Tuesday, September 26, 2006
A free-throw Analogy
So Shaq is a poor free-thrower. I think most people would agree. I'm guessing his career average is somewhere around 50%. It seems like no matter what happens, he just can't improve. So, last season when Shaq hit 8 out of 10 in a game against the Lakers, I had to ask the question, "what's the chance of that?".
When you examine the 'streak' that Shaq went on to hit 8 out of 10, there is a lot of parallels that can be found in other areas (i.e. poker). When do we need to stop considering a good run a "lucky streak" and actually change our expectations? For example, if Shaq were to go onto hit 80 out of 100, we might need to stop considering this simply a hot streak as we wait for him to return to his 50% free-throw average. Instead, we might need to re-adjust our expectations that he is now an 80% free-thrower.
I think you can use the poisson distribution (from Stats 101) to do the math part. If you have excel, you can use the poisson function to answer the question "if we expect Shaq to hit 5 out of 10 free throws (his current average), what is the chance he'll hit 8 out of 10 or more?". The answer is a 13% probability.
What this stats function does not answer is, "when does a 'streak' end and improved performance begin?"
For example, I'm an average poker player. I make way too many mistakes to be considered any better than average. As a matter of fact, average may be a stretch for me. I don't pay attention to my cards. I don't assess situations correctly. I'm average. Being that I'm an average player, I have an expectation that I'll have a winning session about 50% of the time. Some sessions I'll win. Some sessions I'll lose. Some sessions I'll win a lot. Some I'll lose a lot. In the end, I'll win about 50% of the time and break about even on the money.
If I play 20 sessions and win 10 of those session, I'll have confirmed my assumption about being an average player. However, (and this is the important part), if during my next 10 sessions, I win 9 of them, at what point do I stop considering this some lucky streak of cards and actually start adjusting my expectation upward?
I'm having a hard time, considering myself anything other than an average player, but I've been on a hot streak that has me winning 12 of the last 13 home cash game sessions. According to Poisson, the chances of that are 3.4% (like hitting a 1 outer on the river). Maybe I'm just on a lucky streak. Maybe it's like catching that 1 outer. Hey, it happens. I 'dunno.' Maybe I'm thinking about this wrong. Let me know! Maybe I shouldn't be thinking about this at all.
As an offset. I've managed to run my online accounts dry. Nobel was $200 - now $0, Party was $100 - now $0, PokerStars was $400 - now $0. UB was $250 - now $0. Considering I only deposited about $150 total into these accounts to open them, its not quite that bad....but it keeps me humble.
