├── README.md ├── LICENSE └── Validator_Rewards_After_the_Merge.ipynb /README.md: -------------------------------------------------------------------------------- 1 | # merge-private-public-mempool 2 | 3 | The data we used to fit the simulation model can be found via: 4 | 5 | https://drive.google.com/file/d/1_TJS3LQfD2DA-_8q95NtVpQ3ydr7W41o/view?usp=share_link 6 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | MIT License 2 | 3 | Copyright (c) 2023 SciEcon CIC 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /Validator_Rewards_After_the_Merge.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "nbformat": 4, 3 | "nbformat_minor": 0, 4 | "metadata": { 5 | "colab": { 6 | "provenance": [], 7 | "authorship_tag": "ABX9TyMfJqtREdZz6CBBVGRKyvyQ", 8 | "include_colab_link": true 9 | }, 10 | "kernelspec": { 11 | "name": "python3", 12 | "display_name": "Python 3" 13 | }, 14 | "language_info": { 15 | "name": "python" 16 | } 17 | }, 18 | "cells": [ 19 | { 20 | "cell_type": "markdown", 21 | "metadata": { 22 | "id": "view-in-github", 23 | "colab_type": "text" 24 | }, 25 | "source": [ 26 | "\"Open" 27 | ] 28 | }, 29 | { 30 | "cell_type": "markdown", 31 | "source": [ 32 | "#Simulating Post-Merge Returns from MEV for the validator to seek for their \"incentives\"/parameters from the model setup\n", 33 | "\n", 34 | "So, bringing together what we have learned about historical block revenues for miners, let's have a go at modelling what validator returns from MEV might look like over the course of a year. Since we're now thinking about validators instead of miners, I'll express the results as percentage return on 32 ETH. We haven't arrived at an analytical expression for the distribution of per-block revenues (in my time spent trying to come up with a sensible expression based on a Pareto distribution, a suitable formulation proved elusive). This slightly complicates modelling and means in this case we're going to resort to a Monte Carlo simulation.\n", 35 | "\n", 36 | "The basic methodology is simple — generate a random number uniformly distributed between 0 and 1, and use this number to perform a lookup from the ECDF we calculated earlier (with the ECDF scaled to account for the 13.5s to 12s change in average block intervals). Assign the block's revenue to a randomly selected validator. We're going to assume perfect validator performance (no missed block proposals). We're also going to use a validator set size of 420,000, close to the current size of the validator set in August 2022. This number of validators also divides exactly into groups of 32, which will be useful when we look at groups of validators later on." 37 | ], 38 | "metadata": { 39 | "id": "kQI-0WN89Yxl" 40 | } 41 | }, 42 | { 43 | "cell_type": "code", 44 | "source": [ 45 | "import math\n", 46 | "from random import randrange, random, sample\n", 47 | "from datetime import datetime, timedelta\n", 48 | "from time import time\n", 49 | "from matplotlib import pyplot as plt\n", 50 | "import matplotlib.dates as mdates\n", 51 | "import pandas as pd\n", 52 | "import numpy as np" 53 | ], 54 | "metadata": { 55 | "id": "TgBU1Mo53Pbr" 56 | }, 57 | "execution_count": 2, 58 | "outputs": [] 59 | }, 60 | { 61 | "cell_type": "code", 62 | "source": [ 63 | "class Ecdf(pd.Series):\n", 64 | " def __init__(self, data):\n", 65 | " s = pd.Series(data)\n", 66 | " super().