted that Mr. Brooks is not a Limbaugh/Fox News type of conservative voice. His commentary strikes me as much more moderate, respectful and intelligent than the far-right pundits who intentionally position themselves as political lightning rods, but I digress.) Brooks essentially concludes that because of the delegate math, the lack of a Michigan or Florida primary re-vote, the unwillingness of superdelegates to go against the elected delegate count, Obama's recent endorsement from Bill Richardson as well as his slim national poll lead despite the Rev. Wright sound-byte "scandal", there is only a 5% chance of Hillary winning the nomination.

Only five percent? Ok, that sounds good for the Obama-ites, but that doesn't answer the question of how long this heavyweight slugfest will continue. How long will it remain interesting and energizing to Democratic voters before it becomes stale and repulsive? The answer: it's pretty much up to Hillary. She still has the option of taking the high road and withdrawing gracefully in the coming weeks (although the primary calendar doesn't really provide an ideal date for this- May 6th after North Carolina?) or she can continue to drag it out with her current modus operandi, the win-at-all-costs strategy, which some in political junkie-land have referred to as "scorched earth" or "kitchen sink" politics. Brooks calls it "the audacity of hopelessness."

So if he's really got a 95% chance to finally wrap this thing up, why hasn't Obama run out the clock and closed the deal? I believe it's a matter of strengths and weaknesses. In baseball, home run hitters tend to strike out a lot. Their strength, the ability to blast the ball into the stratosphere with one mighty swing, is balanced out by their weakness, the increased likelihood of missing the ball completely when that mighty swing isn't perfectly timed.

Strengths and weaknesses are often two sides of the same coin and it's no different with politicians. George W. Bush's greatest strength has been his tell-it-like-he-sees-it authenticity. You always know where he stands. His weakness: a stubborn unwillingness to respectfully dialogue with those who don't share his point of view. In 2004, John Kerry became his party's nominee because of his lengthy record of public service and his ability to articulate the details and nuances of his positions. Unfortunately for him, his vast experience also provided Republicans with an all-you-can-eat buffet of out-of-context attack fodder, while his wordy, meandering speeches came across as aristocratic elitism from someone who seemed out of touch with reality. The Swift Boat, originally an image of Kerry's military heroism, was hijacked to become the torpedo that would sink his campaign. As America's 42nd President, Bill Clinton's greatest strength was his youthful charisma that enabled him to bridge political divisions to build a "centrist" economic policy that resulted in a 65% approval rating at the time he left office, the highest end-of-presidency rating of any post-WWII president. His weakness, well, I think we all know about the dark side of his youthful charisma.

Back to the Obama vs. Clinton standoff. It seems that Mr. Obama's inability to "finish off" Mrs. Clinton stems from the same quality that has gained him such a large following in the first place: he is a different kind of politician. He continually rejects the politics-as-usual tactics of divide and conquer, slash and burn. His ability to energize younger voters and re-invigorate the disillusioned has been his greatest strength. On the flip side, his reluctance to "go for the kill" has allowed the Clinton campaign to stay in the race and even draw him into some of the tit-for-tat political skirmishes that he's been trying to avoid.

As for Hillary, her intelligent, quick-witted, all-out competitive determination has made her a political force to be reckoned with as well as the most successful female Presidential candidate in American history, regardless of whether she wins or not. She does well in debates and no one exploits a weakness the way team Clinton does. At the same time, the persistence and killer instinct that has brought her this far will not likely allow her to throw in the towel until she has exhausted every possible tactic that she's learned in her 35-year climb to the top. Who else would have stayed in the race after 12 consecutive defeats? In the end, she might actually be undone by her dogged willpower that turns people off and leaves a bitter aftertaste. In any case, it's very clear that she's not going down without a fight. Until the clock runs out, she will explore Obama's every unflattering angle. Poll numbers can be replaced with more favorable ones. Defeats can be spun into contests that she wasn't really counting on. Each victory can be magnified as a glorious comeback in a crucial state. Delegates can always change their mind. This won't be over until she says it's over.

There are still a few seconds on the clock. Hillary can still foul Barack Hussein Obama and hope he misses his free-throws. She can still hoist up off-balance three pointers from half-court. She can still work the refs or lobby for a new way of keeping score. Just because her strategy isn't working doesn't mean that it won't continue until the final buzzer. And who is the happiest spectator of all? That would be John McCain. In fact, I think he's heading back to the concession stand for more popcorn.

March 18, 2008

The Math of March Madness

Unless your college basketball antenna is completely out of order, you are probably aware that 'bracket season' has begun. This week, millions of Americans are penciling in their annual predictions for the NCAA Basketball Tournament, better known as March Madness, which essentially begins on Thursday. If you haven't yet participated in this indispensable slice of Americana, here is a blank bracket you can fill out.

