I can't help the feeling research happens way too quickly in the midgame and switching from uncommons to rares, then very rares happens faster than it should.
This might just be a feeling - afterall the costs are pretty high - but I'll attempt to do some calculations.
One thing is certain - it's not the result of excessive research availability. Aside from specialized wizards, a significant part of research tends to come from the power base.
So first, let's look at some goals. Since power distribution is done between skill, mana and power, but mana is used to fuel skill, I believe setting the goals in casting skill for each spell tier is the best.
Commons.
I believe these are the primary thing players should aim to use while their skill is in the 0-40 range.
Players start at 20 Skill so they have 400 SP and need to reach 1600 SP for 40 skill.
So it costs 1200 SP to build up the skill needed to consider seriously advancing into uncommons.
At this phase of the game, buildings generally don't yet produce a lot of RP, it's a safe assumption to consider 10/turn. Power income is likely around 35/turn (20 at start, 50 at the end of the phase from a node or two, maybe some wizard's guild or population). Treasure is likely around 1200 mana total.
So the overall income is turns*45+1200.
I believe it's realistic that we want this phase to last roughly 6-7 years, 80 turns.
So we have 80*45+1200=4800 power to use up.
Out of this, 1200 goes for skill.
In 80 turns, an average of 30 skill means 2400 cost for overland spells. That buys 3 full stacks of the expensive creatures, or 6 from the cheaper ones if nothing else is cast. Enough to ensure the spells will see a relevant amount of use.
Combat spending is a different question, as it varies a lot per game. I'm going to go by the assumption that if any major combat spending happens, it conquers enough cities or nodes from enemy players, or finds enough treasure to at least cover its own cost, in other words, I'll assume combat spells pay for themselves in this phase. (Battles are still not frequent and skill is low.)
That leaves 1200 total power for research for this phase. Having 10 common spells to research (5 in your realm and 5 arcane), each should cost 1200 RP on average. That about matches the current settings.
Uncommons.
These should generally be the thing to use while skill is in the 40-100 range. That costs 10000-1600=8400 SP. This puts the average skill for the phase at 70.
In this phase, having a power income of 125/turn on average is realistic - we start from 50 and will likely reach 200 by the end of the phase.
Players will likely also produce around 40 RP from buildings (8 universities, or a few Sage's Guilds), so overall income is 165/turn. Treasure is less abundant in this phase as easy targets are already cracked, but the hard ones yield more. An expectation of 3000 MP (two strong nodes or four medium ones) is reasonable. *(Note that treasure amounts assume you spend some of it in gold and don't convert it all to mana, or find things that cannot be converted.)
Assuming we want this phase to be long enough to summon at least 5 full stacks of an uncommon creature (if nothing else is cast), and they cost 130 on average, we need 5850 skill used. At 70/turn, this is ~80 turns again.
In 80 turns, we produce 165*80+3000=16200 total resources.
Out of that, 5850 is used on overland spellcasting.
We also need 8400 SP, totalling 14250, leaving only 1950 for research. Assuming 12 uncommons to get, this yields a cost of 165 RP/spell.
This explains why research on uncommons goes so slowly in most games. In this phase, players don't own a large amount of highly productive cities or nodes, so power production is not very high while demand for it and casting skill is massive. However players are likely to only research half their uncommons before switching to get a few rares. Assuming they "only" want 6 of the uncommons, we get a cost of 325 which is still below current.
But the real problem I see is the massive discrepancy in skill and research costs. For giving up 4 casting skill, (4% of your assumed total skill at end of the phase) you can have the 400 RP to get another uncommon spell.
At this point I'm not sure how to proceed with the calculation.
We could assume we want a certain ratio of SP to RP, for example that each new spell costs as much as gaining 5% casting skill. In this case players will likely need to invest heavily into power and research buildings to be able to proceed to rares, and the uncommon phase gets longer. Or we could assume we want an RP cost that's affordable from the expected amount of resources in the expected amount of turns in which case research will be cheaper it becomes more profitable to skip uncommons and go straight for doing rares with a lot casting skill, hoping the stronger spells make up for it. The two lead to entirely different results but maybe the former approach is better? That weird feeling that research is too fast might come not from the excessive availability of it, but the relatively low cost compared to SP and MP spendings?
(PS : I haven't forgot Amplifying Towers but I believe it's more reasonable to assume they start becoming relevant in the "rares" phase at 100+ skill. Before then producing power is more profitable.)
