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Billington's cross-crease move requires two separate pushes. There isn't a lot of power in the pushes and instead of digging his foot in, he's lightening up as much as he can. It's not just the shortness of the pushes that give this away, but also the movement of the arms. Four times in this brief move the arms wing out.
You might do this on any move for temporary weight removal on the feet--it gives the pushing leg a brief window in which to move--but four times is a lot. He has the power to move but he can't use it. It literally gets thrown away by the arm waving which removes weight (= power) in the pushing leg so it can re-cock.
Here, Hextall gets a good, strong push across the crease. What's interesting is what happens to his center of gravity. It goes way up. His push is great but instead of sending it all to his right, it has a lot of 'up' in it. What happens is if the pushing foot (in this case, the left) has rolled to 45°, you can't get any more reach if you push left but, you can get a little extra if you keep the boot locked at that angle and push 'up' and right. That's what Hextall does here. It's a quick move but the shooter gets him down low. Of course the arms go way up as well. This lightens up the pushing leg and the weight transfers to the lead leg but it still represents wasted power.

If it helps to clarify the arm waving, imagine tiptoeing or walking on thin ice. We do it for the same reasons. Also try to imagine fast tiptoeing or powerful walking on thin ice. Waving the arms makes for a gentler transfer of the weight but it slows you down.

In the clip above, I easily go from one edge of the crease to the other. It's a fast move and you can tell by how hard the stops are that I could have gone farther. The arms stay tight and there's no head bobbing so the center of gravity stays low and the move is controlled. Every bit of push goes into the move. The pushing leg has no weight left in it when it's done, it's all been transferred to the lead leg. The stop is clean and sharp and the foot doesn't have to reposition at all to power a strong reverse move.

How Overdrive Increases Main Blade Power.

On a push in the direction of the arrow, you get more power at angle B than angle A. The lower the angle the better and, like sprinters blocks, the best angle for power transfer is about 45 degrees. At this angle, the blade also cuts into the ice better. The problem is that 45 degrees is where goalie skates slip out so. You have to raise the pushing angle slightly to avoid a blowout. Raising the angle reduces the power transfer and the cutting ability of the main blade. With Overdrive, you can safely angle the boot to 45 degrees for optimum main blade power.

Drawing of skate

How You Stop Harder With Overdrive.

On a two-footed stop in the direction of the arrow, the lead foot (left) can safely go down to a lower (better) cutting angle. It can dig in and take all of your pressure and the foot won't slip. The left Overdrive scrapes but the right one cuts in to add stability to the rear foot and sharpen the stop.