There are a few formulas at play. One calculates your costs for first encounter of Spire and another calculates costs for first encounter of tourney. This number is different for everyone depending on techs, wonders, plots, etc. Then the Spire and tourney each have their own progression table based off the first encounter numbers. As you go deeper into tourney or higher in Spire, the multiplier increases, with the difference between your stack size and enemy’s stack size growing wider in enemy’s favor. The progression multiplier is the SAME FOR EVERYONE, regardless of techs, wonders, plots, etc. The “difficulty” is up to individual players as to how deep in tourney or high on Spire they want to go since none of it is mandatory. Eventually though, the increase in cost of troops from unlocked techs outgrows the increase in troop production from military building upgrades in later chapters. Therefore, it becomes a matter of a player’s ability to replenish greater number of dead troops each week.
They are related, but Spire has an end whereas tourney is more open-ended. Players can do an insane amount of provinces if they have the stomach for it. The higher chapter players going really deep in tourneys feel the hurt the most bc they are extrapolating the effects of the progression formula the furthest. Hence, formula discussions tend to veer to tourney.
Yes, all of this. However, there is so much misunderstanding that people blame the formula for everything when sometimes, the problem is between the screen and the chair. For example, ALL players have a numbers advantage for the first 8 provinces of tourney, particularly the first 5. You can practically win the first 5 provinces blindfolded picking any combo of troops autofighting. Therefore, it’s not difficult to hit 1k in tourney just milking the first 5 provinces for several stars. If you can’t win even when you’re greatly outnumbering the enemy, the problem ain’t the formula. For the formula to outpace production of troops required for fighting just 5 provinces, you’d prob need to be in like chapter 60. Yet, there are people crying foul saying the formula is making things too difficult when they’re only doing 500pts or so. That’s rubbish. There are a lot of scenarios where people freak out in hysterics over the formula when they fall under “the effects won’t be felt”.