__init__(s.value_counts().sort_index().cumsum()*1./len(s))\n", 67 | " \n", 68 | " def get_quantile(self, q):\n", 69 | " #self[self.ge(random())].index[0]\n", 70 | " return self.index[np.argmax(self.array >= q)] # faster\n", 71 | " \n", 72 | " def get_scaled_ecdf(self, scaling_factor):\n", 73 | " index = [v * scaling_factor for v in self.index.values]\n", 74 | " scaled_ecdf = self.set_axis(index)\n", 75 | " scaled_ecdf.__class__ = Ecdf\n", 76 | " return scaled_ecdf" 77 | ], 78 | "metadata": { 79 | "id": "ysZrh52m32dm" 80 | }, 81 | "execution_count": 3, 82 | "outputs": [] 83 | }, 84 | { 85 | "cell_type": "code", 86 | "source": [ 87 | "df = pd.DataFrame(np.random.exponential(scale=2/3, size=10000), columns = ['miner_extracted'])" 88 | ], 89 | "metadata": { 90 | "id": "uSl5V56c4qcK" 91 | }, 92 | "execution_count": null, 93 | "outputs": [] 94 | }, 95 | { 96 | "cell_type": "code", 97 | "source": [ 98 | "# simulate a year's worth of block proposals\n", 99 | "SECONDS_PER_SLOT = 12.0\n", 100 | "mev_ecdf = Ecdf(df['miner_extracted'])\n", 101 | "# calculate average block interval\n", 102 | "mean_interval = 12.58\n", 103 | "scaling_factor = SECONDS_PER_SLOT / mean_interval\n", 104 | "scaled_mev_ecdf = mev_ecdf.get_scaled_ecdf(scaling_factor)\n", 105 | "\n", 106 | "num_validators = 420000\n", 107 | "validators = [0] * num_validators\n", 108 | "validators_h1 = [0] * num_validators\n", 109 | "validators_h2 = [0] * num_validators\n", 110 | "seconds_per_year = 31556952\n", 111 | "slots_per_year = int(seconds_per_year // SECONDS_PER_SLOT)\n", 112 | "\n", 113 | "start_time = time()\n", 114 | "last_update = 0\n", 115 | "\n", 116 | "for slot in range(slots_per_year):\n", 117 | " # random selection of validator as proposer\n", 118 | " ind = randrange(num_validators)\n", 119 | " rn = random()\n", 120 | " # random sampling of MEV level for the block\n", 121 | " validators[ind] += scaled_mev_ecdf.get_quantile(rn)\n", 122 | " \n", 123 | " t = time()\n", 124 | " if t - last_update > 0.1:\n", 125 | " percentage = 100 * (slot+1) / slots_per_year\n", 126 | " elapsed = timedelta(seconds=int(t - start_time))\n", 127 | " print(f\"{percentage:.2f}% / {elapsed} elapsed\", end='\\r')\n", 128 | " last_update = t\n", 129 | "\n", 130 | "rtn = pd.Series([100 * v / 32 for v in validators])\n", 131 | "annual_mev_ecdf = Ecdf(rtn)" 132 | ], 133 | "metadata": { 134 | "colab": { 135 | "base_uri": "https://localhost:8080/" 136 | }, 137 | "id": "_pF-L-a40Hk1", 138 | "outputId": "f3bded7e-196e-4735-d245-698ab6f4e3b1" 139 | }, 140 | "execution_count": 14, 141 | "outputs": [ 142 | { 143 | "output_type": "stream", 144 | "name": "stdout", 145 | "text": [] 146 | } 147 | ] 148 | }, 149 | { 150 | "cell_type": "code", 151 | "source": [ 152 | "fig, (ax1, ax2) = plt.subplots(2, figsize=(10, 10))\n", 153 | "\n", 154 | "bins = [e/5 for e in range(151)]\n", 155 | "rtn.hist(ax=ax1, bins=bins, density=True, grid=False)\n", 156 | "ax1.set_title(\n", 