Free reinforcement is often stated as a problem with area scoring. This page shows that unnecessary reinforcement is just as often more costly (loses more points) under area scoring compared with territory scoring as when it is less costly. When it is less costly, it is in fact "free" (loses no points) as the main page shows. Perhaps this is the important distinction.
Reinforcement refers to a player playing inside his own territory, perhaps to protect a cut which could lead to death or perhaps to prevent posible seki. Suppose that there are only dame left and the reinforcement is actually unnecessary. Under territory scoring the reinforcement always loses the player one point. Under area scoring the play either loses the player two points if there were an odd number of dame, or no points (is free) if there are en even number of dame. Because of the coarse granularity of area scoring, the average loss of one point is "rounded" sometimes to two points and sometimes to no points.
No prisoners not shown; half a point komi. Here there are no dame (even number). Black isn't sure whether he needs to play again to make his group safe. Under territory scoring, Black will lose by a half point if he makes the unnecessary reinforcement. He will make a half point win if he doesn't play and is, in fact, alive. How exciting! Under area scoring, Black can reinforce "for free" and wins without needing to consider whether the play is necessary or not. How boring. Here, territory scoring is interesting because Black must decide whether the reinforcement is necessary.
However, consider the following example.
Here there is one dame (odd number). Under territory scoring, White can make the unnecessary reinforcement and win by half a point anyway. How boring. Under area scoring, if White reinforces she loses the dame and the game. If she instead takes the dame, she can win but only if her group is actually alive. How exciting! Here, area scoring is interesting because White must decide whether the reinforcement is necessary.
The argument is that although a player can sometimes reinforce for free with area scoring, it is not important. Because he can reinforce at less cost than in territory scoring does make a difference. Equally though, sometimes it costs more.
Practically-speaking, in the second example White must actually count the score to find out if he can afford to make a perhaps-unnecessary reinforcement. In the first example, Black does not need to count.
This example shows that "bad" plays can still be free in button go (or equivalently, territory scoring). Black can play the dame first and get the best result, even though its miai value is less than either of the 1-2 points. With five buttons ranging in value from 1/4 to 5/4 points, this is not the case. In fact, no matter how many 1-point and 3/2-point plays (like in the diagram) are left, the wrong play will never be "free" using these five buttons. Therefore, if the free teire effect as described above really is a downside of area scoring, then because the finer-grained button go also has a similar effect which the five-button go just described doesn't, it can be seen that it is just a special case of the granularity effect.
-- The Count
Bill: First, the above ignores the fact that a and b are exact miai, canceling each other out. In this case we cannot call c a bad play by either area or territory scoring. Second, there is a conceptual difference between button go and multiple button go. Button go is a form of go that bridges territory and area scoring. Multiple button go, also known as environmental go, token go, or coupon go, is a form of go that reduces the effect of tedomari within the range of the sizes of the buttons. Play c is smaller than a button of size 5/4, and it is never better to play c before that sized button. The existence of smaller buttons has nothing to do with that. The granularity effect, as here defined, has only to do with the difference between area and territory scoring. Multiple button go with buttons of size greater than 1 has other effects than just reducing the gap between area results.
The Count: Are we saying that d is not a "bad" play by plain area scoring because the remaining points are miai? But if we don't like it when unnecessary reinforcement is free, isn't that because it's a bad play? Hence, if unnecessary reinforcement is considered a free bad play that area scoring exhibits, then playing c above should be considered an example of a free bad play that territory scoring exhibits.
Bill: A play at d is bad under territory scoring, not under area scoring. Similarly, unnecessary reinforcement is bad under territory scoring, not under area scoring. One virtue of territory scoring is that there are more bad plays.