Within a given season, you could estimate how minutes covary with PER by running a regression analysis. Since better players tend to receive more minutes, this should be a significantly positive relationship. (You could even run separate regressions for each coach, assuming the relationship b/t PER and minutes assigned is different for each coach.) The regression analysis can then basically serve the function of a quantitative prediction of how players are rewarded more minutes as a function of increases in PER. Call this “the coaching effect.”

Now, the key variable of interest is not how a player’s PER changes b/t 2 seasons where he sees a big increase in minutes. The variable of interest is how the player’s actual change in PER as a function of minutes played differs from the quantitative prediction of how his PER should have changed with the increase in minutes, according to the coaching effect. By subtracting the predicted change from the actual (i.e. by calculating the residual displacement of each data point from the regression line), we will have cancelled out any variance in the data attributable to how coaches dole out minutes according to performance (at least in theory).

With this data set, the hypothesis to be tested would be that the residuals are negatively correlated with the change in minutes played (i.e. after controlling for the coaching effect, we should see that PER drops proportionately to the increase in minutes played).

For instance, suppose player A plays 10 mpg one season and then 25 mpg the next. Suppose that the coaching effect predicts that in order to have earned 15 more mpg, his PER must have increased by 5 points. If his PER actually only increased by 2 or 3, though, then his actual rise in efficiency is lower than that predicted by the coaching effect. If a pattern like this could be established to occur with consistency, where on average actual changes in PER undershoot predicted changes in PER according to the coaching effect, we would conclude that in fact, increases in minutes do tend to decrease PER, once we take the coaching effect into account.

“You are more likely to be struck by lightning that bit by a shark or stung by a bee.” that might be true, but I know one thing, if you lock me in a room with 1000 bees or dropped me in a tank of great white sharks, those odds are reversed.

Sports are no different than anything in life, it’s all about timing, being in the right place at the right time, and having the right people around you.

Let’s talk sports people NOT STATS!

Imagine we wanted to test the relationship between duration of exercise and reports of fatigue. We have two experimental conditions, one group jogs for 10 minutes and the other for 30 minutes. We predict that the group that jogs 30 minutes will report more fatigue.

But we must assign people to the two groups randomly in order for the data to have any bearing on the hypothesis. If we systematically assign people who are in better shape to the 30 minute jogging condition, we may find that in fact, if anything, people report less fatigue with longer durations of exercise. But the study is flawed in a fundamental way and so the data don’t tell us much of anything. At most what the results of this poor experiment tell us is that the effect of exercise duration on reported fatigue is not so strong that it overrides the differences in health between the two groups. But that is a really limited conclusion, especially if we don’t even have means to quantify how much the two groups differed in health to begin with.

this is a totally mistaken conclusion. you need to factor in how many car rides people take versus plane trips, and if it’s more than 200 times more (as I’d assume), then flying is in fact more dangerous.

For it to be true that a increase in playing time means a decrease in production then both of these must be true:
A. Of the ~70% of players who didn’t decline, a majority improved on their own to earn the playing time.
B. Of the ~30% of players who did decline, coaches were forced to play a majority of them due to injury/roster problems.

That seems to be a bit of a stretch to me. I don’t see that as being analogous to there being a blurry picture. It’s not a clear picture but there is a decent amount of evidence to the contrary, without anything substantial to backup the opposing theory.

I don’t see why the picture is as murky as that analogy. The study results may blur cause and effect, but as a group the players studied played significantly better when they played more minutes. If there were a strong current in the opposite direction – if players were frequently exposed when the coach gave them more burn – I don’t think you’d have such robust numbers. Of course my opinion is subject to change as new evidence comes in.

Even a blurry picture is better than no picture. You might not be able to tell what shade of red the building is, but you can tell if it’s a house or a skyscraper.

Imagine we are debating whether a building in a secret government location is colored red or not. Since it’s top secret we can’t just go and look for ourselves. But suppose someone sends out a spy camera that gets near the building and snaps a photo. But the photo is just a mush of nonsense because the lens was cloudy and scratched, and there were trees in the way of the shot.

Now the guy who snapped the photo shows it to everyone and says “there is no evidence that the building is red.” Sure, the photo shows no evidence that the building is red. But this is a trivial result; the photo doesn’t really tell you much of anything because it didn’t get a clear shot of the building in the first place. So it does not help the discussion to even bring up what the photo recorded.

If anybody was game, I do think a look at the player universe that didn’t improve would be interesting. Were they mostly centers?…were they guys who got time because a starter was injured (vs. improvement in ability)?…Bad foul shooters? Guys who couldn’t shoot threes? What did they have in common with one another?

What factors can be teased out that over-index with the group that doesn’t improve performance with more time?

In theory, it would be interesting to do the same analysis on different stats – TS, points/shot, rebounds, defensive measures, etc. – to see which aspects of a player’s game tend to stay flat, and which improve or worsen with additional minutes. (I suspect you’d see players shoot and score at a higer rate as they get a more prominent role, even if their overall game doesn’t improve)…

…but in practical terms, it’s complicated enough just to run one set of numbers (with PER, for example).