filecoin-1559-analysis.ipynb

{
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    "# A quick analysis of the EIP-1559-style fee mechanism in Filecoin\n",
    "\n",
    "[Davide Crapis](https://twitter.com/DavideCrapis)\n",
    "\n",
    "**Main Variables**\n",
    "\n",
    "There are 3 types of variables that are relevant for the Filecoin fee market:\n",
    "\n",
    "- set by user: gas_fee_cap,\tgas_premium, gas_limit\n",
    "\n",
    "- set by protocol: parent_base_fee\n",
    "\n",
    "- calculated by protocol: gas_used, gas_refund, gas_burned, base_fee_burn, over_estimation_burn\n",
    "\n",
    "A few relations between these variables are clear from their [implementation](https://github.com/filecoin-project/lotus/blob/v0.10.0/chain/vm/burn.go#L70-L102), the following is particularly useful `gas_limit = gas_used + gas_refund + gas_burned`.\n",
    "\n",
    "**Filecoin Fee Mechanism**\n",
    "\n",
    "[User fees](https://github.com/filecoin-project/lotus/blob/v0.10.0/chain/vm/burn.go#L70-L102) are similar to Ethereum, with an additional component - number (3) below - that is burned to explicitly disincentivize overestimation of gas used - beyond the implicit disincentive of number (2). The total cost of a transaction is:\n",
    "\n",
    "(1) GasUsage * BaseFee (burned) +\n",
    "\n",
    "(2) GasLimit * GasPremium (storage provider’s reward) +\n",
    "\n",
    "(3) OverEstimationBurn * BaseFee (burned)\n",
    "\n",
    "The [basefee update mechanism](https://github.com/filecoin-project/lotus/blob/65ee059591c10c7d89565cc3d8dfcffbfb148593/chain/store/basefee.go#L16) in filecoin is the same as Ethereum's EIP-1559. In particular, the [current parameters](https://github.com/filecoin-project/lotus/blob/65ee059591c10c7d89565cc3d8dfcffbfb148593/build/params_shared_vals.go#L121) specify a gas limit of 10B gas units and a gas target of 5B gas units per block. The base fee update formula is\n",
    "\n",
    "$$\n",
    "b_{n+1} = b_n \\left( 1  + \\frac{1}{8} \\cdot \\frac{g_n - g^*}{g^*}\\right),\n",
    "$$\n",
    "\n",
    "where $g_n$ is the average amount of gas consumed by a block in tipset $n$ and $g^*$ is the sustainable gas target of 5B (possibly scaled by packing efficiency coefficient, in which case the target is 4B).\n",
    "\n",
    "This mechanism was initially [proposed by Vitalik](https://ethresear.ch/t/first-and-second-price-auctions-and-improved-transaction-fee-markets/2410) as an improvement to the previous Ethereum mechanism, a simple first-price auction where miners kept all the fees. It was implemented by Filecoin even before Ethereum itself! The mechanism has a few desirable practical properties:\n",
    "\n",
    "- Simple bidding strategies for users and inclusion strategies for miners are incentive compatible. (Thus making the protocol robust against economic attacks and manipulations.)\n",
    "\n",
    "- Reduced variance of fees and improved predictability.\n",
    "\n",
    "- Burning base fees further reduces incentives to manipulate for miners and native token inflation. (Alternatively, capturing them as protocol revenue can increase flexibility, protocol can decide distribution policy, over time to different participants.)\n",
    "\n",
    "- The update mechanism ensures that average block size is kept close to a sustainable target, which is typically smaller than maximum block burst limit.\n",
    "\n",
    "We will conduct an EDA with an eye at these properties. We will then propose further directions for more in depth analyses that can potentially give better measurements of these properties and generate ideas for new mechanisms that improve upon the current one."