157 | " 'Histogram of Simulated Validator Return from MEV (420k validators, 1 year)'\n", 158 | ")\n", 159 | "ax1.set_xlim(0, 30)\n", 160 | "ax1.set_ylabel('Frequency density')\n", 161 | "\n", 162 | "annual_mev_ecdf.plot(ax=ax2, label=\"whole dataset\")\n", 163 | "quantiles = [.01, .1, .25, .5, .75, .9, .99, .999]\n", 164 | "\n", 165 | "table = pd.DataFrame({\n", 166 | " 'quantile': quantiles,\n", 167 | " 'centile': [100 * q for q in quantiles],\n", 168 | " 'all': [annual_mev_ecdf.get_quantile(q) for q in quantiles],\n", 169 | "})\n", 170 | "table.set_index('quantile', inplace=True, drop=False)\n", 171 | "table.plot('all', 'quantile', kind='scatter', ax=ax2)\n", 172 | "\n", 173 | "c1 = table['all'].loc[0.01]\n", 174 | "ax2.annotate(f'1st centile: {c1:.2f}% APR', (c1 + 0.5, 0.02))\n", 175 | "d1 = table['all'].loc[0.1]\n", 176 | "ax2.annotate(f'10th centile: {d1:.2f}% APR', (d1 + 0.5, 0.075))\n", 177 | "lq = table['all'].loc[0.25]\n", 178 | "ax2.annotate(f'25th centile (lower quartile): {lq:.2f}% APR', (lq + 0.7, 0.225))\n", 179 | "med = table['all'].loc[0.5]\n", 180 | "ax2.annotate(f'50th centile (median): {med:.2f}% APR', (med + 1, 0.475))\n", 181 | "uq = table['all'].loc[0.75]\n", 182 | "ax2.annotate(f'75th centile (upper quartile): {uq:.2f}% APR', (uq + 1.3, 0.725))\n", 183 | "d9 = table['all'].loc[0.9]\n", 184 | "ax2.annotate(f'90th centile: {d9:.2f}% APR', (d9 + 1.8, 0.875))\n", 185 | "c99 = table['all'].loc[0.99]\n", 186 | "ax2.annotate(f'99th centile: {c99:.2f}% APR', (c99 - 5, 0.925))\n", 187 | "\n", 188 | "ax2.set_title(\n", 189 | " 'ECDF for Simulated Validator Return from MEV (420k validators, 1 year)'\n", 190 | ")\n", 191 | "ax2.set_xlabel('Rate of return (% APR)')\n", 192 | "ax2.set_xlim(0, 30)\n", 193 | "ax2.set_ylabel('Cumulative frequency density')\n", 194 | "ax2.set_ylim(0, 1)\n", 195 | "ax2.legend(title='MEV distribution based on:', loc='lower right')\n", 196 | "\n", 197 | "plt.show()\n", 198 | "\n", 199 | "table.drop('quantile', axis=1, inplace=True)\n", 200 | "cols = [\n", 201 | " ('','Centile
(%)'),\n", 202 | " ('Rate of return (% APR)
based on data from:','Sep 2021
to Aug 2022'),\n", 203 | "]\n", 204 | "\n", 205 | "fmts = ['{:.1f}'] + ['{:.2f}'] * 3\n", 206 | "col_formats = {c: f for c, f in zip(cols, fmts)}\n", 207 | "table.columns = pd.MultiIndex.from_tuples(cols)" 208 | ], 209 | "metadata": { 210 | "colab": { 211 | "base_uri": "https://localhost:8080/", 212 | "height": 621 213 | }, 214 | "id": "GiYfri176DnN", 215 | "outputId": "fcc37b39-d5c7-46ee-b0b0-ed3b02794768" 216 | }, 217 | "execution_count": 17, 218 | "outputs": [ 219 | { 220 | "output_type": "display_data", 221 | "data": { 222 | "text/plain": [ 223 | "
