In here i will go more in depth on the maths of why Innovativeness is as strong as it is. First of all, let’s note a few facts:

• I will consider here that you take Innovative ideas first, e.g. on tech 5. This will of course not always be the case, but the maths are easy to adapt to tech 7 or 10. I do not recommend taking Innovative ideas later than

that however.

• I will go from the assumption that you had to spawn renaissance and thus will get Admin tech 5 around the time the tech leaders would be at tech 6.

• I will also take the assumption that you will never tech Admin or Dip tech ahead of time until past tech 10.

• I will also assume that you will miss the Innovativeness from technology twice before tech 10, as this is what I have noted to be a solid average for my games.

• I will take that you need to tech roughly 2-3 years ahead of time on average to gain Innovativeness. Tech 4 is normally a guaranteed Innovativeness gain on Mil with 0% cost, so I will count this for techs 5 and beyond.

• I will assume that over the course of the first 150 years you will always take Innovativeness gain from events, unless it causes national unrest. Since an Innovativeness event is guaranteed every 2 years, we can easily calculate this average. Per 2 years, 9 would gain you 1 Innovativeness, 1 event would gain you 3 Innovativeness, and one event has no effect, counting only events that can trigger before printing press. This puts the average bi-yearly gain at (1 * 0+9 1+1 * 3)=11 = 1.1 Innovativeness, or (1* 0+9 1.5+1 * 4.5)=11 = 1.63 after getting the second Innovative idea. This value is divided then by 11, due to the Innovativeness bi-yearly pulse being shared by other event categories, of which there are 10-12 depending on your nation. So the gain is 0.1 resp. 0.15 bi-yearly, or 0.05 resp. 0.075

yearly. While this is not entirely accurate due to trigger conditions, it gives a solid estimate. Note that the event with 3 Innovativeness is among the most likely to trigger, and the one that would give nothing is among the least likely.

• I will assume that you get full Innovativeness from the Innovative group itself, and for all subsequent groups I will assume that you will miss out on 2, then 4, then 6 ideas, which feels like a reasonable estimate from my private games.

• Other Innovative gains are:

– +1= + 1.5 for being first to get an idea

– +2= + 3 for being first to get a tech

– +0.06=0.09 yearly for being ahead (Note that I will assume that you manage to keep ahead on tech since you’re teching for Innovativeness. Plus in one of my unluckiest runs where I managed to never get even a 3 Mil ruler by 1600, i managed to stay ahead on Mil tech at all times except when filling ideas, in which case I’d be ahead on Dip or Admin anyways).

• Cf section 4 for this point, but I will assume you optimise your gameplay around Innovativeness. E.g. this means using vassals to offset the early Admin spending from taking the idea, not spending Mil excessively unless it is to tech up with Innovativeness bonus, and other things I will get into later. This basically means that I assume you get the Innovativeness from techs 4-10 except 2, let’s assume tech 5 and 6, then manage to get the Innovativeness from both Dip and/or Mil starting tech 10 on every tech level. I will also assume you’re waiting for tech 10 to get a Mil group.

This concludes the notes, now let’s get into the nitty-gritty of how much you actually have to spend to stay ahead on tech.

Starting at tech 4: It takes roughly until 1450 to tech up, so you will not have any Innovativeness before that normally. This means in 1450, we start with 2 Innovativeness + 0.06 from being ahead that year until 1453 +0.05 * 10 = 0.5 from events, so: 2 + 0.06 4 + 0.05 * 10 = 2.74

Onto tech 5: Since I assumed you would be spawning renaissance and missing the Innovativeness from Mil tech 5, you will tech this one as soon as you can. This usually ends up being around 1456 assuming a 3 Mil ruler, Mil focus, no advisor and no stockpiled Mil after taking tech 4 in 1450. This means you will lose 3 years of Innovativeness, or 1.08, leaving you at 2.74+0.053-1.08 = 1.81 Innovativeness in 1456. This also results in 6% tech cost, or 36 Mil spent due to not having renaissance.

As assumed I suppose you reach tech 5 Admin and Dip as soon as you get Mil tech 6, so Innovative ideas are not accounted for yet. As said before, assuming you get Mil tech 6 3 years early, it’ll be at a cost of 180 mil, minus 0.2% of the tech, or 1 Mil, for a total of now 2 Innovativeness. The Innovativeness discount will now be counted in implicitly. So in the year 1463, we have reached 1.81 + 0.05 * 7 + 0.06 * 7 + 2 = 4.58 Innovativeness.

Now, we have a few years to go before getting the Innovativeness bonus. Assuming you are a duchy, your focus will still be on Mil at this point, until 69, so let’s assume for simplicity that we get the Innovativeness bonus in 69. This comes out to another 6 years of passive gain + 2 Innovativeness from the 2 Innovative ideas, e.g. 4.58 + 0.05 * 6 + 0.06 * 6 + 2 = 7.24.

Now as for the next tech, we will be missing out on the Innovativeness gain despite having Innovative ideas, for the sake of the example, even though this should never actually happen in any game. So Mil tech 7 and Dip tech 7 are reached on time without any costs, resulting in the usual passive gain + completing Innovative ideas for 1.5 * 5 = 7.5 Innovativeness. This comes out to 7.24 + 0.075 * 10 + 0.09 * 10 + 7.5 = 16.39 Innovativeness in 1479.

