I think I had that roughly right, considering that a TX can be broadcasted durring the 10 minutes it takes to find a block (on average) and still end up in the block.
You'd think so, wouldn't you? And yet, that's not how it works.
If you start timing exactly 10 minutes after the last block was solved, the average amount of time until the next block is solved will still be 10 minutes. If you start timing exactly 1 hour after the last block was solved, the average amount of time until the next block is solved will still be 10 minutes.
Poisson distributed, yes. Like the lifespan of lightbulbs.
If you start timing exactly 5 minutes after the last block was solved, the average amount of time until the next block is solved will still be 10 minutes. Assuming the current mining difficulty is reasonable accurate, the average duration from any moment in time until the next solved block is broadcast is always 10 minutes.
It's not 10 minutes on average for a confirmation. It's 10 minutes on average until the next block. This only means 10 minutes for the confirmation if your transaction happens to be included in the next block.
That being said, if difficulty is rising at every difficulty adjustment it means that there is additional hash power being added to the network and that therefore the average time between blocks is less than 10 minutes. Additionally, the fact that the average is 10 minutes doesn't mean that most transactions are anywhere near 10 minutes.
For example, if there are 100 blocks that occur in exactly 5 minutes, and 100 blocks with the same number of transactions that occur in exactly 15 minutes, your average among those 200 blocks will still be 10 minutes even though half of the transactions are confirmed in 5 minutes. Furthermore, if you have 180 blocks that occur in exactly 5 minutes, and 18 blocks that occur in exactly 60 minutes, your average among those 198 blocks will still be 10 minutes even though 91% of the blocks occur in 5 minutes.
When talking about statistical events, the words you choose can completely change what it is that you are saying.
There was an statistical calculation done on this a while back. 10 minutes (on average) for a confirmation would assume that no transaction is added to a block while miners search for it. I think thats true only if there is a significant backlog with transactions that pay a higher fee than you do.
It's not 10 minutes on average for a confirmation. It's 10 minutes on average until the next block. This only means 10 minutes for the confirmation if your transaction happens to be included in the next block.
That being said, if difficulty is rising at every difficulty adjustment it means that there is additional hash power being added to the network and that therefore the average time between blocks is less than 10 minutes. Additionally, the fact that the average is 10 minutes doesn't mean that most transactions are anywhere near 10 minutes.
For example, if there are 100 blocks that occur in exactly 5 minutes, and 100 blocks with the same number of transactions that occur in exactly 15 minutes, your average among those 200 blocks will still be 10 minutes even though half of the transactions are confirmed in 5 minutes. Furthermore, if you have 180 blocks that occur in exactly 5 minutes, and 18 blocks that occur in exactly 60 minutes, your average among those 198 blocks will still be 10 minutes even though 91% of the blocks occur in 5 minutes.
When talking about statistical events, the words you choose can completely change what it is that you are saying.
I messed up average and median...
While it might be completely correct to say that "most transactions will be confirmed within 6 minutes", it is incorrect to say that "the average time for a confirmation is less than 9 minutes".
... as the typical TX (median) will be part of the above majority even though the average TX is confirmed at a different point in time.
Thanks.
