Wednesday, 27 October 2010

Payrolls and Baseball Success

There's been a lot of buzz about the teams in this year's World Series because each has a relatively small payroll.  Given the recent success of other low payroll teams, it's interesting to consider how strongly correlated payroll size and team success are. To get a quick sense, I took the Pearson r number for 2010 total team payroll and 2010 total regular season wins.  In the case of payroll and wins, the number was a relatively small .35.  Compare that to a value of .66 when one considers total wins and average age, or .38 when one correlates total wins with the age of the oldest player on the team. In other words, someone using only the age of the oldest player on the team to predict success in 2010 would have been more successful than someone who used payroll size.   (Data sources: payroll:, age data:, win totals:

ETA:  Data and calculations link

Friday, 15 October 2010

Hitchens's Wager (Pascal's Wager Revisited)

I've been reading about some of the recent debates that Christopher Hitchens has been having or will be having with people like his brother and Tony Blair. Apparently the debate or discussion focus has shifted from a direct question about God's existence to the practical effects of religious belief.  I'm not sure if the debate is supposed to have anything to do with the question of God's existence, but let's suppose, for the sake of argument that it does.

If it does, one might contend that it's an odd claim, i.e., whether or not a belief  X has good practical effects isn't what should inform whether or not we believe it.  We should believe X based on whether or not we have evidence for X.  If I believe that my wife is cheating on me that may end up having negative practical effects that could harm our marriage, but nonetheless, I should base my belief in this matter on the evidence that I have, not the effects that I want to see.    Similarly, can one actually choose whether or not to have a belief based on anything other than evidence?  For example, it seems that I can't choose whether or not to believe that Ottawa is the capital of Canada, it's just something about which I have knowledge based on evidence.  You can offer me $1000 if I'll stop believing it, but I'll only be able to pretend I don't believe it, I won't actually be able to stop believing it.

However, it's worth thinking about American pragmatism in this regard.  Pragmatism sees belief as something other than just the degree of psychological certainty we have with respect to some proposition based on some reliable epistemic process. Rather, belief can be a matter of the will.  It's not unreasonable, according to pragmatists,  to choose to believe X even if we don't feel certain about it.  William James gives the mountain pass example. A climber is caught in the mountains and must get down before night fall.  He doubts his ability to jump a chasm but convinces himself that it's possible, despite a lack of evidence and in choosing that belief actually manages to give himself the requisite confidence to make the jump.  Bas van Fraassen is a voluntarist with respect to belief  contending that one can choose to believe X over Y even if one doesn't feel as certain about X as they feel about Y.  Of course, this all hearkens back to Pascal's Wager. Pascal famously argued that even if you don't feel very confident in God's existence, you should choose to believe in God anyway because there's not much to lose in so believing and much to gain if you actually do believe.  Decision theory shows us the way.  Pascal assures that we can simply act as if we find the belief compelling and it will become compelling.  But the key is that we choose what to believe, not because of the evidence we have at hand but because of the positive benefits of holding the belief.

So, now let's consider Hitchens's discussions of the effects of religious belief.  We might actually consider this as reworking of the decision theoretic data that's factored into Pascal's wager.  In fact, if religious belief has a significantly detrimental effect overall and if, in fact, the probability of an afterlife is very small (although one might contend if the overall benefit is infinite, because one would live forever, than it can become almost vanishingly small and still be reasonable, but let's set that aside), then the wager comes out the other way.  If the effects of believing aren't negligible, then belief itself, in the absence of solid data for or against may well compel us to reject the belief rather than accept it.