THE BOOK--Playing The Percentages In Baseball

Monday, November 02, 2009

Probability illusions

Before Game 5, if you asked baseball fans if they thought that the Phillies might still win the Series (being down 3-1), most of them would say something like, “No way.”

If you asked a sabermetrician or even a fan who was a statistician the same question, their response would likely be, “I don’t know, but they have around a 9% chance, so it is unlikely but obviously possible.”

If the Phillies do come back and win, again, from the perspective of before Game 5, people will be shocked and they will be talking about the comeback for many, many years.

But....

Is something happens that has a 9% chance of occurring, shocking?  Typically, no they aren’t.  9 and 10% things happen all the time.  Sports fans see it ALL the time.  But as far as public perception goes, it depends.  What does it depend on?  One thing is the importance of the event.  A team, even an inferior one, winning 3 games in a row during the regular season?  No big deal.  Happens all the time.  When the Pirates win 3 games in a row, they don’t talk about that for years do they (well, maybe Pirates fans do)?  But in the WS?  Different story even thought the percentages and likelihood are the same.

Another thing it “depends on?” How many opportunities there were in history.  Why is that?  Because the human mind remembers how many times the unlikely event occurred and not necessary the number of opportunities.  An inferior team winning 3 games in a row during the regular season?  Happens all the time.  That is because there are hundreds of opportunities.  But we are not necessarily aware of the number of opportunities, only that it happens a lot.  But, it only happens 10% of the time or so, exactly the same as a team coming back from a 3-1 deficit in the WS.  That too will happen 9 or 10% of the time, but we have had so few opportunities for that in history that people only recall how infrequently it has actually occurred (4 times in history I think).

I’ll give you one more example of how our “shocked meter” is nowhere near congruent or commensurate with probabilities.  Barry Bonds steps up to the plate. How many people would be shocked if he hit a HR or said, “No way he hits a HR?” The Phillies come back to win the WS after being down 3 games to 1.  How many people would be shocked or said, “No way!”

Chance of Bonds hitting a HR?  6%.  Chance of Phillies winning the Series?  9%.  Which should be WAY more shocking from a purely statistical perspective?