Between now and April 7th when the champion is crowned, 63 games played over three weekends of basketball bliss will reduce the field of 64 teams (I know, it's technically 65 but I never include the all but meaningless play-in game) down to one. Four gigantic regionals, each consisting of teams seeded 1 through 16, serve as the treasure map leading to hoops glory. As discussions of #1 seeds, upsets and predictions are made, a question often arises: "What are the chances of guessing the entire bracket correctly? Has anyone ever done it?"

Those are valid inquiries indeed. After all, there is a 1 in 64 chance of picking the national championship winner. The fact that no team seeded worse than 8th (Villanova in 1985) has ever cut down the nets reduces the list of possible winners down to 32 (as there are 4 teams of each seed). Besides, there have been numerous instances when someone (including yours truly in 2004) has accurately picked the fabled Final Four teams. Surely then, it must be at least possible that someone somewhere could pick the winner of all 63 tournament games. With millions of people making their guesses every year, it shouldn't be long before some unsuspecting Grandma in Looneyville, West Virginia (a real town by the way) fills out the perfect bracket by chance. Right?

Such a theory, while grand and glorious, is more than unlikely. In fact, the mathematical probability of the perfect bracket is a mind-boggling 4.2 BILLION to one, by far the worst odds of any lottery in world history. So that's why Yahoo is offering 5 million bucks to anyone who fills out a perfect bracket (and only 10 grand for most accurate bracket in the land). With odds of 4.2 billion to one, that means that every single man, woman, child, dog, cat, rabbit, hamster, squirrel and skunk in America would have to each submit 14 uniquely separate brackets that no other man, woman, child, dog, bird, beast, loon etc. had already filled out in order for that one lucky individual to emerge with a golden ticket as the Charlie Bucket of bracketology. But 4.2 billion ways to fill out a bracket? How could there be so many possibilities from such an innocent looking single-page tournament diagram? If you are brave enough to continue, here's the math:

If the tournament only had four teams (we'll call them A, B, C and D), there would be 4 possible scenarios for the final game, assuming that Team A plays against Team B while Team C plays against Team D in the semis.

(A vs. B) + (C vs. D) =

1. A vs. C
2. A vs. D
2. B vs. C
4. B vs. D

Simple enough. Well, it gets a bit trickier for an 8-team bracket with four first round games:

(AB) (CD) (EF) (GH)

With 8 teams in the tournament, there are now 16 possibilities for the first round games alone. Each letter represents who would win each of the 4 games:


With me so far? Let's look at a 16-team bracket with 8 games in the first round:
(A vs. B) (C vs. D) (E vs. F) (G vs. H) (I vs. J) (K vs. L) (M vs. N) (O vs. P)

By adding 8 more teams, we've added 240 more permutations! Even if we're only looking at the first round, there are still 256 permutations:

128 of them begin with A (the other 128 begin with B)
64 begin with AC
32 begin with ACE
16 begin with ACEG
8 begin with ACEGI
4 begin with ACEGIK
2 begin with ACEGIKM

To give you a feel for the number of possibilities, here are the first 32 permutations. Keep in mind, this is just for the first round of a tournament with 16 teams!


ONLY 224 to go!

SUMMARY: As you increase the size of the tournament, the number of permutations grows exponentially. By the time you look at the real NCAA bracket of 64 teams, you will have 4,294,967,296 different ways of filling out the first round alone! The good news is that the rest of the tournament is a walk in the park if you can just get those first 32 games exactly right. If you do somehow beat the odds in that first round, it gets a lot easier in the second round. There is just a 1 in 65,000 chance of accurately predicting the Sweet 16; no sweat compared to 4.2 billion. The table below shows how guessing all 32 games correctly in the first round is almost as hard as guessing the whole bracket:


Teams ------------- No. of Games --------- No. of Permutations
2 (Championship) ------- 1 --------------------- 2
4 (Final Four) ------------ 2 --------------------- 4
8 (Elite Eight) ----------- 4 --------------------- 16
16 (Sweet Sixteen) ----- 8 --------------------- 256
32 (Second Round) ----- 16 -------------------- 65,536
64 (First Round) -------- 32 -------------------- 4,294,967,296


Although 4.2 billion is a huge number, the odds significantly improve when you consider the fact that a #16 seed has never beat a #1 seed in the first round. So by using history to forecast 4 of the first 32 first round games, there are only 28 outcomes up in the air. Amazingly, you have actually removed over 4 billion possibilities from the first round just by eliminating these 4 outcomes from the equation!

