Anchoring an element to the browser's vertical scrollbar The problem

I'm trying to position a chosen element so that it's always horizontally aligned against the right-hand side of the page, and vertically aligned with the center of the web browser's vertical inner scrollbar, i.e. the part of the scrollbar that moves as you scroll up and down the page. The &quot;handlebar&quot;, if you will.
I've been tweaking this code for so long that it's starting to do my head in, so would like a sanity check, i.e. am I going about this the right way?
The key part of this function is the line beginning offset = scroll_position ...
The code
barFollower = function (e) {
  var target = $(e.data.target),
    scrollbar_button_height = 20,
    window_height = $(window).height(),
    window_height_adj = window_height - (scrollbar_button_height * 2),
    scroll_position = $(window).scrollTop(),
    body_height = $('body').height(),

  offset = scroll_position // The top of window
    + ((scroll_position / body_height) * window_height_adj) // The position of the top of scrollbar
    + (((window_height_adj / body_height) * window_height_adj) / 2) // Half the height of the scrollbar
    + scrollbar_button_height // The scrollbar button height (depends on browser chrome, unfortunately) - see notes below
    - element_offset; // offset for chosen 'position' based on element height - see notes below

  /* Some catches for when element height might mean it would get positioned outside the window */
  if (body_height &lt; window_height) { // If there's no scrollbar.
    offset = (window_height / 2) + (target.height() / 2); // Position halfway down the window
  } else if (offset &lt; scroll_position) { // Top bounds
    offset = scroll_position; // Fix it to the top of the window
  } else if (offset &gt; scroll_position + window_height - target.height()) { // Bottom bounds
    offset = scroll_position + window_height - target.height(); // Fix it to the bottom of the window
  }
  target.css('top', offset);
};

Notes
Triggering
This function is triggered once on page load, and subsequently on every window scroll event.
Scrollbar button size
The tricky part here is that I can't find a way to determine the height of the scrollbar 'up' and 'down' buttons, so I have made an assumption (20px), although this will potentially vary from browser to browser, and depends the browser chrome.
If anyone knows a way to accurately determine scrollbar button sizes, please let me know.
The element_offset variable
The element_offset is set outside this function, and can have one of three values to offset the element so that either the top, middle, or bottom of the element align with the middle of the vertical scrollbar. How it is set is not relevant at this point, so I've left it out to keep things simple.
What is wrong with:

&lt;body&gt;
    ...
    &lt;div id="myfloatingElement"&gt;This is the element&lt;/div&gt;
&lt;/body&gt;


css:

#myfloatingElement
{
    position: fixed;
    right: 0;
    top: 50%;
}