Innovation speed is affected by 3 primary inputs. These are under various levels of player control, and are listed below in order from least in your control to most:
Factor 1: Exposure
A culture’s exposure can be found by navigating to the innovations tab and finding the one with the blue border. These are completely out of any character’s control, but it is helpful to understand what it means. This mechanic chooses one innovation at a time and greatly speeds up its acquisition. It determines which innovation by choosing a random innovation that another culture has already gotten, with the condition that either: In the example above, the gavelkind innovation is being sped up due to the Occitan culture having it. This is using the shared religion requirement, as no Occitan culture counties border any Croatian.
Factor 2: County Development
If you aren’t the current cultural head, the only real option you have to affect innovation speed is development. The average development of all the provinces of a certain culture affects the speed, so focusing on developing your provinces of your own culture will speed up innovations. The below images compare my Croatian character’s innovation gain due to average development to that of the Bosnians. At the first starting date, the average development of Croatian provinces is just over 4.47. Bosnian average is at a flat 5. In this example, it should be noted that there are over 3 times as many Croatian provinces as Bosnian (17 vs 5). As such, if I were of the Bosnian culture, I’d have an easier time raising the total average development of all Bosnian provinces. So, without being the cultural head, your actual effect on innovation speed is extremely limited. Either way, there are ways to increase the speed at which you develop provinces. The main method is using buildings. To do this, simply look for buildings that increase development growth and construct them.
Factor 3: Cultural Head
If your goal is to speed up innovation growth, then your focus should be on becoming your culture’s head. This requires you to be the following: Under these conditions, even if you are a vassal to a liege that is the same culture as you, you may still find yourself the occasional cultural head. If your liege dies and their heir is not of age, you (assuming condition 1 and 3 are met) will become the cultural head. This naturally puts a time limit on it, similar to a regency. However, the following tips will still speed up your innovation gain, even in this restricted timeframe. As the cultural head, you can choose a cultural fascination. At its base value, a fascination speeds up innovation gain half of that which an exposure does. However, the amount that a fascination speeds up innovation is affected by your character’s learning stat, as seen below. Each learning skill point your character has increases innovation gain by 1% at base value. With this in mind, it is best as the cultural head to boost your character’s learning stat as high as it can go. The best way to do this would be to go down the scholar route in the learning lifestyle tree. The traits marked above are what will help boost innovation gain. Even if your character starts with a low learning stat, filling out this single tree can easily put them past 20, sometimes even 30. A pious character with a good starting learning stat can get well beyond 50. In these images above, I show that simply increasing my character’s learning by 3 (from a bad 7 to a just okay 10) decreases the time it’ll take to get the barracks innovation by 5 years. Those 5 years were gained with the simple act of taking the scholarship focus. By filling out the scholar tree like I suggested, you will find yourself blowing past your rival cultures in innovations.