Thursday, October 21, 2010

Fun with numbers

Last night, while listening to Tim McCarver drone on and on about something that eventually go to Joe Dimaggio's hitting streak, I wondered what the chances were of seeing something like that again.  So I did some very simple calculations, using what seemed like decent stabs at integrating the variety of baseball history.  Came out very close to even odds.  Here are the steps I took:

1) Assume a 0.300 batting average, which translates to a 0.700 non-batting-average

2) Assuming 4 plate appearances a game, there's a (0.700)^4 = 0.2401 chance of being held hitless, or a 0.7599 chance of getting at least one hit

3) So, the chance of getting at least one hit is 56 consecutive games is (0.7599)^56, or 2.1 x 10^-7, or a 1 in 4.76 million chance.

4) 4.76 million divided by 162 games in a season, divided by 30 teams, divided by 9 batters per team, divided by 108 seasons in the World Series Era (i.e. back to 1903) and you are left with: 1.0077, or damn close to even odds.  So yes, it pretty much makes sense that someone has hit in 56 consecutive games, which means there's also a decent chance we'll see it again before I'm dead.

I should add that, as MG pointed out, if you assume a 0.285 batting average, the odds drop to about 1 in 5 against, while a 0.315 batting average makes it 5:1 in favor.

Wednesday, October 20, 2010

Good Idea of the Day

I've never done a football suicide pool, but they seem fun.  The basic idea is that, each week, you pick the result of one NFL game, and if you're right, you survive to the next week, but if you're wrong, you're out.  To prevent people from just riding really good teams (or just always picking against really bad teams) you can even things out by either using the Vegas line or limiting the number of times you can bet on or against a given team. 

The problem with this set-up, though, is that people very quickly get eliminated: give or take, about half the league will be out after Week 1, another half after Week 2, etc.  So unless you have hundreds of people, it'll be over by Week 6 or 8. 

One way around this (and here's my good idea) is to allow people to come back to life by picking more games correctly.  For example, the week after you get a game wrong, you must now pick two games right.  Don't hit?  Now you gotta pick three games.  If you succeed in resurrecting yourself, though, you're back to one game a week.  Or maybe you don't have it escalate, you just have a loser's track that stays on two-games-a-week until they get both right, then they're back on the winner's track.  The winner is whomever has the best winning percentage, rather than just who's alive at the end. 

Or maybe the best way to do it is reserve half the prize for whoever survives the longest without losing (i.e. the suicide pool aspect of it) and the other half for overall picking percentage. 

A decent twist, I think.