   ]
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  {
   "cell_type": "markdown",
   "id": "839d1f66-de7e-42d7-a90b-7700426100f3",
   "metadata": {},
   "source": [
    "## EDA"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f58c5ee6-961c-4059-ad0a-6a895c9fc3df",
   "metadata": {},
   "source": [
    "**Data**\n",
    "\n",
    "Means and aggregate data are not granular enough to carry on a satisfactory analysis of the blockspace market. In order to gain a good understanding of how the fee mechanism works in practice and the dynamics induced by users interacting with it we need to get granular data.\n",
    "\n",
    "Fortunately, we can leverage open data and tooling built in the PL ecosystem. We leverage the Sentinel system and download [Lily data dumps](https://lilium.sh/data/dumps/) files from the fil-archive public s3 buckets. For this exercise we focus on one of the most interesting days identified in high level exploratory analysis (June 11th 2021). Looking at the [data model](https://lilium.sh/data/models/#derived_gas_outputs) we identify 3 main tables of interest:\n",
    "\n",
    "- block_headers: get unix timestamp\n",
    "- block_messages: get messages\n",
    "- derived_gas_outputs: message details\n",
    "\n",
    "Notes: \n",
    "- We won't be using the first table but it is useful if one wants to reconstruct what happened in UTC time by linking block height to the time it was added;\n",
    "- The epoch time in Filecoin is 30 seconds and there are five blocks in a tipset on expectation. A tipset is a set of blocks that each have the same height and parent tipset; the Filecoin blockchain is a [chain of tipsets](https://filecoin.io/blog/posts/tipsets-a-closer-look-at-filecoin-building-blocks). Each tipset is assigned a weight corresponding to the amount of storage the network is provided per the commitments encoded in the tipset’s blocks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c579b400-ec00-45cd-9f99-e529c44ffc92",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "4b3cc814-05a8-4aed-a6ea-0cc5157ca36a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3410301, 3)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bm_messages = \"height,block,message\"\n",
    "bm_cols = bm_messages.split(\",\")\n",
    "\n",
    "bm = pd.read_csv('block_messages-2021-06-11.csv', names=bm_cols)\n",
    "bm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "789412d6-7060-4b82-bba0-d391e03a50a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>height</th>\n",
       "      <th>block</th>\n",
       "      <th>message</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2859.000000</td>\n",
       "      <td>2859.000000</td>\n",
       "      <td>2859.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>836880.735922</td>\n",
       "      <td>4.923400</td>\n",
       "      <td>517.805876</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>831.968699</td>\n",
       "      <td>2.179989</td>\n",
       "      <td>129.726740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>835441.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>42.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>836160.500000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>441.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>836880.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>509.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>837601.500000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>591.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>838320.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>1102.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              height        block      message\n",
       "count    2859.000000  2859.000000  2859.000000\n",
       "mean   836880.735922     4.923400   517.805876\n",
       "std       831.968699     2.179989   129.726740\n",
       "min    835441.000000     1.000000    42.000000\n",
       "25%    836160.500000     3.000000   441.000000\n",
       "50%    836880.000000     5.000000   509.000000\n",
       "75%    837601.500000     6.000000   591.000000\n",
       "max    838320.000000    16.000000  1102.000000"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# blocks and messages per tipset\n",
    "bm.groupby('height').nunique().reset_index().describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d024de5a-8a2b-49ee-8025-7bc36b9eb675",
   "metadata": {},
   "source": [
