THE BOOK--Playing The Percentages In Baseball

In the social sciences the use of the term “quantitative methods” almost always begins with regression-based statistical analysis and grows more complex from there.

I think he is trying to say that even a rational observer cannot correctly determine how much randomness was in each observation.  In other words, those “quantitative methods” would be some form of regression to the mean.

The human brain does not have the capacity to recall every play Player A made and compare it to every play Players 1-Player 1,000,000 made.

Methods to capture what was observed as quantitative data are necessary, even if what was observed was subjective.

These numbers in baseball are in part subjective. 

A hit is a hit because the umpire ruled the ball was fair and the scorer did not rule an error.

An error is an error because a scorer made a subjective ruling it was an error, and so it was not a hit.

A batter is walked because the umpire ruled that the pitch was a ball.

A pitcher got credit for a K because the umpire ruled the pitch was in the strike zone, or that the batter swung and did not foul the ball.

A base is stolen when an umpire rules that the runner reached the base before he was tagged.

BIS observers decide what zone a ball is hit in and how hard it was hit, and based on some theoretical calculations based on assumptions and averages UZR and DRS come up with a number for the player.

Virtually all data in baseball, including those used by newer metrics, are in part based on subjective observations that are systematically collected and quantified, then counted and in some cases massaged and adjusted to give us other numbers.

Some of these numbers are more real than others.

"Quantitative methods” means looking at stats from games. What the author is saying is “you can’t figure it out just by watching, you need to look at the stats showing what actually happened to figure it out.”

Yes, scouts may be putting things on a 20-80 scale. But it’s a qualitative shortcut, rather than actually being quantitative.

How many times do we remember the great diving catch outfielder x made and forget that he took two steps in the wrong direction first?  This, to me, seems to be the type of thing he is referring to with the “over a large number of events and/or a long period of time” comment.  Our brains easily remember the Wow! but forget little details that made it necessary.