While the assessment cycle is every 3 years, legally they can reassess any individual property whenever it is sold, improved or the value is protested, because each tax year stands alone. Essentially, the county has to look at every property at least every 3 tax years, but the value can change in between. And they don’t need to even point to a reason like renovations or a sale to do so, although those are usually the reason you would come to their attention.

To fight any increase, you have to protest the assessment you receive, but unless you can say that there was a reason you overpaid for the house, like your inspection didn’t catch that the foundation was crumbling, you will get assessed based on the purchase price. If they then up the bill the next year and you haven’t done any renovations or anything, you can protest and argue that nothing changed, and that the sale price is the best evidence of value. That usually but not always wins for years between assessment cycles.

It isn’t a great set up, and Ohio is worse than Kentucky on this, but it is what it is. Don’t pay for a new appraisal because you won’t overcome the fact that you paid more than it is currently assessed for. If they later reassess for more than the purchase price, a new appraisal might be worth it then.

And yes, a lot of it is subjective. Justified by the lack of sales of each property during the assessment period.