My experiment (while helpful in giving me experience with comfortably playing both strategies) is really hard to analyze the data because table conditions can be so different. Both strategies are profiting although the open shoving strategy has higher variance. I'm abandoning the experiment to answer this question and resorting to plain old math. I'll show my math below. Or feel free to skip to the 2 sentence summary at the bottom!
: We have to make some assumptions for this to work and I'll keep all the assumptions constant.
*UTG our range is 99,ATo,KQo (medium strength hands)
*blinds and antes = 2.8bb
*when raising, we're choosing a 2.5bb raise
*33% of the time we win the blinds when raising
*67% of the time we get 1 caller or shover
*we will Cbet the flop 100% of the time 4bb
*opponent will play straightforwardly and only call our Cbet when they hit the board or a strong draw (40%)
*The hand is considered over, or lost the times our Cbet is called
*when shoving we only get called by JJ+ and AK (3% range) which will happen 13% of the time at a full table
OK given the above parameters here is the math for raising:
win 2.8bb x0.33= +0.92bb
get 1 flatter
2.8+2.5+2.5= 7.8bb pot
Cbet 4bb and get called 40% we lose 6.5bbx0.4= -2.6bb
Cbet 4bb and win 60% we win 5.3bb x 0.6 = +3.18
0.92 +3.18 -2.6= +1.50bb for raising and Cbetting.
This figure will be the same regardless of our stack size assuming we have at least 13bb.
So now all we have to do is find the set of stack sizes and assumptions for shoving and discern which stack sizes do better than 1.50bb for shoving and which do worse than 1.5bb for shoving. Don't worry, I've done the math below:
13bb open shove from early position with 99, AT, KQ
87% you win blinds 2.8bb x 0.87 = +2.44bbs
13% you get called by JJ+, AK and have an equity of 26% vs that range.
13+2.8=15.8bb x 0.26= +4.1bb when you're called and win
13 x 0.74= -9.62bb w hen you're called and lose
-9.62 + 4.1bb= -5.52bb x 0.13= -0.72bb.
+2.44bb - 0.72 = +1.72bb for the shove as a whole.
This is higher than the expected 1.50bb for raising and Cbetting, so shoving 13bb is better.
Next up: 14bb same parameters
you'll win the 2.8 blinds 87%= +2.44bb
when called and win it's 16.8bb x 0.26= +4.37
when called and lose it's 14bb x 0.74= -10.36
-10.36 +4.37= -5.99 x 0.13= -0.78bb when called. +2.44 -0.78= +1.66bb for the shove as a whole.
This is higher than the +1.50bb expected value
from raising and Cbetting so shoving 14bb is better.
Now 15bb using same parameters:
87% you win the +2.8bb 2.8x.87=+2.44bb
when called and win its 17.8bb x 0.26= +4.63bb
when called and lose it's 15bb x 0.74 = -11.1
-11.1 +4.63= -6.47 x 0.13= -0.84bb when called
+2.44 -0.84= +1.60bb for the shove as a whole.
This is higher than the +1.50bb expected value from raising and Cbetting so open shoving 15bb is better.
Now 16bb using the same parameters:
87% you win the 2.8bb = +2.44bb
when called and win it's 18.8bbx 0.26 = +4.88bb
when called and lose it's 16bb x 0.74 = -11.84
-11.84 + 4.88 = -6.96bb x 0.13 = -0.90bb when called
+2.44bb - 0.90 = +1.54bbs for the shove as a whole.
This is slightly higher than the 1.50bb EV from raising and Cbetting so open shoving 16bb is slightly better.
And finally a 17bb stack using the same parameters
87% win 2.8bb = +2.44
when called and win it's 19.8 x 0.26 = +5.14
when called and lose it's 17 x 0.74 = -12.58
-12.58 + 5.14 = -7.44 x 0.13 = -0.96bb when called
+2.44bb - 0.96= +1.48bb from shove as a whole
This is slightly worse than the +1.50 EV from raising and Cbetting so raising is slightly better.
In case you didn't want to read all that or check my math somewhere between a 16 and 17bb stack is where the scale slightly tips from shoving to raising given these parameters. Or in other words, Duggs was exactly correct.
The changer of minds strikes again! (and WiZZiM and HooDooKoo and everyone else too!)