    "We notice that there are too many messages, this is because in the Filecoin blockchain, multiple blocks in a single tipset may [include the same message](https://spec.filecoin.io/systems/filecoin_vm/interpreter/). Messages are processed only the first time they are encountered in the tipset’s canonical order, subsequent duplicates do not result in any state mutation, produce a receipt, or pay gas to the block producer. We thus exclude them before merging with derived gas outputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "66f4d4da-9189-4b5a-a1d3-a40cc4e53dd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1480407, 3)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmm = bm[~bm[['message']].duplicated()]\n",
    "bmm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f4ec42e9-2426-49b5-a0df-5d3857d0fcb4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1463902, 24)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dgo_header = \"height,cid,state_root,from,to,value,gas_fee_cap,gas_premium,gas_limit,\\\n",
    "size_bytes,nonce,method,actor_name,actor_family,exit_code,gas_used,parent_base_fee,\\\n",
    "base_fee_burn,over_estimation_burn,miner_penalty,miner_tip,refund,gas_refund,gas_burned\"\n",
    "dgo_cols = dgo_header.split(\",\")\n",
    "\n",
    "dgo = pd.read_csv('derived_gas_outputs-2021-06-11.csv', names=dgo_cols)\n",
    "dgo.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "c8145ec1-dcc5-4f2b-bc96-b3347fea3ef9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1480407, 26)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf = bmm[['block','message']].merge(dgo, left_on='message', right_on='cid', how='left')\n",
    "gf.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "3ceee4f8-6951-4171-91a5-ed012a12c465",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>height</th>\n",
       "      <th>gas_used</th>\n",
       "      <th>block</th>\n",
       "      <th>parent_base_fee</th>\n",
       "      <th>avg_gas_per_block</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>835441.0</td>\n",
       "      <td>1.645633e+10</td>\n",
       "      <td>4</td>\n",
       "      <td>1.384664e+09</td>\n",
       "      <td>4.114083e+09</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>835442.0</td>\n",
       "      <td>1.962443e+10</td>\n",
       "      <td>5</td>\n",
       "      <td>1.389373e+09</td>\n",
       "      <td>3.924886e+09</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>835443.0</td>\n",
       "      <td>1.774932e+10</td>\n",
       "      <td>5</td>\n",
       "      <td>1.383129e+09</td>\n",
       "      <td>3.549865e+09</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>835444.0</td>\n",
       "      <td>1.378103e+10</td>\n",
       "      <td>3</td>\n",
       "      <td>1.361956e+09</td>\n",
       "      <td>4.593678e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>835445.0</td>\n",
       "      <td>1.564567e+10</td>\n",
       "      <td>5</td>\n",
       "      <td>1.384518e+09</td>\n",
       "      <td>3.129134e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>835446.0</td>\n",
       "      <td>1.827184e+10</td>\n",
       "      <td>6</td>\n",
       "      <td>1.345610e+09</td>\n",
       "      <td>3.045307e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>835447.0</td>\n",
       "      <td>1.204632e+10</td>\n",
       "      <td>2</td>\n",
       "      <td>1.305119e+09</td>\n",
       "      <td>6.023161e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>835448.0</td>\n",
       "      <td>1.914485e+10</td>\n",
       "      <td>8</td>\n",
       "      <td>1.389064e+09</td>\n",
       "      <td>2.393106e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>835449.0</td>\n",
       "      <td>7.866642e+09</td>\n",
       "      <td>1</td>\n",
       "      <td>1.317775e+09</td>\n",
       "      <td>7.866642e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>835450.0</td>\n",
       "      <td>7.933401e+09</td>\n",
       "      <td>1</td>\n",
       "      <td>1.482228e+09</td>\n",
       "      <td>7.933401e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>835451.0</td>\n",
       "      <td>1.822076e+10</td>\n",
       "      <td>4</td>\n",
       "      <td>1.665046e+09</td>\n",
       "      <td>4.555191e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>835452.0</td>\n",
       "      <td>2.203740e+10</td>\n",
       "      <td>5</td>\n",
       "      <td>1.693167e+09</td>\n",
       "      <td>4.407480e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>835453.0</td>\n",
       "      <td>2.023558e+10</td>\n",
       "      <td>8</td>\n",
       "      <td>1.710996e+09</td>\n",
       "      <td>2.529447e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>835454.0</td>\n",
