Chef, Scroll-Keeper, Buddy's #1 Fan
This is easy to check. Use his spreadsheet. Punch in the values and it will spit out your expected squad size and then there's a cell to enter what you actually see for the encounter. It then calculates the % error. From my experience, this % error is low enough to consider it a very accurate picture of what's going on mathematically. The fact that he got the error down to that low is a wonder in itself. Admittedly, I haven't done this in awhile, but last time we played with it a few months ago was to compare the two mini cities in our FS that are designed for climbing Gold Spire. Both are chap 3 cities at the same point in tech tree. One used regular plots and the other used premium plots. One was afraid of Relics and the other tourneyed away. We were then able to determine that his costs would still be within reason of his tiny city if he maxed out relics by doing tourney too. In one case, for T1, It said 55 for her squad size and she saw 57 in the encounter. For fun, we were playing with my city too. All the numbers were super close. That is accurate enough for me!I am skeptical, thinking that minmaxgame's regression formula-fit, or back-engineering is not inclusive for all factors; my experience does not fit the numbers.
It describes both cost and difficulty! Well, more specifically, there are 2 different formulas at play (3 if you count Spire Progression), CAL and Tourney progression. CAL is like the index number, for lack of better term, of how the game determines how far your city has advanced and is influenced by all those variables we know. The Tourney Progression formula is what hashes out "difficulty" in terms of the ratio of your troops to enemy troops at each province.And as far as difficulty goes in contrast to the cost: it may well be the the minmaxgame regression describes only cost but I put forward the possibility that there is another algorithm working that increases the difficulty which - as you know - can be increased by tweaking the opposing forces slightly and by terrain even while keeping the battle ratio the same as it might have been at less costly levels.
Since your original squad size is based on CAL with a multiplier and every subsequent province is pegged to this squad number, then the whole Progression table also has a direct relationship to CAL. Hence, most of the time, people only talk about CAL, as that is the basis for everything else, but there are separate calculations for Spire and Tourney progression that determines what happens at each encounter. What the Progression table does NOT account for are the type of enemy combos, like how many dreaded Mist Walkers show up in the encounter or if you have to fight one of each class type in the same encounter, all of which affects "difficulty".
I'm not sure this can provide an accurate metric of difficulty either. Even within the same tournament, the enemy combos can differ from one encounter to the next. I don't think there is a consistent average mauling index by troop type by tournament. Sometimes I get mauled in like province 17, but will skip to the finish line unscathed in province 35 and obviously 35 is supposed to be way harder. There's too much RNG on combo, terrain, etc.The reason I say this is because I monitor the degree of a battle success by by losses according to slot and not by numbers of troops killed. For a given round for a given province level in the Tourney if I usually lose 1/2 slot of Archers and 1/2 slot of Golems, then that is going to happen, approximately, every time that type of Tourney comes around. So it does not matter if 1/2 slot is 320 Archers or 3000 Archers; I am using the 'slot metric' as a measure of success (=difficulty) and not cost.