I've been playing around with the code for estimating fees and found a few issues with the existing code.   I think this will address several observations that the estimates returned by the existing code appear to be too high.  For instance see @cozz in Issue 4866.

Here's what I found:

1) We're trying to answer the question of what fee X you need in order to be confirmed within Y blocks.   The existing code tries to do that by calculating the median fee for each possible Y instead of gathering statistics for each possible X.  That approach is statistically incorrect.  In fact since certain X's appear so frequently, they tend to dominate the statistics at all possible Y's (a fee rate of about 40k satoshis)

2) The existing code then sorts all of the data points in all of the buckets together by fee rate and then reassigns buckets before calculating the medians for each confirmation bucket.  The sorting forces a relationship where there might not be one.  Imagine some other variable, such as first 2 bytes of the transaction hash.  If we sorted these and then used them to give estimates, we'd see a clear but false relationship where transactions with low starting bytes in their hashes took longer to confirm.

3) Transactions which don't have all their inputs available (because they depend on other transactions in the mempool) aren't excluded from the calculations.  This skews the results.

I rewrote the code to follow a different approach.  I divided all possible fee rates up into fee rate buckets (I spaced these logarithmically).  For each transaction that was confirmed, I updated the appropriate fee rate bucket with how many blocks it took to confirm that transaction.  

The hardest part of doing this fee estimation is to decide what the question really is that we're trying to answer.  I took the approach that if you are asking what fee rate I need to be confirmed within Y blocks, then what you would like to know is the lowest fee rate such that a relatively high percentage of transactions of that fee rate are confirmed within Y blocks. Since even the highest fee transactions are confirmed within the first block only 90-93% of the time, I decided to use 80% as my cutoff.  So now to answer "estimatefee Y", I scan through all of the fee buckets from the most expensive down until I find the last bucket with >80% of the transactions confirmed within Y blocks.

Unfortunately we still have the problem of not having enough data points for non-typical fee rates, and so it requires gathering a lot of data to give reasonable answers. To keep all of these data points in a circular buffer and then sort them for every analysis (or after every new block) is expensive.  So instead I adopted the approach of keeping an exponentially decaying moving average for each bucket.  I used a decay of .998 which represents a half life of 374 blocks or about 2.5 days.  Also if a bucket doesn't have very many transactions, I combine it with the next bucket.

Here is a link to the code.  I can create an actual pull request if there is consensus that it makes sense to do so.

I've attached a graph comparing the estimates produced for 1-3 confirmations by the new code and the old code.  I did apply the patch to fix issue 3 above to the old code first.  The new code is in green and the fixed code is in purple.  The Y axis is a log scale of feerate in satoshis per KB and the X axis is chain height.  The new code produces the same estimates for 2 and 3 confirmations (the answers are effectively quantized by bucket).

I've also completely reworked smartfees.py.  It turns out to require many many more transactions are put through in order to have statistically significant results, so the test is quite slow to run (about 3 mins on my machine).

I've also been running a real world test, sending transactions of various fee rates and seeing how long they took to get confirmed.  After almost 200 tx's at each fee rate, here are the results so far:

Fee rate 1100   Avg blocks to confirm 2.30 NumBlocks:% confirmed 1: 0.528 2: 0.751 3: 0.870

Fee rate 2500   Avg blocks to confirm 2.22 NumBlocks:% confirmed 1: 0.528 2: 0.766 3: 0.880

Fee rate 5000   Avg blocks to confirm 1.93 NumBlocks:% confirmed 1: 0.528 2: 0.782 3: 0.891

Fee rate 10000  Avg blocks to confirm 1.67 NumBlocks:% confirmed 1: 0.569 2: 0.844 3: 0.943

Fee rate 20000  Avg blocks to confirm 1.33 NumBlocks:% confirmed 1: 0.715 2: 0.963 3: 0.989

Fee rate 30000  Avg blocks to confirm 1.27 NumBlocks:% confirmed 1: 0.751 2: 0.974 3: 1.0

Fee rate 40000  Avg blocks to confirm 1.25 NumBlocks:% confirmed 1: 0.792 2: 0.953 3: 0.994

Fee rate 60000  Avg blocks to confirm 1.12 NumBlocks:% confirmed 1: 0.875 2: 1.0   3: 1.0

Fee rate 100000 Avg blocks to confirm 1.09 NumBlocks:% confirmed 1: 0.901 2: 1.0   3: 1.0

Fee rate 300000 Avg blocks to confirm 1.12 NumBlocks:% confirmed 1: 0.886 2: 0.989 3: 1.0

Alex

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