Alright. I’m pretty sure the odd increase is around 370.4%, maybe different by a couple hundreths of a percent for different marks. This isn’t proven or anything, but let me tell you why I’ve come to this conclusion:
Bulbapedia:
https://m.bulbapedia.bulbagarden.net/wiki/Mark
For the Lunchtime Mark, the base chance to get it is 1 in 50. With a 3 Title sandwich, the chances become 1 in 13.5. 50 divided by 13.5 is 3.7037, or a 370.4% increase.
For the Joyful Mark, there is a base 1 in 2800 chance to get it. With a Title Three Sandwich, the odds become 1 in 755.9. 2800 divided by 755.9 is 3.7041, or a 370.4% increase.
For the Rare Mark, there is a base 1 in 1,000 chance to get the mark. With a Title Three Sandwich, the odds become 1 in 270. 1,000 divided by 270 is 3.7037, or a 370.4% increase.
For other Marks, I’ve seen about the same 370.4% increase.