According to these numbers, one should encounter a QoT in almost every 2nd 6player game (to be exact, the probability is 43.5%).
How are you calculating this? Your question is a little flawed IMO.
Those stats show, that demigods make 61006 total appearances in game.
Of those 61006 appearances, only 4285 are from QoT, a lot less than 10%. How did you work out that you should see a QoT 43.5% of the time?
There are no exact figures of exactly how many games there are, how many are 3v3, how many have DGs double, tripled, quadrupled up. So you cannot adjust for those factors. If you are making some quasistatistical adjustment by dividing 61006 by 6 (players in game), then creating a percentage from that for the total of 4285 for QoT, then your math is very flawed! As the QOT figure would also need to be adjusted.
By that measure then there is an almost 100% chance that UB and Regulus will be in a match. I certainly have played matches without them.
The probability is fairly straightforward that a slot will be filled on average by the following DG :
<! BODY,DIV,TABLE,THEAD,TBODY,TFOOT,TR,TH,TD,P { fontfamily:"Arial"; fontsize:xsmall } >
Erebus 
7508 
12.31 
Oak 
7437 
12.19 
QoT 
4285 
7.02 
Regulus 
9776 
16.02 
Rook 
7049 
11.55 
Sedna 
7175 
11.76 
TB 
7822 
12.82 
UB 
9954 
16.32 

61006 

So each slot will have the probability to see a QoT take it 7% of the time. To actually calculate what that means for a 6 slot game is far beyond what I can be bothered to work out. However, you cannot simply say it is 6 x 7%. The probability is that you have 6 chances at a 7% outcome, likely meaning that you will not see it as often.
I have worked it out now :
You have a roughly 1 in 15 chance of seeing QoT in a slot. So with 6 slots you end with a 3861089 in 11390625 chance of seeing the QoT. This roughly makes a chance of 34% of seeing QoT.
However, this does not account that there is a trend that more recently less players have been using QoT, due to an established player base and she is deemed weaker so less players use her.