The values do not match the array descriptors at all. If you have to know exactly how much space is being taken up by an annotation, use the following:
<?php
$text = "Algbqdj";
$im = new Imagick ();
$draw = new ImagickDraw ();
$draw->setStrokeColor ("none");
$draw->setFont ("Arial");
$draw->setFontSize (96);
$draw->setTextAlignment (Imagick::ALIGN_LEFT);
$metrics = $im->queryFontMetrics ($draw, $text);
$baseline = $metrics['boundingBox']['y2'];
$textwidth = $metrics['textWidth'] + 2 * $metrics['boundingBox']['x1'];
$textheight = $metrics['textHeight'] + $metrics['descender'];
$draw->annotation (0, $baseline, $text);
$im->newImage ($textwidth, $textheight, "white");
$im->drawImage ($draw);
$draw->clear ();
$im->writeImage ("test.png");
$im->clear ();
?>
The file test.png should now contain pretty much the complete text with no borders. This may not work for very unusual fonts, but will work OK for Times New Roman and Arial.