Change X position with condition

Your expression says that if the X position is less than or equal to the layer's height, add 1 to the Y value.  It also says if the X position is greater than the height of the layer to make the X position a random value between zero and the layer width. 

The problem is if you start out with the layer lower than the layer height, you get the second half of the expression working. The layer will have a random X position but the Y position will not change. 

If you start out with the layer with a Y position value equal to or less than the layer height, the expression will add 1 to the original layer's Y position for every second the comp runs. If the comp runs 10 seconds long, the layer will move down in Y 10 pixels. The "else" part of the statement is never activated because you use the original Y position instead of the value at time for Y generated by the expression. 

Start with Y less than the layer height, and the layer will move down one pixel per second. Start with the Y value greater than the height of the layer, and the X value will be a random number between zero and the layer width and the Y value will never change. 

If you want an expression to move a layer down until it reaches the bottom of the frame, then pop it up to the top and start down again, you have to set up the Y part of your expression so that it starts animating the layer's position at the layer in-point by moving the layer above the top of the composition, then move the layer down until it leaves the bottom of the comp panel. To simplify things, the Anchor Point must be in the middle of the layer. You need to calculate half the layer height and subtract that from Zero (top Y) for the first frame, then move down a specific number of frames per second until the position equals the Composition Height + half the Layer height. Then you have to use a calculation of how long that move will take instead of the Y position to make the loop start over again. There would be no if/else statement in an expression that looped a move from the top to the bottom of the frame.

The code is never going to do anything. Aside from the random stuff not making sense, there's the simple matter of your coordinates being upside down. And in expansion to Rick's explanations you probably don't even need any expressions. this could be thrown together by parenting the Circle to a Null and animating the positions with a bunch of keyframes - Y on the Null, the rest on the circle itself.

Mylenium

Your expression says if the Y position is less than or equal to minus ten keep the X position the same and add  one to the current Y position every second but if the Y position is greater than minus 10 make the X position random and keep the Y position at minus 10. 

A position of 0, 0 would put the circle in the top left corner of a composition unless the circle is the child of. another layer. 

A random value for x is going to change every frame. If the layer is anywhere above minus ten, it will move down one frame every second, but the else condition will never cause random movement in x because it is looking at the Y position before the expression moves it down. If the original position for Y is -10 or more, then the layer will never move down, it will just randomly move in X every frame. 

I'm not sure what you want to happen. If you want the layer to jump down 10 pixels every second then you simply add 10 to the Y value every second. 

y = value[1] + 10 * Math.round(time);
[value[0], y]

If you want to also have a random X position every second, then you need to set the random seed to change every second and then establish a random number range based around the comp center.

y = value[1] + 10 * Math.round(time);
seedRandom(Math.round(time), true);
x = thisComp.width/2 + random(200);
	
[x, y]

 There is no if condition required. You could modify the expression so that you could place the layer anywhere you want to start and it would move down 10 frames every second and have a new random x position plus or minus 200 pixels from the original position by using this expression:

y = value[1] + 10 * Math.round(time);
seedRandom(Math.round(time), true);
x = value[0] + random(200);
	
[x, y]

That is how I usually write expressions that automatically move layers. Using the value of the property in an expression even allows you to animate the movement of the layer and throw in the random movement.