       "      <td>1.330026e+10</td>\n",
       "      <td>4</td>\n",
       "      <td>1.615104e+09</td>\n",
       "      <td>3.325066e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>835455.0</td>\n",
       "      <td>1.509762e+10</td>\n",
       "      <td>7</td>\n",
       "      <td>1.580225e+09</td>\n",
       "      <td>2.156803e+09</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "      height      gas_used  block  parent_base_fee  avg_gas_per_block\n",
       "0   835441.0  1.645633e+10      4     1.384664e+09       4.114083e+09\n",
       "1   835442.0  1.962443e+10      5     1.389373e+09       3.924886e+09\n",
       "2   835443.0  1.774932e+10      5     1.383129e+09       3.549865e+09\n",
       "3   835444.0  1.378103e+10      3     1.361956e+09       4.593678e+09\n",
       "4   835445.0  1.564567e+10      5     1.384518e+09       3.129134e+09\n",
       "5   835446.0  1.827184e+10      6     1.345610e+09       3.045307e+09\n",
       "6   835447.0  1.204632e+10      2     1.305119e+09       6.023161e+09\n",
       "7   835448.0  1.914485e+10      8     1.389064e+09       2.393106e+09\n",
       "8   835449.0  7.866642e+09      1     1.317775e+09       7.866642e+09\n",
       "9   835450.0  7.933401e+09      1     1.482228e+09       7.933401e+09\n",
       "10  835451.0  1.822076e+10      4     1.665046e+09       4.555191e+09\n",
       "11  835452.0  2.203740e+10      5     1.693167e+09       4.407480e+09\n",
       "12  835453.0  2.023558e+10      8     1.710996e+09       2.529447e+09\n",
       "13  835454.0  1.330026e+10      4     1.615104e+09       3.325066e+09\n",
       "14  835455.0  1.509762e+10      7     1.580225e+09       2.156803e+09"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf1 = gf[['height','block','gas_used','parent_base_fee']].groupby(['height']).agg({'gas_used': np.sum, 'block': 'nunique', 'parent_base_fee': np.mean}).reset_index()\n",
    "gf1['avg_gas_per_block'] = gf1['gas_used'] / gf1['block']\n",
    "gf1.head(15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7b2308f-c219-496a-8e18-8a6bfcfb254f",
   "metadata": {},
   "source": [
    "The table above shows the dynamic fee mechanism at work! We can see how when the avg gas per block is above the 4B threshold the protocol increases the base fee and when it is below it decreases it.\n",
    "\n",
    "The table below shows that the mechanism does a good job at keeping avg gas per block on track with the 4B gas units target (average deviation over the entire day is less than 1%). This can also be appreciated by the first chart below where we plot the rolling average. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "3f930996-0540-4b76-a063-0a843d108270",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>height</th>\n",
       "      <th>gas_used</th>\n",
       "      <th>block</th>\n",
       "      <th>parent_base_fee</th>\n",
       "      <th>avg_gas_per_block</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2858.000000</td>\n",
       "      <td>2.858000e+03</td>\n",
       "      <td>2858.000000</td>\n",
       "      <td>2.858000e+03</td>\n",
       "      <td>2.858000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>836880.232330</td>\n",
       "      <td>1.706467e+10</td>\n",
       "      <td>4.822603</td>\n",
       "      <td>1.328703e+09</td>\n",
       "      <td>4.043909e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>831.678352</td>\n",
       "      <td>4.746997e+09</td>\n",
       "      <td>2.078362</td>\n",
       "      <td>8.240803e+08</td>\n",
       "      <td>1.462103e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>835441.000000</td>\n",
       "      <td>2.009423e+09</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>6.414598e+08</td>\n",
       "      <td>1.004711e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>836160.250000</td>\n",
       "      <td>1.394034e+10</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>9.048156e+08</td>\n",
       "      <td>2.943712e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>836879.500000</td>\n",
       "      <td>1.654535e+10</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>1.036600e+09</td>\n",
       "      <td>3.758718e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>837600.750000</td>\n",
       "      <td>1.986468e+10</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>1.336636e+09</td>\n",
       "      <td>4.878757e+09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>838319.000000</td>\n",
       "      <td>3.910842e+10</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>6.273926e+09</td>\n",
