Startup stuff
Kevin Day, May 15th, 2008Tonight I’m going to Startup Drinks at the Bier Markt.
Also, Saturday is a SCORE business class at the U.S. Bank building downtown. The first session covers business plans and legal stuff. The second half is business finance. Only $20.
Really looking forward to both events. Should be fun and educational.
What’s on your (Safari) bookshelf?
Kevin Day, May 10th, 2008I’ve been trying out the Safari bookshelf recently and it’s really nice. Despite the recent buzz that programmers don’t read books, I think published books (electronic or dead-tree) are the best way to lean a subject because they’re more complete and have been thoroughly edited.
For Safari, I have the 10-book-per-month plan, which is $23. I plan on needing a lot of reference material in the next few months so it’s a valuable resource to me at the moment. Some of the larger books take up more than one “book” on my 10-slot book shelf though. The books on my shelf right now are:
- JavaScript: The Definitive Guide, 5th Edition (2 slots)
- PHP Hacks (1 slot)
- Programming Amazon Web Services (2 slots)
- Programming Python, 3rd Edition (2 slots)
- JavaScript: The Good Parts (1 slot)
PHP Hacks is kind of a let-down, but the other four books are pretty good. I’m interested to find out if I’ll find any books that are useful enough to buy hard copies of after I’m done using Safari.
Best fortune cookie ever
Kevin Day, April 28th, 2008Do not be timid or squeamish in your actions. All life is an experiment.
I feel so dirty…
Kevin Day, April 24th, 2008I was signing up for a Fox Sports fantasy league and at the end of the registration process I found that I had accidentally signed up for a (ugh) Microsoft Live ID. I thought the whole Passport thing was just a myth, but I guess I was wrong. I’m lucky now though because I can use my one account at ALL of Microsoft’s participating sites.
Yipee!
Rick-rolled by the fiancée
Kevin Day, April 17th, 2008Kristen called me on my cell phone just now, but instead of my regular ring tone, I was greeted to:
Never gonna give you up
Never gonna let you down
Never gonna run around and desert you…
Damn. I didn’t know what I was up against.
Well played, Kristen. Well played.
Model for Success
Kevin Day, April 13th, 2008I stumbled on this motivational article and I like it’s perspective on success and failure.
This is the traditional way of relating success and failure:
SUCCESS <– YOU –> FAILURE
But this is the way it really works, and is how you should view success and failure:
YOU –> FAILURE –> SUCCESS
FTA:
What if, rather than seeing failure as something to be avoided, it became a “stepping stone” on the path to success? Put another way: Yes is the destination, but “no” is how you get there. To achieve significant success in today’s world, top performers do not see success and failure – yes and no – as opposites, rather opposite sides of the same coin that depend on each other.
How can you not want to be an artist?
Kevin Day, April 5th, 2008Despite enjoying other things in life such as technology, real estate, finance, or what have you, how can anyone not want to also do some sort of artistic endeavor like music, writing, poetry, painting, or drawing? These are the only activities that emphasize enjoying life and living in the moment.
I think the answer is that people (especially myself) get distracted with their primary interest but forget that there are other subjects that ultimately focus on simply enjoying life.
The weather is beautiful today in Cleveland after a dreary extended winter. I couldn’t help but stand on my street for a minute and look around me at the tiny details I’ve been too busy to notice. I’ve been missing a lot, but I plan to change that now.
Sweet sixteen probabilities
Kevin Day, March 23rd, 2008Thanks to my fiancée, Kristen, for proposing this interesting question: What is the probability that someone has a perfect bracket just through the first two rounds this year?
First, as a baseline, the odds of there being no upsets in the first two rounds of the Men’s NCAA Basketball Tournament are one in 13.2 million. This was calculated with the same winning model as used in my last post.
The odds of the first two rounds occuring like it has so far in the 2008 tournament are one in 376 billion.
Like I showed the other day, that doesn’t mean that the odds are 1 in 376 billion that someone would have correctly predicted the first two rounds. Without doing all of the simulations, I would guess that the odds would increase by about 10,000 because that’s how much they improved last time from the random model to the smarter model.
That means the probability of a perfect bracket through the two rounds so far this year are about one in 37.6 million.
[Edited to give Kristen proper credit for the question]
The Perfect NCAA Bracket
Kevin Day, March 22nd, 2008In grade school, my favorite game was “Starting Lineup Talking Baseball”, which simulated baseball games based on the players you had on your team. The success of each player depended on their real-life statistics, so it was important to memorize everyone’s stats.
The direct correlation of the players’ statistics to their success in that game may be why I think sports are deterministic and why I love trying to predict things about sports.
For a few years now, I’ve been thinking about the NCAA tournament. There are a few simple questions that I don’t think have been appropriately answered. This post answers the question, “What are the odds of picking the perfect bracket?”
