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At zone 25 you start getting an upgrade called Gymystic. You will get one:
- every 5 levels starting with zone 25 ending with zone 55
- every 25 levels starting from zone 75 ending with zone 150
The first upgrade makes each gym you have gives a compounding 5% more block (retroactive) to every gym. Subsequent upgrades gives an additional 1% more block. When fully upgraded (11 in total), each gym you have gives a compounding 15% more block to every gym.
What this means is that increasing the number of Gyms not only adds a certain amount of Block, it also increases the Block added by all the Gyms.
Comparing with Shield, buying which only adds Block, leads to the conclusion that buying Gyms is a much more cost-effective method in the late game. This is why most players avoid purchasing the Shieldblock upgrade after their first few runs.
The formula for getting the amount of Block is y = 6 * (( 1.04 + 0.01 * n) ^ ( k )), where n is Gymystic level, k is number of Gyms and y is Block per Gym. ( this formula only works after you have researched Gymystic )
Each Gymystic upgrade costs 1B wood and 5M science, making it fairly difficult to purchase the first upgrade, but trivially easy to afford every other one.