This might just be a feeling - afterall the costs are pretty high - but I'll attempt to do some calculations.
One thing is certain - it's not the result of excessive research availability. Aside from specialized wizards, a significant part of research tends to come from the power base.
So first, let's look at some goals. Since power distribution is done between skill, mana and power, but mana is used to fuel skill, I believe setting the goals in casting skill for each spell tier is the best.
Commons.
I believe these are the primary thing players should aim to use while their skill is in the 0-40 range.
Players start at 20 Skill so they have 400 SP and need to reach 1600 SP for 40 skill.
So it costs 1200 SP to build up the skill needed to consider seriously advancing into uncommons.
At this phase of the game, buildings generally don't yet produce a lot of RP, it's a safe assumption to consider 10/turn. Power income is likely around 35/turn (20 at start, 50 at the end of the phase from a node or two, maybe some wizard's guild or population). Treasure is likely around 1200 mana total.
So the overall income is turns*45+1200.
I believe it's realistic that we want this phase to last roughly 6-7 years, 80 turns.
So we have 80*45+1200=4800 power to use up.
Out of this, 1200 goes for skill.
In 80 turns, an average of 30 skill means 2400 cost for overland spells. That buys 3 full stacks of the expensive creatures, or 6 from the cheaper ones if nothing else is cast. Enough to ensure the spells will see a relevant amount of use.
Combat spending is a different question, as it varies a lot per game. I'm going to go by the assumption that if any major combat spending happens, it conquers enough cities or nodes from enemy players, or finds enough treasure to at least cover its own cost, in other words, I'll assume combat spells pay for themselves in this phase. (Battles are still not frequent and skill is low.)
That leaves 1200 total power for research for this phase. Having 10 common spells to research (5 in your realm and 5 arcane), each should cost 1200 RP on average. That about matches the current settings.
Uncommons.
These should generally be the thing to use while skill is in the 40-100 range. That costs 10000-1600=8400 SP. This puts the average skill for the phase at 70.
In this phase, having a power income of 125/turn on average is realistic - we start from 50 and will likely reach 200 by the end of the phase.
Players will likely also produce around 40 RP from buildings (8 universities, or a few Sage's Guilds), so overall income is 165/turn. Treasure is less abundant in this phase as easy targets are already cracked, but the hard ones yield more. An expectation of 3000 MP (two strong nodes or four medium ones) is reasonable. *(Note that treasure amounts assume you spend some of it in gold and don't convert it all to mana, or find things that cannot be converted.)
Assuming we want this phase to be long enough to summon at least 5 full stacks of an uncommon creature (if nothing else is cast), and they cost 130 on average, we need 5850 skill used. At 70/turn, this is ~80 turns again.
In 80 turns, we produce 165*80+3000=16200 total resources.
Out of that, 5850 is used on overland spellcasting.
We also need 8400 SP, totalling 14250, leaving only 1950 for research. Assuming 12 uncommons to get, this yields a cost of 165 RP/spell.
This explains why research on uncommons goes so slowly in most games. In this phase, players don't own a large amount of highly productive cities or nodes, so power production is not very high while demand for it and casting skill is massive. However players are likely to only research half their uncommons before switching to get a few rares. Assuming they "only" want 6 of the uncommons, we get a cost of 325 which is still below current.
But the real problem I see is the massive discrepancy in skill and research costs. For giving up 4 casting skill, (4% of your assumed total skill at end of the phase) you can have the 400 RP to get another uncommon spell.
At this point I'm not sure how to proceed with the calculation.
We could assume we want a certain ratio of SP to RP, for example that each new spell costs as much as gaining 5% casting skill. In this case players will likely need to invest heavily into power and research buildings to be able to proceed to rares, and the uncommon phase gets longer. Or we could assume we want an RP cost that's affordable from the expected amount of resources in the expected amount of turns in which case research will be cheaper it becomes more profitable to skip uncommons and go straight for doing rares with a lot casting skill, hoping the stronger spells make up for it. The two lead to entirely different results but maybe the former approach is better? That weird feeling that research is too fast might come not from the excessive availability of it, but the relatively low cost compared to SP and MP spendings?
(PS : I haven't forgot Amplifying Towers but I believe it's more reasonable to assume they start becoming relevant in the "rares" phase at 100+ skill. Before then producing power is more profitable.)
