## What, Me Worry?

It doesn't seem like all that long ago I was gloating a bit over a Yankers team that was 12 or so games behind the Red Sox. It's mostly because it

*wasn't*all that long ago. As of today, MLB.com has the spread down to 7 games. ESPN is saying 6, but there seems to be some issue over a game with Baltimore that got rained out or something. Even my Yanker fan coworkers are stating 7. My questions then:Is it time to freak out yet?

According to an article on MVN.com (which I cannot verify the validity of) it is still not time to lose sleep (although that is exactly what I did last night.) Basically, this article talks about how, so far, the Yankers are playing about .500 ball, the Sox .600.

*Pizza Cutter,*the author of the piece, states that the odds of a team that is truely .500 playing .600 ball for half a season is something like 2.5%. Translation: This is the chance that the Sox are playing over their heads. similarly, the odds of the Yankers playing .500 ball when they are really a .600 or better team is about the same. I am not a statistical genius, so I'll have to trust*Pizza Cutter*when he (or she, I suppose) states that the chances of*both*of these things being true is something like .06%. This then means that for there to be a reversal of the first half of the year, which is pretty much what needs to happen for the Yankers to end up over the Sox, the odds are less than 1%.There's lots of talk about the trade deadline, also, and the Sox apparent need for relievers. While One week doesn't mean everything, the last few losses for the Sox have seen pretty steady relief. All but one had relievers shutting out oppoents. This has me thinking that perhaps the issues that needs to be addressed is run production, particularly in the latter innings. When the Sox get a lead lately, the pen holds it (for the most part). When Boston is behind, the bats aren't producing rallies. Now, not only I don't think that the Sox run production is an issue that has to be addressed by trading (though they are apparently looking at Mark Teixeira), picking up the wrong reliever could possibly mess with the mojo of the part of the equation that

*isn't the problem*.Labels: hitting, Red Sox, relievers, statistics, trade, Yankers

## 2 Comments:

Here's the quick mathematical explanation: Imagine that every baseball game is decided by a coin flip. We assume that the coin has a 50/50 shot of landing heads/tails, but sometimes, you flip it ten times and it comes up 7 heads/3 tails. Does that mean that it's not really a 50/50 coin? You might be saying, well, what are the odds of that happening?

Now suppose I flipped it 100 times and it came up 97 heads and 3 tails. You'd definitely say that it wasn't a 50/50 coin (I hope). Yeah, 97 heads could happen, but it's just so unlikely that you start thinking that the more likely explanation is that the coin is weighted. In fact, in statistics, we start saying that it's unlikely when it drops below a 5% chance of happening. It's not impossible to have 97 heads, just not likely.

We can calculate the exact probability that these events will happen using something called the binomial distribution. It works when there are only two possible outcomes. In this case, heads or tails. In the case of baseball, win or loss.

Coming back to baseball, the Red Sox, or any team have a "true" winning percentage. If they played a billion games or so, we'd know what it was. But, we can only infer what it is from what they did over the 87 games that they played in the first half.

The Sox won 53 of their first 87 games. What are the chances that they really were a .500 team that got lucky? The chances of a "true" .500 team playing .600 ball are about 2.5%. We can flip the process around on the Yankees. What are the chances that a true .600 team would play .500 ball? Around 2.5%.

In order for the Yankees to overtake the Sox, the Yankees would have to be a true .600 team and the Red Sox .500, (plus or minus some luck). The chances of both of those things being true at once is 2.5%.

The formula for the probability of two different events happening at once is to multiply the probabilities of both events together. 2.5% x 2.5% is .0625%.

It's not impossible for the Yankees to overtake the Sox. It's just not likely.

pizza cutter -

Thanks for taking the time to lay it out!

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