Due to the 14% tech cost from completing Innovative ideas and the 10% tech cost from Innovative, it is safe to assume that we tech Admin to 7 on time. This means that, teching tech 8 ahead 3 years ahead on mil, then 3 years later getting Admin tech 7 is entirely realistic. This comes out to 16.39+0.075 * 10+ 0.09 10 + 3 = 21.04 Innovativeness, with a 1.8% discount on the overspending on mil, e.g. 171 Mil spent again, or 385 total by 1489.

At this point we will be completing some Dip group for 5 * 1.5 = 7.5 Innovativeness. With the right focus this can usually be done by the time we tech Mil tech 9 ahead (with a level 2 advisor and 4 Dip skill ruler, we generate enough to complete the idea in 13 years + given the stockpile from not teching Dip ahead of time), e.g. in 1502. So in 1502, our Innovativeness comes out to 21.04+7.5+13 * 0.075+13 * 0.09+3 = 33.685 Innovativeness. At this point, we tech Mil ahead for 156 additional cost, totalling for 541 Mil spent in 50 years. Not too bad so far!

By tech 10 you should be able to tech Admin, Dip AND Mil ahead of time, but for the sake of simplicity, let’s assume you’re conquering too much to tech

Admin ahead on time, which is a safe assumption to make. So on tech 10, we stand at 33.685+13 * 0.075+13 * 0.09+6 = 41.83 Innovativeness in 1515. The cost comes out to approximately 156 Mil and Dip, for a total of 697 Mil and 156 Dip spent so far.

At this point, since you teched Mil ahead of time it’ll take two techs to get back ahead, so tech 11 is done on Dip alone, and tech 12 on both Dip and mil. This comes out to, in 1554, 41.83 + 49 * 0.075 + 49 * 0.09 + 4.5 + 9 = 63.415 Innovativeness at a cost of an added approximate 295 Dip and 145 mil, resulting in a total of 842 Mil and 451 Dip. From this point onward it is safe to assume that you will be getting Innovativeness from Admin tech as well, resulting in 24 Innovativeness for techs 13-16 +1.5 Innovativeness from taking another idea group, and missing out on 3 Innovativeness from that tech. The total by 1600 comes out to 63.415 + 24 + 1.5 + 46 * 0.075 + 46 * 0.09 = 96.505 Innovativeness. At this point you can just let the ticking Innovativeness from being ahead do the rest of the work. The total cost then comes out to roughly 1250 mil, 580 Dip and 130 Admin to get 100 Innovativeness. Note that in usual games, you will often be able to generate surprisingly more Innovativeness for the same costs as I described above

Now comes the question, is this worth it?



On average your Innovativeness will be 50 for the first 150 years of the game, then 100 for the entire rest of it. Assuming a constant 4/4/4 king, which is safe to assume due to disinheriting, events and republics, assuming a level 2 advisor for the first 150 years and a level 5 for the rest (you can afford it, you should have Innovative Influence at this point, plus enough blobbing/tall play to be rich), assuming maximum milking of estates (150 monarch points / 20 years) you will generate a total of (3+4+2)12150 = 16200+7150 = 17250 monarch points of each type and save 5% of it in the first 150 years. This comes out to 862 of every single monarch point type. This is without counting the fact that Innovativeness is an additive bonus, saving you more than the actual % it indicates. E.g. with

20% tech cost from legalism + Innovative ideas the 5% difference actually comes out to make 5%/80% = 6.25%, so you actually save quite a lot more than what is said here. Also this does not account for events. In the latter 220 years of the game, you will end up saving (3 + 4 + 5) 12 220 = 31680 + 11 150 = 33330 monarch points, of which you save a whopping 3333. Of every single type. Without mentioning that what I said earlier about Innovativeness stacking with other modifiers being a bigger and bigger deal as the game goes on, and without mentioning that in certain cases Innovativeness can actually reduce costs to 0 flat. One such edge case is Mughals+Administrative ideas+Indian Sultanate = 80%CCR+claim = 90%CCR+Innovativeness = 100%CCR. And Innovativeness stacks above the caps.



On this note, the total cost was also offset by our 10% tech cost, picked up on tech 5-6, resulting in a saving of 10 600 10% = 600 monarch points of each type saved by 1600. The key thing to note here is that this is ALL monarch point types, from a single idea of Innovative ideas.

Second question, how does this compare to an Administrative opener?

Assuming you have the monarch point described above and tech Admin exactly on time every time, by 1600 you will have generated the aforementioned 17250 monarch points, among which 12 * 600 = 7200 will be sunk into tech and 2800 into ideas. Past roughly tech 7 you will also save 10% Admin cost, coming out to 8 * 60 = 480 saved, resulting in a total of 7730 left over. Assuming you have to stab up twice per monarch life time and assuming your monarchs live from 15-65, e.g. for 50 years (which is optimistic) you will spend roughly 600 Admin on stab. Adding to this having to develop renaissance and printing press, which will cost roughly 800 Admin each assuming you develop sparingly with mil, you’ll be left with 5530 Admin for coring, of which you save 25%. This results in saving 1383 Admin +480 from tech, resulting in a total of 1863. In essence, Administrative ideas save you roughly 400 more Admin points, without saving Dip or Mil and without any of the other added benefits of Innovative ideas.