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Sample Size and Mental Health

Some stream of conscience thinking here... hope others can add their streams...

 

One of the most common reoccurring themes we see here on the high school baseball web goes something like this:

 

"My son is always a dominant pitcher on his summer team where the ex-pro pitching coach loves him.  Every year, his high school coach tinkers with his mechanics to improve his control (or some other adjustment like increase velocity) during high school season and tells him he needs to improve or others will see more playing time.  His confidence is in the tank and now he can't seem to throw the ball over the plate.  I wish the high school coach would just leave him alone."

 

"My son has always been a great hitter.  He has always hit over .450 in high school and on his summer team.  He's started on varsity since he was a freshmen.  Now the coach is trying to get him to turn on the inside pitch more (or make some other adjustment) and the hits are not falling this spring his junior year.  I am worried college coaches are going to lose faith in my son and his confidence is in the tank.  I wish the coach would leave him alone and not pressure him to improve."   

 

There are millions of variations on these feelings.  Some kids can go years without experiencing a downturn but many times the panic that sets in when things "appear" to go wrong is the "problem" rather than the short term "results" that are not happening as expected.  My theory is if a kid can hit, he can hit - a coach (or other factor) cannot change that over the short term.  If a kid can pitch, he can pitch, a coach (or other factor) cannot change that over the short term.

 

What we see every year, is parents and players panicking when their numbers are not the same as they have always come to expect during the high school season.  Thus, they demand reasons.  The real problem (or reason) may be small sample size and not any other influence.  There is an inherent fallacy people can make with respect to averages in small sample sizes which high school seasons generally represent.

 

From Wikipedia with my comments inserted in bold underline:

 

The law of averages is a layman's term used to express a belief that outcomes of a random event (your son's statistics) will "even out" within a small sample (a high school season).

As invoked in everyday life, the "law" usually reflects bad statistics or wishful thinkingrather than any mathematical principle. While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that unnatural short-term "balance" MUST occur. Typical applications of the law also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.

Examples

  • Belief that an event is "due" to happen: For example, "The roulette wheel has landed on red in three consecutive spins. The law of averages says it's due to land on black!" Of course, the wheel has no memory and its probabilities do not change according to past results. So even if the wheel has landed on red in ten consecutive spins, the probability that the next spin will be black is still 48.6% (assuming a fair European wheel with only one green zero: it would be exactly 50% if there were no green zero and the wheel were fair, and 47.4% for a fair American wheel with one green "0" and one green "00"). Similarly, there is no statistical basis for the belief that lottery numbers which haven't appeared recently are due to appear soon. This sort of belief is called the gambler's fallacy.
  • Belief that a sample's average must equal its expected value. For example, if one flips a fair coin 100 times, there is only an 8% chance that there will be exactly 50 heads.

I realize that a player has more control over probabilities than the roulette wheel or coin toss.  However, the kids they are competing against influence the probabilities in the other direction.  A short sample size ( a high school season's worth of statistics) may not mean anything other than the sample size is too small to draw a conclusion. 

 

If that is the case then:

 

- Encourage your kids that the numbers will eventually turn back around in their favor.

- Encourage them to be open to coaching and that they can learn from each of them.  No coach can screw up a good hitter or pitcher (I am sure there are those who will swear otherwise).

- Encourage them to welcome pressure.  There is pressure in high school to get your name in the paper and to help the team win.  This pressure does not exist when the summer team coach loves you and the consequences for losing are small.  

- Don't let panic become a self-fulfilling prophesy.

- Relax

- Enjoy the blessing of a healthy child

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