Gaming Innacuracies: Parallax Effects

Ever sit on the other side of the table and watch as your opponent moved a model and you thought to yourself "Gosh, it seems like he moved way more than he should have"? Well it's entirely possible that your well-meaning opponent was the victim of a parallax effect. And what's more, you might have done it yourself as well. Curious to understand more? Read on!

Disclaimer: I'm not a formal mathematician.

What is a Parallax Effect?
Although strictly speaking, a Parallax is the apparent difference in position of a single object based on 2 different viewpoints, for the purposes of this article I'm reversing the object and viewpoints. In gaming speak, the Parallax is the effective error encountered when measuring is done from a closer position than the distance being measured. More specifically, when I go to move a model I typically hold my tape measure above the model and then move the model using the tape measure as a visual guide for where to move my model to. What's wrong with that? Well let's take a closer look...

How does it work?
So this diagram shows the math behind the situation...
The top corner represents the viewpoint (or where your eye would be). The line in the middle of the triangle is where the tape measure is being held, with Y being the distance above the table that it's being held. M is the distance attempting to be measured, whereas M' is the projected distance due to the displacement of the tape measure from the table surface.
In order to keep the math fairly simple and straightforward, I've assumed that the angle of the two sides joining at point A (the start point of the measure) is a right angle. If it wasn't, the math gets much harder. However with this simple assumption then the calculation is simply a ratio between the sides. I've done the basic algebra to solve for M'. Now that the math is out of the way, let's look at some examples...

What are some examples?
First let's talk about moving a model. Most small based models are 2" or less in height, so let's assume that we're holding the tape measure 2" above the table. Next, let's assume that we're standing about 24" above the table surface (I took a sample of myself standing at my dining room table), or 22" above the tape measure. Now's let's assume I'm moving my Knight Exemplar forward 5" in a straight line. Using our math from above, we discover that the 2" displacement of the tape measure results in an actual movement of 5*(22+2)/22 = 5.45", almost half inch.

Now let's look at measuring an AOE. Let's say I've just dropped the 3" AOE on an Ironclad. This time I lean in closer to the table (12" above the table surface), and due to the height of the Ironclad I have the template 3" above the table surface. Now the math gets further exaggerated. Normally the radius of the template would be 1.5", but due to the displacements it creates an effective viewing of 1.5*12/9 = 2". So your 3" AOE has suddenly become a 4" AOE, all due to not moving the viewpoint appropriately.

Now let's look at an extreme example. Let's say I'm about to surge across the table with my Uhlans on the first turn, running a full 16". And let's say I've leaned in a bit on the table so I'm only 18" above the table surface. And due to the height of the models, I've got my tape measure 3" above the table surface. What's the net effect on the movement? Well instead of 16", the angle of viewing turns it into 16*18/15 = 19.2". That's over 3" of extra movement!

Ok I know what some of you are saying out there, and no, it really isn't that bad in practice. Lots of things help mitigate it: looking to the side rather than from straight above, laying down the tape measure closer, and actually moving your head around just to name a few things. But there are definitely times when having a bit more precision is important. Let's look at some alternatives...

What are some alternatives?
First is obviously to lay the tape measure down right on the table. This is not always possible, particularly when lots of models are jammed in. But if it's in option, it definitely helps.
In that same vein, when doing a charge, doing a combined measure of the move and reach all at once before touching the model is great. Sometimes moving the model first results in some introduced inaccuracy. If the distance is at all in question, then I declare the charge and measure both at once to make it clear whether I was in range or not. Again, not always feasible, but when possible it helps eliminate contention.
Next, try rolling the melee gauge when measuring small movements. Set the melee gauge on the table against the model's base. Then gently "roll" the gauge up on it's corner, keeping it in contact with the table. Then just slide the model forward so the base touches the gauge again. This lets you measure 1/2", 1" and 2" very accurately. I'll do this a lot when I need to maneuver a model around a bunch of other models/terrain but the total distance traveled is critical.
Ask your opponent to check the range. This is particularly common for checking ranged attack distances to targets. Just measure your end and ask them to look over the end of the tape measure to check whether it's in range or not.
Finally, know the AOE and base size matches. For example, a 50mm base is pretty close to 2" in diameter. If a 3" AOE drops on a large based model and you want to see if models nearby are in the AOE, use the 1/2" end of your melee gauge to check the distance between those models and the hit model.

When should I worry about parallax effects most?
Ok, so let's talk frankly here: All the above stuff is good to know but how often is it important to pay attention to this? In an ideal world we would have fancy gaming tables that would light up from below and show you what's in an AOE and how far a model could move, but we're a few years from that probably. And by it's very nature, moving physical models around is going to have some amount of inaccuracy. On top of that is a balance between accuracy and not bogging the game down. So what's a good practice for when to make attempts at being more precise?
I tend to bring in the more accurate methods when distances in the following two key types of situations:

Distances are not clearly obvious to my opponent (or myself). I'm particularly of this for charges since a failed charge is pretty critical.

Critical models are involved. It's one thing when an AOE lands on a bunch of tightly packed Temple Flame Guard, but another thing when Nicea is potentially clipped by an AOE.

Closing thoughts:
Well hopefully I haven't put you to sleep with all this. I think much of this was already intuitive to many players, but the other day I pointed it out to my opponent and they responded with "Oh, hey, that's a good point." So after doodling the math during a very boring meeting at work and plugging in a few sample numbers (and being shocked at the results), I figured a post on the topic wouldn't hurt.