Spoiler
Here’s the answer if you’re in a hurry and don’t care about the details. The chance that your bracket is perfect is:
1 in 924 trillion
… so you’re saying there’s a chance?
Well, put it this way. If 10 million people fill out brackets this year, there’s only a 1 in 100 million chance that anyone will have a perfect bracket.
Traditional Answer
The common way that I’ve seen this question answered (WSJ, Math Forum) is that the total number of possible brackets are calculated as 2^63, (neglecting the play-in game) which is 9.22 * 10^18. Then they go on to say that the chance of getting a perfect bracket is one in 9.22 * 10^18.
However, this assumes that every bracket is equally probable. Usually studies mention this caveat, but they don’t really take the next step and find out what the real probabilities are.
The Wall Street Journal article linked to above makes some simplifications about how accurate people guess winners and how many games can be considered a lock for the favorite, but in my opinion they’re still just guesses.
A better way to find the probability of the bracket being perfect is to first model the probability of each seed winning a game. Then, use that model to calculate the probabilities of different selection strategies people might use.
Modeling with Tournament Seeds
There have been a few studies that have modeled the relationship between a team’s tournament seed and their probability of winning a game (Carlin; Schwertman, et al). One of the simplest and most accurate models is
P(Team A) = Team B’s Seed / (Team A’s Seed + Team B’s Seed)
This says that if a #2 seed plays a #6 seed, the chance that the #2 seed will win is 6 / (2 + 6), which is 75%. The chance the #6 seed will win is 2 / (2 + 6), which is 25%.
This model does a good job representing historical win probabilities in the NCAA tournament, except for when #1 seeds play #2 seeds. Historically, #1 seeds only win 43% of the time instead of 67% predicted by the model (Schwertman, et al).
If you adjust for the #1 vs. #2 error, the model can be used to estimate the probability that any bracket will be perfect. All you have to do is go game by game through the bracket multiplying the win probabilities of each predicted winner. The result is the chance that every predicted winner in the entire bracket will actually win.
Below I calculate the probabilities of perfect brackets for five different strategies for selecting winners.
All Favorites
This strategy picks all higher-ranked seeds. At the Final Four, each team has an equal shot of winning since they’re all #1 seeds, so there’s actually 8 possible All Favorites brackets.
1 in 546,000,000,000
Most Favorites
This strategy is the one used by nearly everyone when they pick their bracket. Most of the higher seeds win, but there are several upsets as well.
I’m not making any distinction between strategies such as “teams hot at the end of the year are better” or “teams with big guys inside do better in the tournament.” Any bracket that choses favorites to win as frequently as they have in past NCAA tournaments fall within this strategy.
Since there can be many different Most Favorites brackets, I generated 8,000 brackets and took the average probability of all of them.
1 in 924,000,000,000,000
Random
This strategy assumes each team has an equal chance of winning. Again, I generated 8,000 brackets and took the average probability.
1 in 308,000,000,000,000,000,000
Most Upsets
This strategy is the opposite of the of the Most Favorites strategy. Underdogs are favored in most of the games, but higher-ranked teams win occasionally. Number 16 seeds are frequently chosen to win the championship with this strategy. This is the average probability of 8,000 brackets.
1 in 893,000,000,000,000,000,000,000,000,000
All Upsets
The opposite of the All Favorites strategy is picking 100% upsets. That’s right, your Final Four is all #16 seeds. What are the odds of that happening?
1 in 144,000,000,000,000,000,000,000,000,000,000
Conclusion
Not all brackets are created equal. A bracket with all upsets is 10 sextillion times less likely to occur than one with all favorites.
Unless you honestly have a legitimate way of predicting winners better than most people, the odds of your bracket being perfect are 1 in 924 trillion. Although not very good, these odds are 10,000 times better than the number usually reported. All right!
However, your odds could be a thousand times better if you just picked all of the higher seeds to win. Why don’t you?
First of all, it’s not fun. Most people like to take risks and then feel proud when they correctly predict upsets.
But I think there are other reasons as well. For instance, if everyone in your league picked all favorites, then someone would have the exact same bracket as you and you would have a lower chance of winning the league.
Or would you?
My next post will look into the trade-offs between these strategies when competing in a league. There’s some game-theory type questions that I’m not qualified to address but will try to answer anyways.
Stay tuned.
Negligent web surfer
Kevin Day, March 1st, 2008When I was reading football news today, I discovered that the NFL has a Chinese website, nflchina.com. It’s mostly news articles that are translated into Chinese.
I used Google to translate the text to English, unsure of the results. I think it did a decent job. Here’s the Cleveland Browns page:
However, when I was browsing the site I got this error message at the top of a page:
You did not examine the competence of this website. Please sign.
I guess I’ll have to do a more thorough evaluation next time.
Also, I was disappointed that Google wouldn’t let me translate an already translated page. I wanted to see how the translations of translations would turn out.
