From: Alex Morcos <morcos@gmail•com>
To: Mike Hearn <mike@plan99•net>
Cc: Bitcoin Dev <bitcoin-development@lists•sourceforge.net>
Subject: Re: [Bitcoin-development] Reworking the policy estimation code (fee estimates)
Date: Tue, 28 Oct 2014 08:12:57 -0400 [thread overview]
Message-ID: <CAPWm=eXBUNd2WeCwnTtocuofiEq+Ccn0-hZTrMQCQiuHRvVZEQ@mail.gmail.com> (raw)
In-Reply-To: <CANEZrP0tpnES7=SuaVHOfWdf=CDkzhx2V=4mqRGDpW3ELsGkKA@mail.gmail.com>
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Yeah, so to explain points 1 and 2 a bit more
1) It's about what question you are trying to answer. The existing code
tries to answer the question of what is the median fee of a transaction
that gets confirmed in Y blocks. It turns out that is not a very good
proxy for the question we really want to know which is what is the fee that
is necessary such that we are likely to be confirmed within Y blocks.
What happens is that there are so many transactions of the 40k satoshis/kB
feerate that they turn out to be the dominant data points of transactions
that are confirmed after 2 blocks, 3 blocks, etc. and not only 1 block.
So for example. A hypothetical sample of 20 txs might find 2 of your 1k
sat/kB txs and 18 of the 40k sat/kB txs. Perhaps 15 of the 40k txs are
confirmed in 1 block and the other 3 in 2 blocks, and 1 of the 1k txs in 1
block and the other in 2 blocks. So if you analyze the data by
confirmation time, you find that 15/16 1-conf txs are 40k and 3/4 2-conf
txs are 40k, so the median feerate is 40k for both 1 and 2 confirmations.
Instead, the correct thing to do is analyze the data by feerate. Doing
that, we find that 15/18 (83%) of 40k txs are confirmed in 1 block and 1/2
(50%) 1k txs are. But 100% of both are confirmed within two blocks. This
leads you to say, you need 40k feerate if you want to get confirmed in 1
block but 1k is sufficient if you want to be confirmed in 2 blocks.
Put another way, Let's imagine you wanted to know how tall you have to be
no longer fit in the coach seats on an airplane. If you looked at the
median height of all people in coach and all people in first class, you
would see that they were about the same, and you would get a confusing
answer. Instead you have to bin by height, and look at the percentage of
people of each height that fly first-class vs coach, and I'd guess that by
the time you got up to say 6'8" you were finding greater than 50% of the
people flying first class.
2) The code also presupposes that higher fee rate transactions must be
confirmed quicker. And so in addition to binning all transactions by
confirmation time, the code then sorts all of the transactions and re-bins
them such that the highest fee transactions are all in the 1-confirmation
bin and the lowest fee transactions are all in the 25-confirmation bin. If
we'd been trying to predict whether the first 2 bytes of transaction hash
influenced our confirmation time, we would have started by having a random
distribution of hashes in each confirmation bin, but then after doing the
sorting, we'd of course have found that the "median hash" of the
1-confirmation transactions was higher, because we sorted it to make that
the case.
In the airplane example this would have been equivalent to taking the
median height of the 20 tallest people on the plane (assuming first class
is 20 seats) and saying that was the height for first class and the median
height of the remaining people for coach. This will appear to give a
slightly better answer than the first approach, but is still wrong.
There are still a lot of additional improvements that can be made to fee
estimation. One problem my proposed code has is there really just aren't
enough data points of low feerate transactions to give meaningful answers
about how likely those are to be confirmed, so its answers are still a bit
conservative. This will improve though as the actual distribution of
transactions spreads out. The other major needed improvement is to not
just state some description of what has happened in the past, but to
actually make a prediction about what is going to happen in the future.
For instance looking at the feerates of unconfirmed transactions currently
in the mempool could tell you that if you want to be confirmed immediately
you'll need to be high enough in that priority queue.
On Tue, Oct 28, 2014 at 5:55 AM, Mike Hearn <mike@plan99•net> wrote:
> Could you explain a little further why you think the current approach is
> statistically incorrect? There's no doubt that the existing estimates the
> system produces are garbage, but that's because it assumes players in the
> fee market are rational and they are not.
>
> Fwiw bitcoinj 0.12.1 applies the January fee drop and will attach fee of
> only 1000 satoshis per kB by default. I also have a program that measures
> confirmation time for a given fee level (with fresh coins so there's no
> priority) and it aligns with your findings, most txns confirm within a
> couple of blocks.
>
> Ultimately there isn't any easy method to stop people throwing money away.
> Bitcoinj will probably continue to use hard coded fee values for now to try
> and contribute to market sanity in the hope it makes smartfees smarter.
> On 27 Oct 2014 19:34, "Alex Morcos" <morcos@gmail•com> wrote:
>
>> 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
>> <https://github.com/bitcoin/bitcoin/issues/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 <https://github.com/morcos/bitcoin/pull/3> 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
>>
>>
>> ------------------------------------------------------------------------------
>>
>> _______________________________________________
>> Bitcoin-development mailing list
>> Bitcoin-development@lists•sourceforge.net
>> https://lists.sourceforge.net/lists/listinfo/bitcoin-development
>>
>>
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next prev parent reply other threads:[~2014-10-28 12:13 UTC|newest]
Thread overview: 9+ messages / expand[flat|nested] mbox.gz Atom feed top
2014-10-27 19:33 Alex Morcos
2014-10-28 9:55 ` Mike Hearn
2014-10-28 12:12 ` Alex Morcos [this message]
2014-10-28 13:59 ` Gavin Andresen
2014-10-28 14:30 ` Alex Morcos
2014-10-28 14:55 ` Alex Morcos
2014-10-28 14:58 ` Gavin Andresen
2014-10-28 15:39 ` Alex Morcos
2014-10-29 20:08 ` Peter Todd
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