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Date: Sat, 19 Dec 2015 11:49:25 -0500
From: jl2012 <jl2012@xbt.hk>
To: bitcoin-dev@lists.linuxfoundation.org
Message-ID: <b19eb676c18ba451605cb02159541dd9@xbt.hk>
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Subject: [bitcoin-dev] Segregated witness softfork with moderate adoption
 has very small block size effect
Precedence: list

I have done some calculation for the effect of a SW softfork on the 
actual total block size.

Definitions:

Core block size (CBS): The block size as seen by a non-upgrading full 
node
Witness size (WS): The total size of witness in a block
Total block size (TBS): CBS + WS
Witness discount (WD): A discount factor for witness for calculation of 
VBS (1 = no discount)
Virtual block size (VBS): CBS + (WS * WD)
Witness adoption (WA): Proportion of new format transactions among all 
transactions
Prunable ratio (PR): Proportion of signature data size in a transaction

With some transformation it could be shown that:

  TBS = CBS / (1 - WA * PR) = VBS / (1 - WA * PR * (1 - WD))

sipa suggested a WD of 25%.

The PR heavily depends on the transaction script type and input-output 
ratio. For example, the PR of 1-in 2-out P2PKH and 1-in 1-out 2-of-2 
multisig P2SH are about 47% and 72% respectively. According to sipa's 
presentation, the current average PR on the blockchain is about 60%.

Assuming WD=25% and PR=60%, the MAX TBS with different MAX VBS and WA is 
listed at:

http://i.imgur.com/4bgTMRO.png

The highlight indicates whether the CBS or VBS is the limiting factor.

With moderate SW adoption at 40-60%, the total block size is 1.32-1.56MB 
when MAX VBS is 1.25MB, and 1.22-1.37MB when MAX VBS is 1.00MB.

P2SH has been introduced for 3.5 years and only about 10% of bitcoin is 
stored this way (I can't find proportion of existing P2SH address). A 
1-year adoption rate of 40% for segwit is clearly over-optimistic unless 
the tx fee becomes really high.

(btw the PR of 60% may also be over-optimistic, as using SW nested in 
P2SH will decrease the PR, and therefore TBS becomes even lower)

I am not convinced that SW softfork should be the *only* short term 
scalability solution