How is this possible? Let's go back to the earlier example of an 8-team bracket with 4 first round games. Again, each letter represents who would win each of the 4 games:


Let's say that some #1 seed like Memphis or North Carolina was 'Team A' and they were matched up against an ill-fated #16 seed represented here by 'Team B'. If you knew for sure that Team A was going to win, you could eliminate the 8 permutations that have Team B winning, or half of the 16 possibilities listed above. In other words, you cut the number of permutations in half with each outcome you eliminate!

Let's apply this to the real-life NCAA first round which involves 32 games. To go from 32 down to 28 games, we will divide 4,294,967,296 in half 4 times (once for each of the doomed #16 seeds):

4,294,967,296 ÷ 2 = 2,147,483,648
2,147,483,648 ÷ 2 = 1,073,741,824
1,073,741,824 ÷ 2 = 536,870,912
536,870,912 ÷ 2 = 268,435, 456
TOTAL ------------ 4,026,531,840 permutations lost by forecasting losses by the #16 seeds

4,294,967,296 - 4,026,531,840 = 268,435,456 first round permutations with 28 winners

When you add 268,435,456 with 65,814 possibilities for the remaining rounds, the new total is 268,501,270 total March Madness permutations- a reduction of over 4 billion!!

SUMMARY: When you eliminate the possibility of any #1 seeds losing in the first round, the odds are roughly 1 in 268 million for guessing the entire bracket correctly.

You may also be wondering to yourself (or not), "If it's basically impossible to get the whole first round correct, then why is it that people can regularly predict the Final Four accurately?" There are several reasons for this:

1) In order to guess the Final Four correctly, you only need to guess (at minimum) 16 of the first 60 games correctly (4 wins for each of the 4 teams that make it). In other words, it's possible to guess wrong 70% of the time and still get the Final Four correct. Of course, you could also guess 98% correctly and still NOT get the Final Four correct if the one game you missed involved a Final Four team. Still, 16 out of 60 (27%) is a lot easier than 60 out of 60.

2) To guess the Final Four correctly, you don't need to get more than 50% correct in any of the first 4 rounds of the tournament. You only need (at minimum) 1/16th of the 1st round, 1/8th of the second round, 1/4th of the Sweet 16 and 1/2 of the Elite 8. Difficult, but not impossible.

3) Over half of the time (12 out of the last 23 years), all of the Final Four teams have been seeded no worse than #4. In other words, more often than not, you could have picked the correct 4 teams from a pool of just 16 teams (those seeded 1 through 4). Since the current 64-team format began in 1985, there have been only 11 final four teams (out of 92 possible) seeded worse than #4. That means that over 89% of the time, you can safely make your Final Four predictions from those top 16 teams.

4) If you narrow the options down to the top 4 seeds in each regional, the mathematical probability of accurately predicting the Final Four is only 1 in 256, which are much better odds than the 268 million to 1 chance of guessing the whole bracket correctly. How can that be? Again, here's the math:

Using only the #1 and #2 seeds, there are 16 possible Final Four scenarios:

1111 1211 2221 2121
1112 1212 2222 2122
1121 1221 2211 2111
1122 1222 2212 2112

If you add in the #3 seeds, there are an additional 63 Final Four permutations:

1113 1311 2131 2321 3111 3232 3333
1131 1313 2132 2312 3122 3233 3331
1133 1331 2113 2323 3113 3222 3311
1123 1333 2123 2332 3131 3223 3313
1132 1321 2133 2333 3123 3211 3312
1231 1322 2213 2331 3132 3212 3321
1232 1323 2231 2313 3112 3221 3332
1233 1312 2223 2311 3121 3213 3323
1213 1332 2232 2322 3133 3231 3322
1223 2233

65 + 16 = 81 total permutations for seeds #1 through #3

Based on the pattern above, we can calculate the number of possible Final Four scenarios depending on the number of seeds included by multiplying to the 4th power.

No. of seeds Multiplied to the 4th power = Total number of Final Four permutations
1 ------------- 1
2 ------------- 16
3 ------------- 81
4 ------------- 256
5 ------------- 625
6 ------------- 1,296
7 ------------- 2,401
8 ------------- 4,096
9 ------------- 6,561
10 ----------- 10,000
11 ----------- 14,641
12 ----------- 20,736
13 ----------- 28,561
14 ----------- 38,416
15 ----------- 50,625
16 ----------- 65,536

As you can see, the permutations are much smaller for predicting the Final Four compared to correctly filling out the whole bracket. Even if you allow the possibility of a #11 seed reaching the Final Four, (as George Mason did in 2006) there are only about 20,000 possible Final Four scenarios compared to roughly 268 million bracket permutations!

