As a preface, for this post general terms like "stronger climber," "better climber" etc. are interchangeable terms for what is really a vague system of measuring more factors than I could list. To simplify things, just assume that I'm referring to a climber who, for the relative grade, has an average ability in all areas of climbing: power, lockoff strength, technical aptitude, mental acuity, etc. I'll try not to use definite phrasing, because all things in climbing are relative.
One big question that will be discussed a lot on this blog is this: when routesetters talk about forcing a move, what are we really talking about?
There's several perspectives. As with all things climbing-related, the talking points of each point of view will vary wildly with the difficulty of the climb being discussed. Forcing a move on a V10 being climbed by a V10 climber, and forcing a move on a V3 being climbed by a V10 climber are different propositions with distinct obstacles; greater technical aptitude, raw power and breadth of experience allows V10 climbers to visualize, attempt and perform sequences that, regardless of the routesetter's intended method, will result in a successful climb. The subject is further muddled by another major issue, organic diversity between climbers: weight, height, finger strength, finger size, body tension, ape index, hip turnout flexibility, and a vast number of other factors.
One perspective of "forcing" a move is creating a choice for the climber. The choice will affect the climber's relative chances of success on the climb through what I see as a reward/punishment system. Successfully choosing the correct sequence will reward the climber with better body position, a better hold, or an opportunity to move to the next choice; choosing the wrong sequence will punish the climber with a poor body position, a bad hold, and often either necessitate retreating and making the choice again, or result in a failure. I'll talk more about the choice-reward system in climbing in a different post.
To illustrate one perspective of "forcing" a move, here's a simple graph. The line of probability reflects the point at which a climber should be able to climb a route. The colors indicate a routesetter's relative ability to force a move. As a climber's raw ability increases, their ability (and number of options) on a route increases. Thus, the green area on the graph is a point where a routesetter may find it easier to get the climber to do the intended sequence. A red area on the graph indicates that a routesetter might find it very frustrating to try and get a climber to do the intended sequence.
As a way of understanding this concept, here's a simple example. Joe, a V3 climber, arrives at the crux of a boulder problem at his absolute physical limit. Matched on a crimp rail with high feet, he must lock off and make what is, for him, a big right hand move to a slot. He barely makes it, and then is able to move his left hand to a good jug hold slightly higher. Exhausted, he completes the sequence and goes on his weary way. Tim, a V10 climber, wanders up to the problem and quickly climbs into the same move. His better lockoff strength and higher body tension allows him to move all the way directly to the jug. He finishes, drops off and moves on.
In this example, one difference between the two climbers was Tim's greater reach due to being a stronger climber. Another way of looking at the example is that Tim's climbing ability and experience offered him a wider variety of choices. He had the ability to reach the bigger hold, but still could have chosen to do the intended sequence. His ability and instincts were more developed than Joe's.
One critical element of this example is this: the red area must represent not the ability to do ONE move, but the relative difficulty of all possible choices that the climber could make that would result in a successful rock climb. In other words, if Tim finds the lockoff to the jug just as hard as Joe finds the 2-move sequence, the routesetter has done an effective job forcing the sequence. (Not that V3 will feel hard for Tim - but as long as it feels V3 to both of them, the routesetter has still succeeded.)
Therefore, from this perspective, forcing a sequence can be looked at as: a) limiting the number of choices that a climber can make from any given point in the route, regardless of organic discrepancies between climbers, and b) ensuring that the reward/punishment system involved in those choices will cause a successful attempt to have the same number of rewards (rest points, good body positions, etc.) and a failed attempt to be a result of the same potential wrong choices (i.e. a short climber should not run into five potential stopper moves when a tall climber runs into two.)
Looking again at the graph, you could use the gradient as a vague gauge of how consistent, or "classic" it is. If a move on a moderate climb lands in the red area for a climber, and they still do the intended sequence, the move was pretty well set. If they do a different sequence, that's okay too - as long as it feels consistent to them. Routes where climbers of different grades do the same sequence naturally are often considered classic. When I say naturally, I mean when they are not intentionally trying to skip moves and make the route harder than it is.
This is, based on my limited understanding of the science of routesetting, the most meager introduction to forcing a move that I could pare into words. Further posts will get more specific.