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May 4, 2012

Underestimating the Base Rate

Filed under: Uncategorized — Kevin Pelton @ 12:04 pm

On the surface, transfers in the NCAA and injuries in the NBA don’t seem to have anything in common. However, I think there’s a pattern to the way we discuss both of them. What they share is that a widespread belief that they are increasing–I’d say it even reaches the point of conventional wisdom–isn’t backed up when we seek to quantify the two phenomena, as College Basketball Prospectus contributor Dan Hanner did yesterday in response to John Gasaway‘s question about transfers.

I think there’s a common explanation. When we think about issues like injuries and transfers (and coaching changes, to add another) in a non-statistical sense, I believe our default position is that they are outside the normal scope of basketball. That is, we imagine a world in which nobody ever gets hurt, or transfers, or gets fired, because these things happen relatively rarely. At the individual level, it makes sense to assume each player will be healthy rather than injured, or stay rather than transfer, but instead of adding the small percentages of each outcome, we just apply the same assumption to the entire group. So when change does occur, we perceive it as foreign and unnatural.

Think about it this way: Do you ever remember anyone observing that injuries are down relatively to some other period? Maybe this happens at the team level, like with the Suns, but I don’t think it happens with anywhere near the frequency of people lamenting the increased prevalence of injuries. When injuries don’t occur, it’s invisible because that’s what’s supposed to happen. Same with a college team that doesn’t have any transfers and brings back the same group of players, minus seniors and early entrants.

As a result, it’s easy to underestimate how often these rare events happen. Whenever we do hear about a lot of them at the same time, it tricks our brains into thinking this is more unusual than it really is. So we often perceive injuries and transfers as happening at an increasing rate, when really nothing has changed.

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