See the book Bowling Beyond the Basics
To summarize the math, the power in which the ball hits the pins with is
mass X velocity square
Therefore, as long as the lighter ball is thrown with a slight increase in speed, there is no loss of power. In fact, looking at the physics, this is a huge misconception and it is really best to use the lightest ball you can control, not the heaviest you can manage.
If we plug these numbers into my game - as I have personally thrown different weights once I switched to no-thumb style
I'm just using monitor speed here, but just to make point with the math...
At 14 pounds, my speed is 12 mph
14 lbs X (12 mph) squared = 2016
At 12 pounds my speed is 15 mph
12 lbs X (14 mph) squared = 2352
Therefore I have a little more than 10% increase in hitting power by dropping 2 pounds.
lighter balls deflect more, a fraction of inch for each drop in weight - not significant
On the plus side, lighter balls will transfer more of their energy to the pins.
My story is that I switched to no-thumb style a year and half ago. I used to thrown 15 with thumb. No thumb, I don't have big hands and it puts a lot of pressure on my hands. After getting myself up to 14, I dropped to 12, b/c my hand was hurting.
I thought I needed to use at least 14, but after sitting out months with hand injury, I really didn't have much choice.
And then I read Bowling Beyond Basics totally changed how I think and no longer feel I need heavier ball. I now consider using a lighter ball to be a secret advantage.
I did get a 12 pound cyclone to learn new style with lower weight, when I first starting no-thumb style.
For a long time I would get 5 and 10 pins with it. I just assumed it was the weight. In truth, I was over throwing it through the oil.
If the 13 pound ball doesn't strike, I suggest seeing if you can make an adjustment where the ball is hitting pocket in roll phase.
Also, a lighter ball will not just be thrown faster, but usually has a higher RG, so will roll later. So may need to make an adjustment from how playing compared to heavier balls.
or look at it this way. Take the exact same ball, in 13 and 14 pounds. Same layout. Throw on same line. 14 pound ball will go slower and lower RG - strikes. 13 pound ball is faster and highter RG - 10 pin.
This doesn't mean 13 pounds doesn't hit. It means should throw it a board or 2 further outside so it has a chance to get into roll phase.
Once I stopped assuming my 12 pound cyclone won't hit, and adjusted how I use it, have no problem striking with it.
For me, at a 400 rev rate and 3 degrees of axis tilt, I consider the higher RG cores an advantage, for the peculiarities of my game. (I realize for most people, having the lower RG cores of heavier balls is a big advantage)
I'm not saying that 12 or 13 pounds is for everyone,l but for any no-thumb or two handed bowlers out there I would consider the following advantages:
More speed
Higher RG core
The math and physics says more power