Standard or Quarter Mark This is the standard marking position where you are at a 45 degree angle on the thrower taking away the upfield backhand.
You are stopping them from throwing to a receiver up field on the break side. So this throw would be a break as it is your responsibility to not let that throw off.
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This throw is ok to allow
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This throw is also ok, you are only trying to stop the up field break throw (in this case a righty backhand)
No Around or Half mark This mark you are lined up parallel to the sideline to try and stop the thrower from breaking you with an around throw (in this case an around righty backhand) This is a mark you shift into typically with the disc trapped on a sideline since upfield throws have a more narrow passing lane and it makes the dump so much harder.
So this throw should not be allowed
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This throw is ok
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This throw is ok as it is what we call an Inside throw and is a very high level of difficulty throw.
Straight up or Flat mark This mark you are perpendicular to the sideline and parallel to the endzone. The point is to not let the thrower huck it easily up the field.
So this huck is not allowed
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If they are going to huck it, make them throw the frisbee around you and have to curve it back in. This is a harder throw for most players and will make the disc spend more time in the air thus allowing the defender more time to catch up