This is Not a Random Post

Or is it?

Perceiving Randomness

Humans are not very good at generating random sequences; when asked to come up with a “random” sequence of coin flips from their heads, they inevitably include too few long strings of the same outcome. In other words, they think that randomness looks a lot more uniform and structureless than it really does. The flip side is that, when things really are random, they see patterns that aren’t really there.

This is Highly Significant

Basics: Significant Figures

The idea of significant figures is that when you’re doing experimental work, you’re taking measurements – and measurements always have a limited precision. The fact that your measurements – the inputs to any calculation or analysis that you do – have limited precision, means that the results of your calculations likewise have limited precision. Significant figures (or significant digits, or just “sigfigs” for short) are a method of tracking measurement precision, in a way that allows you to propagate your precision limits throughout your calculation.

Square Day

It’s Square Root Day! – March 03, 2009

If you’re tempted to suppress your inner geek, just remember that Square Root Day only happens nine times a century. The last one was Feb. 2, 2004, and the next one won’t be until April 4, 2016.

And it doesn’t matter which calendar convention you use.

Ultrageekily speaking, the last square (root) day was 12/12/144, but I guess we’re suppressing the leading digits here.

Making Sense of Some Mind-Boggling Stats

Stray Thoughts on 1962

Questions about the connection between gaudy stats and helping your team to win aside, a look at a comparison between the insane stats posted in 1962 and what’s going on today, in terms of the pacing of the game, then vs now.

Okay, so you’ve all seen Wilt and Oscar’s numbers from 1962… but have you ever sat down and looked at the league averages that year? In ‘62, the average team took 107.7 shots per game. By comparison, this year the average team takes 80.2 FGA/G. If we use a regression to estimate turnovers & offensive rebounds, the league pace factor for 1962 was 125.5 possessions/48 minutes, whereas this year it’s 91.7. Oscar’s Royals averaged 124.7 poss/48, while Wilt’s Warriors put up a staggering 129.7 (the highest mark in the league). On the other hand, the 2009 Cavs are averaging a mere 89.2 poss/48. It turns out that the simplest explanation for the crazy statistical feats of 1961-62 (and the early sixties in general) is just that the league was playing at a much faster tempo in those days, with more possessions affording players more opportunities to amass gaudy counting statistics.

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Quest for Statistics

Statistics, and the quest for meaningful statistics, in basketball. Baseball may have the most dubious statistics, but because of the dynamic of the game, in basketball you can amass impressive personal statistics in a way that hurts the team, e.g. the box score shows you scored 20, but that doesn’t indicate if it was on 10-of-20 shooting or 10-of-30, and doesn’t say whether a missed shot was at the expense of a teammate who had a much better opportunity.

The No-Stats All-Star

[T]he big challenge on any basketball court is to measure the right things. The five players on any basketball team are far more than the sum of their parts; the Rockets devote a lot of energy to untangling subtle interactions among the team’s elements. To get at this they need something that basketball hasn’t historically supplied: meaningful statistics. For most of its history basketball has measured not so much what is important as what is easy to measure — points, rebounds, assists, steals, blocked shots — and these measurements have warped perceptions of the game. (“Someone created the box score,” Morey says, “and he should be shot.”) How many points a player scores, for example, is no true indication of how much he has helped his team. Another example: if you want to know a player’s value as a rebounder, you need to know not whether he got a rebound but the likelihood of the team getting the rebound when a missed shot enters that player’s zone.

There is a tension, peculiar to basketball, between the interests of the team and the interests of the individual. The game continually tempts the people who play it to do things that are not in the interest of the group. On the baseball field, it would be hard for a player to sacrifice his team’s interest for his own. Baseball is an individual sport masquerading as a team one: by doing what’s best for himself, the player nearly always also does what is best for his team. “There is no way to selfishly get across home plate,” as Morey puts it. “If instead of there being a lineup, I could muscle my way to the plate and hit every single time and damage the efficiency of the team — that would be the analogy. Manny Ramirez can’t take at-bats away from David Ortiz. We had a point guard in Boston who refused to pass the ball to a certain guy.” In football the coach has so much control over who gets the ball that selfishness winds up being self-defeating.

Risky Business

The benefits of teaching the statistics of risk analysis.

Probability lessons may teach children how to weigh life’s odds and be winners

“You can tick off story after story that’s probably interesting to the people it happened to, but not statistically unusual at all. There was a recent story about a family in Gloucestershire with three children all born on January 29. We were contacted by a journalist and asked what are the chances of this happening.

“The chances are about one in 135,000, or seven in a million. But there are a million families with three children in the UK. So it’s almost certain that this family is not unique and when the story went online, someone wrote in and said, ‘I was born on the same day as my two brothers’.”

[…]

The unfounded scare over the MMR vaccine, and outlandish claims of success for alternative medicines, were prime examples.“One must think all the time of what is not being reported – the dog that didn’t bark. When we see a hole-in-one video on YouTube we are sensible enough to know that this has been selected out of millions of shots that missed. We need to think the same way every time we hear of someone claiming that some new treatment has cured them.”

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