But before you begin to think that there is a method to this madness, I offer this final word of caution. Although #1 seeds are the most likely to make the Final Four, there has never been a case when all four #1 seeds did this- 3 out of 4 is the most ever, which has happened 3 different times. Two years ago in 2006, none of the #1 seeds survived to Big Dance's final weekend. Champion Florida was a #3, runner up UCLA was a #2, LSU was a #4 and George Mason was a #11 seed. It was just another typically unpredictable year. Last year, finalists Florida and Ohio State were both #1s, while UCLA and Georgetown were both #2 seeds.

For mathematical and other reasons, this tournament is my absolute favorite sporting event of the year. As you fearlessly complete your 2008 bracket, your best bet might just be to ignore the advice of the so-called "experts" and pick a few carefully chosen upsets- but not too carefully! Let the madness begin.

March 14, 2008

Blogging vs. Facebook

I haven't always been up to cultural speed. I've never owned an ipod or mp3 player. I didn't get a CD player until 1997. I didn't have one in my car until 2003, the same year I got my first cell phone. I don't own a laptop or a video game console of any kind. I got my first digital camera in 2007 which was a tough pill to swallow given my lifelong loyalty to the technological wonder known as the disposable camera. In my mind, blue tooth is what happens when you eat a popsicle and PDA refers to a frowned upon behavior, not those now-ubiquitous devices that promise to organize your life at the touch of a button or, if you'd prefer, with the the touch of one of those plastic-toothpick-screen-presser-sticks. I've never had a MySpace or Facebook account and I still have yet to observe the "unprecedented" quality of a BluRay DVD. I've also never had a blog... until now.

So what gives? If you haven't noticed, there seems to be a change in the air this year. It's been a while since I first began thinking about starting, no 'creating' sounds better, I mean LAUNCHING a blog for all the typical reasons: to express my inner self, to prove that my voice has something to add to the blogosphere, to give back to the virtual world that has given me so much. The reason I haven't done so until now has largely been due to the fact that I was equally tempted to obtain a Facebook account. I knew that having both a blog and a Facebook (let me fix that- no one says, "I HAVE a Facebook." It's always, "so-and-so is ON Facebook") would suck up gallons of precious time and reduce my existence to little more than a screen-dependent parasite- which I already am fast becoming.

So I was faced with a choice. Start a blog or start a Facebook page (it took me long enough to determine that MySpace was not the space for me). Blogging vs. Social Networking. To "publish" thoughts and ideas or share pictures and personal updates with long-lost friends. There were pros and cons to both, but I ended up deciding to blog for the same reason many of my friends have become long and lost: I'm simply terrible at keeping in touch with people if I don't see them regularly. Of course, I suppose that's the whole premise of social networking, but there was something irresistible about offering my opinions, reflections and observations to anyone who might take a pit stop along the information superhighway.

I don't seem like the Facebook type, but I could fancy myself a closet blogger. My Facebook credentials are weak: I'm (sadly) not the kind of person who travels a lot or takes lots of pictures. If I were on Facebook, what would I show? My life consists of doing almost the same thing day after day, week after week. Even if my pictures were exceedingly interesting, something about transferring / uploading / attaching them from the the camera to the computer involves too many steps for me. My schedule of activities doesn't vary much, but I'm enamored with the thought that my ideas and opinions might. My pictures and personal updates are limited by my dull and predictable life, but the only restrictions for my ideas are the length of my internal rabbit trails and the extent of my vocabulary. It doesn't bother me if no one ever sees the pictures I've taken or hears a description of "what I'm doing right now." For some reason though, it really does matter to me that my ideas and opinions are validated and understood. Blogging seems to be the logical next step after posting comments at the end of online articles, a practice that just doesn't float my cyberboat anymore. Blogs are essentially comments with an identity. Commentary meets social networking.

I also enjoy the anonymity of blogging. Who am I? Who could I be? Displaying a picture of me would spoil it all. That cross-legged geek on the purple paper trail is not me (besides, I already said that I don't own a laptop). Of course, the only people even likely to read this are the ones who already know me, but it's much more exciting if we pretend like there's some mystery to this whole charade. I always tell myself that I need to write more, reflect more, journal more. Is blogging to journaling what movies are to reading? Hmm. They're both bite-sized forms of storytelling that have evolved into widespread cultural phenomena. Just as there are a thousand lousy movies for every gem on the silver screen, thoughtless blogs are becoming more common than junk e-mail.

So if no one ever reads these dime-a-dozen words of mine, do they have any significance? I suppose that's the blogosphere version of the "If a tree fell in the forest..." question. Maybe that's why I likened blogging to journaling. It's a sort of midpoint between the mindless and the reflective, the intentional and the random. Halfway between writing a speech and playing fantasy baseball.

I still haven't ruled out the possibility of joining Facebook, though. It will probably happen around the same time that I give up my beloved CD collection.