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## The myth of the ‘law of averages’

Posted by Derek Carty at 8:30pm

Those who are regular readers here probably already understand why we should not rely on the "law of averages." Most competitive opponents will not trust or use it. However, I'm still running into people who use it to justify moves they make.

Wikipedia describes the law of averages as "a belief that outcomes of a random event shall 'even out' within a small sample." Essentially, the law of averages says that bad luck early will be evened out by good luck late, regardless of sample size.

###### The law of averages in fantasy baseball

In fantasy baseball terms, let's say that David Ortiz is absolutely a true .300 hitter, that his batting average skill level is exactly .300, and that he has simply been unlucky so far this year. A person using the the law of averages may say that because Ortiz is a true .300 hitter and/or because he had him projected to hit .300 at the beginning of the year, his current .247 batting average is simply bad luck. To simplify things, let's say that we're exactly one-quarter of the way through the season (even though we're further along than that now).

This person will then conclude that Ortiz should hit .318 over the final three-quarters of the season because, while he is only a .300 hitter, he has to hit that .318 to even out the bad luck early on. That way, he will finish at .300, his true skill level.

Even if Ortiz is truly an exact .300 hitter, it is ridiculous to think he'll hit better than that simply because he's had bad luck. Luck doesn't work this way. If you believe (or know, in this case, since we're working with absolutes to make the point) that a player's true skill level is .300, he should simply be expected to hit .300 going forward. In Ortiz's case this would leave him with a final average under .300.

###### Simple law of averages scenario

As unlikely as this scenario is, let's pretend that we just flipped 1,000 fair coins and every single time we flipped heads. We're preparing to flip 1,000 more coins and want to predict how many times it will land on heads and on tails. Because the first 1,000 coins landed on heads, should we predict that the next 1,000 will land on tails? I hope you're saying to yourself "absolutely not." That would be ridiculous. We should expect 500 to land on heads and 500 to land on tails.

When making predictions, we must ignore all past luck and assume that luck will be neutral. Just because someone has experienced bad luck in the past doesn't mean we should assume he'll receive good luck in the future. Over a long period of time (in baseball terms, this means several seasons), luck will tend to even out. In a sample as small as a single season, though, luck most certainly does not have to even out. It will in the case of some players, but this is not because of the law of averages.

###### Variability

Every season (and every subset of a season, like the three-quarters of a season we dealt with for Ortiz), without question, some players will get lucky and some will get unlucky. Regardless of whether Ortiz is an unlucky one in the first quarter season, there will always be a chance he will be one of the lucky ones for the remainder of the year. This is completely independent of his prior bad luck, though.

Because we don't know whether he will fall into the lucky or unlucky group, though, it would be incorrect to think he will be one or the other. We can never know for sure, and that's why they call it luck. We must always assume neutral luck and assume he will hit a flat .300.

Even if this isn't news to you and even if you completely disregard the law of averages, it is still possible to use it to your advantage. If you are trying to negotiate a trade with a weaker opponent, try using the law of averages to persuade him or her.

Maybe say something like, "Nate McLouth is hitting .323 this year. He's obviously getting lucky. He's never hit higher than .258 in his career. What do you honestly expect him to hit this year? .270? Maybe? That means he'll probably hit like .250 the rest of the way to even out that luck. It's the law of averages. For me, the batting average doesn't matter much because I really just need the steals."

To a weak opponent, to someone who uses the law of averages, this will make sense. Even if you leave out the "it's the law of averages" part, you are still hinting at its meaning. Depending on the situation, you might even be more successful leaving it out.

In addition, if you're using the "feigning weakness" strategy we discussed last month, saying this type of thing to a strong opponent could further lead him or her to believe that you are weak. In all honesty, I don't take any of my competitors who rely upon the law of averages too seriously—unless, of course, I have reason to believe they're trying to throw me off.

###### Concluding thoughts

Sorry for not having a National League Waiver Wire this week and for the lack of posts over the past couple of days. The weekend got away from me with the holiday and everything, and I spent the past couple of days working on getting all the PITCHf/x stuff in order. I hope the future content will be even better for this. We'll start doing Waiver Wire's earlier in the week anyway, and I'll be sure to do the National League first this week. Look for that maybe tomorrow night.

Derek Carty, 23, has also been published by NBC's Rotoworld, Sports Illustrated, FOX Sports, and USA Today. This season, he'll be contributing to FanDuel and will be linking to all of his work at DerekCarty.com. In his three years competing in expert leagues, he has won 2 titles with 4 top three finishes, including a LABR NL title in 2009, making him the youngest person to ever win a major expert league title. Derek is a proud graduate of the MLB Scouting Bureau's Scout Development Program and is a firm believer in the importance of combining stats and scouting. He welcomes questions via e-mail, Facebook, or Twitter.

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