Closer still

To continue my self-analysis of exercise routines, and specifically to follow up on my squash post, @Bain asked the following: “I'd love to see win percentage by game # within a match. I'd guess that Steve was 75% in the first two games; I was 75% in the third and fourth games, and we were even in game five.” His hypothesis sounded right to me—I also perceived that I tended to come out strong, then fade. Turns out, we were wrong again.

Here are the totals for the full set of games. I think that past the first match we've got some pretty small sample sizes and weird incentives with added on 1 or 3 game sets[1]:

But, this isn’t exactly right, since matches don’t always stretch to five games. Someone’s going to try a lot less hard in game 5 if they’ve already lost the match. In the match-relevant games[2], here is my win percentage by game:

It looks like I had a *slight* edge in game 1, Alex had the edge in 2/3 and I completely dominated Game 4 (reflecting, in part that it's often a "must-win" for me, and in part that I tend to win matches 3-1 and Alex tends to win them 3-2). A final note is that within the games that determined matches we're 44-38 in match *games* (my advantage) even though we're 10-9 in matches. I've won more matches 3-1 while Alex has won slightly more 3-2. Here's how our match scores have broken down (again, all from my perspective)[3,4]:

Put one way, Alex converts his game wins more efficiently into match wins than I do.

1. E.g., “Now that I’ve lost, let’s bet lunch that I can take game 6”*

2. (ignoring games after the match was concluded; e.g., counting only the first four of a LWLLW match -- this is why there aren't 18 games for Game 4 and Game 5)

3. There's one match missing because I recorded only that Alex won the match, not the game totals (methodologically, I also credited Alex with one game in the game totals, since you must have taken *at least* one game more than I did from the first five).

4. Also, methodologically, I’ve got two fewer match win/losses in this analysis than I did in the last one because I excluded three round robins in which we played two games against each other (result: 2-0, 1-1,0-2) for simplicity.

*Most matches included a wager on the match. A post-game Gatorade was common, as was a beer (though those rarely got redeemed). Big bets were usually lunch. Oddly, the post-match bet was often higher stakes than the first bet; e.g., a beer following a Gatorade, or the loser had to listen to a podcast of the winner’s choice or purchase and read a book of the winner’s choice.

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My personal search for alpha

My earliest experience investing didn’t go so well, but that didn’t completely crush my belief that there’s alpha out there somewhere. I know, for instance, that top venture capitalists have consistently delivered higher (risk-adjusted) performance than other securities (The full argument can be found in Paul Gompers and Josh Lerner’s The Venture Capital Cycle). But that doesn’t seem to be true of mutual funds. What’s the difference? It looks like venture capitalists get to take advantage of network effects (the best VCs have lots of connections, making them better, giving them more connections, adding up to a substantial advantage over median VCs), and market illiquidity (there are very few VCs (and fewer “excellent VCs) providing funding for an enormous number of potential entrepreneurs). These two factors add up to a unique (non-public) informational advantage and strong bargaining power. Mutual funds, on the other hand, rely on mostly public information and trade primarily in liquid markets.

“Illiquid markets and unique information” sounds like a scam, but if venture capitalists can do it, maybe there are opportunities to be found in other areas as well. After reading Amarillo Slim's amusing biography, I realized I’d already participated in a number of illiquid markets, including some with unique information whenever I engaged in proposition betting -- e.g. wagering on who would win a basketball game or which member of our dinner party would arrive next. The reason why these are so lucrative is not only because people don’t always judge probability well and are risk averse, but also because entry into these bets is restricted, making the market illiquid (ultimately allowing 'incorrect' prices and, therefore, high expected returns/high expected losses for the participants).

For instance, in a class I had a few years ago, a professor was explaining expected value and decision trees with the following game: "You pay $2 for a chance to flip a coin. If it comes up heads, you get nothing; tails you get the opportunity to pay $2 to flip a second coin. If the second coin comes up heads you get nothing; tails you get paid $11." The expected value is positive (50%*[-$2] + 25%*[-$4] + 25%*[-$4+$11] = +$0.75), but three quarters of the time you lose money. It was meant to introduce the concept of expected value, then illustrate one of its limitations. After working through the example, the professor asked if anyone would like to play and about half of our class of 90 raised their hands. Then he asked who would like to play if the stakes went up by a factor of 10. Only one person was willing to risk $20-40, even though the expected value was positive. There would certainly have been other willing participants in the world, but they weren't given access to the game -- the market was illiquid because it was restricted.

This left me thinking about poker, proposition bets, and illiquid markets with imperfect information. Eventually, I found one in baseball.

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