       "      <td>8.426587e+09</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              height      gas_used        block  parent_base_fee  \\\n",
       "count    2858.000000  2.858000e+03  2858.000000     2.858000e+03   \n",
       "mean   836880.232330  1.706467e+10     4.822603     1.328703e+09   \n",
       "std       831.678352  4.746997e+09     2.078362     8.240803e+08   \n",
       "min    835441.000000  2.009423e+09     1.000000     6.414598e+08   \n",
       "25%    836160.250000  1.394034e+10     3.000000     9.048156e+08   \n",
       "50%    836879.500000  1.654535e+10     5.000000     1.036600e+09   \n",
       "75%    837600.750000  1.986468e+10     6.000000     1.336636e+09   \n",
       "max    838319.000000  3.910842e+10    14.000000     6.273926e+09   \n",
       "\n",
       "       avg_gas_per_block  \n",
       "count       2.858000e+03  \n",
       "mean        4.043909e+09  \n",
       "std         1.462103e+09  \n",
       "min         1.004711e+09  \n",
       "25%         2.943712e+09  \n",
       "50%         3.758718e+09  \n",
       "75%         4.878757e+09  \n",
       "max         8.426587e+09  "
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf1.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "fb72d5ce-a7b9-4139-b4e0-5d970555c445",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf1['avg_gas_per_block_rolling'] = gf1['avg_gas_per_block'].rolling(60).mean()\n",
    "gf1.plot('height',['avg_gas_per_block','avg_gas_per_block_rolling'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "7dbbf971-38b0-4285-a2c7-73131e86e745",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gf1.plot('height',['parent_base_fee'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "8903681e-cf87-4b00-9794-2f90e96786df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.034"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf1['parent_base_fee'].corr(gf1['avg_gas_per_block']).round(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "d3e3800b-3fc2-4e95-b9ac-61502a5cdd4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.293"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gf1['parent_base_fee'].corr(gf1['avg_gas_per_block_rolling']).round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2021c646-32b1-4fce-9fa4-c6fa432e30d3",
   "metadata": {},
   "source": [
    "The final insight we focus on is looking more in detail at how the basefee relates to congestion. We can see that there is a negative correlation of -3.4% between base fee and avg gas per block, this is because higher fee locally suppresses demand. At the same time we see that there is a strong positive correlation of 29.3% between base fee and the rolling average, showing that basefee is a signal of network congestion.\n",
    "\n",
    "## Further directions\n",
    "\n",
    "There are many more exciting hypothesis tests and improvements that can be worked out from this granular data. These crucially depend on the priority of problems faced by the Filecoin blockchain as the network scales. Here are a few directions that seem relevant:\n",
    "\n",
    "- Structural demand estimation, including potential demand and the mempool, elasticities, load on different types of resources.\n",
    "\n",
    "- Parameter updates to current base fee update rule, including dynamic updates, smoothing to reduce volatility and spikiness that is currently observed.\n",
    "\n",
    "- Heterogeneous resource pricing to improve efficiency and UX, including pricing different VM resources (e.g. storage and compute) or differentiated pricing for specific types of messages and transactions.\n",
    "\n",
    "More broadly, there are other related questions that seem to be relevant and potentially very impactful:\n",
    "\n",
    "- New mechanisms that are tailored to the specificity and scale of the Filecoin blockchain as new components are built (e.g. Hierarchical Consensus or HyperDrive). Perhaps a new framework so that the mechanism can be easily upgraded as the chain itself evolves.\n",
    "\n",
    "- Macroeconomic policy changes, including tweaking the current \"burn all base fees\", updating miner rewards/punishment schemes. These need to be carefully designed and tested with network revenue as well as inflation in mind."
   ]
  }
 ],
 "metadata": {
  "author": "Davide Crapis",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.8"
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  "latex_metadata": {
   "author": "Davide Crapis"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}