Gambler's Fallacy

[bobbing_headz]

This is what I wrote on the Yahoo blog and is why I don't like the Yahoo take on the subject:

The gambler's fallacy is the wrong example here, or rather even if it applies it's irrelevant in some regards. While it's true that players won't get suddenly "hot" or "cold" to average out stats if a player has definite career numbers to back him then you have to predict that he'll bat the same from here on out [like is mentioned correctly in the original article].

Basically if a guy like Ortiz who is a .300 hitter is hitting only .247 now it's still safe to assume that he'll hit .300 for the rest of the season, not .320+ to average out but rather .300 like he's done in the past (assuming we know there's no external factors like injury, etc.). This would leave him .280. Now it's true that betting on the .320 is not smart but going after Ortiz is still a very smart move because it's a good bet he hits .300 from now on.

With that in mind then buying low or selling high on players suddenly is the right thing to do because of course you must be looking at their career stats. The gambler's fallacy is only relevant if you are going after a player like Ortiz and overpaying for the (erroneously) expected .320 average. Yet, to me, that mistake seems almost forgivable as Ortiz should still outperform his current pace significantly. While I'm not saying the gambler's fallacy is wrong, I'm merely saying it's at the extreme end of what is/was rational thinking.

[jake_harv88]

Don't degrade Yahoo for posting that, not everyone will look at sites such as hardballtimes and not everyone is a fantasy expert. Yahoo is just trying to do as much as they can to help out anyone who was willing to read extra articles posted by them. I'm sure that particular article was helpful to many fantasy newbies.

In my opinion, yahoo shouldnt be running around to different sites and posting "hey look at this awesome article I found". Thats what sites such as the Cafe are for. If yahoo is going to post something like that they need to add something original to it. Adding a video that you can't even hear the players talking and all you really hear is "hey can we have that ball" doesn't do it for me...

[Matthias]

To paraphrase what was said above, but to be clear: the gambler's fallacy is the wrong model to apply.

The gambler's fallacy is a concept to use for things that are statistically independent. Say "black" comes 5 times in a row on a roulette wheel... is red "due"? No. The outcome of the next spin has no relationship to the spins in the past. But when you're talking athletes, the results are correlated. Adam Dunn has a higher probability of hitting 40HRs, at the beginning of each season, than does Juan Pierre. The gambler's fallacy would be to bet that Pierre outslugs Dunn this year, thinking that Pierre was "due".

As far as Yahoo reposting stuff, whatever. That's what the web is: you should check out some political blogs some time.

[JoshExley]

Posted 3 years ago...

http://www.baseballnotebook.com/essay.a ... %20Trading

..and HE (Looch) wasn't even the first. So if Yahoo is wrong, then so is HT.

[George_Foreman]

Interesting that they bring that up. People in general have a very poor understanding of statistics and probability, and they're both rather germane to discussions of baseball. While the result the articles are discussing is pretty basic (basically they're explaining that players (or coins or whatever) are never "due" to have a particular result because they haven't had that result in a while), it leads naturally into the discussion about projecting players and just how strong the correlation between your previous AB and your next AB is. (My guess is that it tends toward zero.) But in a sense, this is the crux of roster construction in fantasy baseball (and real baseball, I suppose): which factors are most important in predicting how a player will perform this season? Next season? The second half of the year? For some player, like Mark Teixeira for example, there is a definitive trend of slow starts and late surges. So while Tex has been sub-par thus far, it's reasonable to expect him to out-perform his career norms the rest of the year and finish around his usual spot. While the conclusion is similar to that we'd get from using the "Gambler's Fallacy", the reasoning is different and, in this case, correct: based on data from previous years, Teixeira is a player who tends to perform better as the year goes on. With other players, such as Travis Hafner, we may not suspect a turnaround given the similarities between his career and those of other high-peak, quick-flameout guys. (This is essentially what PECOTA does.)

All this is just to say that when we try to predict how players will do in the future, it is important for us to note what factors we're looking at when making these predictions, and most of the time, year-to-date numbers don't tell the whole story.