Bank statements for visitor visa sponsor thing - regarding overdrafts?

[joebloggs]

From the information you have divulged I wouldn't see any problems.

but they are a lottery, just don't expect one, but it would be a nice surprise if you get one

[Terpe]

but they are a lottery, just don't expect one, but it would be a nice surprise if you get one

Yes, it can be seen as a 'lottery'. Mainly due to the fact that the ECO is not following a strict protocol, the decision is totally discretionary depending on what the individual ECO believes about the individual application (rightly or wrongly).
Although there is no appeal route against any refusal, the cost is very low