Power tells you how strong a Chief, alliance or State is; the Furnace level tells you how far a Chief has progressed. Most bad comparisons mix the two up, or compare totals without looking at what is behind them.
Power is shortened: 345.6M is 345.6 million, 1.2B is 1.2 billion, and a change such as +12.3M this week carries its sign. Charts have a "Show as a table" option.
Furnace levels
A Chief's page shows Power and its change this week, Level (the Furnace), Kills, and Rank on the power board with their alliance rank beneath it.
Levels 1 to 30 are plain numbers, then come four half steps, 30-1 to 30-4, then the Fire Crystal levels: FC1 is level 35, then FC1-1 to FC1-4, FC2, and so on in steps of five up to FC10, level 80. The raw level is in brackets, so FC9-3 (78) is two steps short of FC10.
The Furnace has a top: an FC10 Chief stops moving while their power keeps growing, so the top of the Furnace board is mostly Chiefs who are all at FC10. Below that, higher levels open over time in each State, so a Chief at the highest level their young State allows is at the limit, not behind.
Alliances
An alliance's power is its members' total, with the change over a week and a month, member count and a daily chart. Because the total follows the members, a sharp drop in one alliance and a rise in another in the same State usually means Chiefs changed alliance. Of two alliances with similar power, the one with fewer members has stronger members. A steady rise is growth; a sudden jump is usually recruitment. When an alliance has set them, "How to join" shows the minimum Furnace level and power it asks for.
Comparing States
A State's page shows its Chiefs, alliances and total power, the change over 7 and 30 days, the strongest alliance and the one that gained most, its alliances by power and its own boards, each viewable as it stood on an earlier date.
Totals favour States with more Chiefs, and they include accounts that stopped playing long ago, so a big total is not a strong State. Compare growth as a percentage, between States of a similar age. For State vs State, compare the two or three strongest alliances on each page instead: most States have one main alliance and a close second, and those are the ones that will fight.
The rankings list the strongest Chiefs and alliances across States, and a State vs State group's page links the same rankings limited to its States. To look up one Chief, see how to find any player by name.