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\n" 226 | }, 227 | "metadata": { 228 | "needs_background": "light" 229 | } 230 | } 231 | ] 232 | }, 233 | { 234 | "cell_type": "markdown", 235 | "source": [ 236 | "# Modelling Full Validator Returns\n", 237 | "Now we can see approximate validator returns from MEV, let's compete the simulation by including rewards for attestation and sync committees too. Since beaconcha.in regularly indicates participation rates over 99% on the beacon chain, we'll keep our simulation simple by assuming perfect participation. In practice, if the conditions we see on mainnet today persist after the merge, the vast majority of variability in validator rewards will come from the random assignment of proposer duties, sync committees and MEV, rather than being due to validator performance.\n", 238 | "\n", 239 | "Therefore in the simulation below, all validators given an identical reward for perfect attestation performance, but a committee of 512 validators is selected at random every 256 epochs, and that committee then earns a full sync committee reward, for perfect participation over the subsequent 256 epochs. MEV per block is selected in the same way as before, but now validators receive beacon chain proposer rewards, as well as execution layer transaction fees (MEV)." 240 | ], 241 | "metadata": { 242 | "id": "2sCii1zF9oVH" 243 | } 244 | }, 245 | { 246 | "cell_type": "code", 247 | "source": [ 248 | "num_validators = 420000\n", 249 | "\n", 250 | "HEAD_WT = 14\n", 251 | "SOURCE_WT = 14\n", 252 | "TARGET_WT = 26\n", 253 | "SYNC_WT = 2\n", 254 | "PROPOSER_WT = 8\n", 255 | "BASE_REWARD_FACTOR = 64\n", 256 | "WEIGHT_DENOM = 64\n", 257 | "EPOCHS_PER_COMMITTEE = 256\n", 258 | "COMMITTEE_SIZE = 512\n", 259 | "SLOTS_PER_EPOCH = 32\n", 260 | "GWEI_PER_ETH = int(1e9)\n", 261 | "gwei_per_validator = int(32e9)\n", 262 | "staked_gwei = gwei_per_validator * num_validators\n", 263 | "epochs_per_year = slots_per_year // SLOTS_PER_EPOCH\n", 264 | "\n", 265 | "base_reward = gwei_per_validator * BASE_REWARD_FACTOR // math.isqrt(staked_gwei)\n", 266 | "total_reward = base_reward * num_validators\n", 267 | "\n", 268 | "att_reward = base_reward * (HEAD_WT + SOURCE_WT + TARGET_WT) // WEIGHT_DENOM\n", 269 | "annual_attestation_reward_eth = att_reward * epochs_per_year / GWEI_PER_ETH\n", 270 | "\n", 271 | "# perfect performance so all validators get full attestation reward for the year\n", 272 | "validators = [annual_attestation_reward_eth] * num_validators\n", 273 | "\n", 274 | "prop_reward = total_reward * PROPOSER_WT // WEIGHT_DENOM // SLOTS_PER_EPOCH\n", 275 | "prop_reward_eth = prop_reward / GWEI_PER_ETH\n", 276 | "sync_reward = total_reward * SYNC_WT // WEIGHT_DENOM // SLOTS_PER_EPOCH \\\n", 277 | " // COMMITTEE_SIZE\n", 278 | "sync_reward_eth = sync_reward / GWEI_PER_ETH\n", 279 | "\n", 280 | "start_time = time()\n", 281 | "last_update = 0\n", 282 | "\n", 283 | "for slot in range(slots_per_year):\n", 284 | " # process sync committee:\n", 285 | " if slot % (32 * EPOCHS_PER_COMMITTEE) == 0:\n", 286 | " # select sync committee\n", 287 | " committee = sample(range(num_validators), COMMITTEE_SIZE)\n", 288 | " for ind in committee:\n", 289 | " validators[ind] += sync_reward_eth\n", 290 | " validators_h1[ind] += sync_reward_eth\n", 291 | " validators_h2[ind] += sync_reward_eth\n", 292 | " \n", 293 | " # random selection of validator as proposer\n", 294 | " ind = randrange(num_validators)\n", 295 | " r = random()\n", 296 | " validators[ind] += scaled_mev_ecdf.get_quantile(r) + prop_reward_eth\n", 297 | "\n", 298 | " t = time()\n", 299 | " if t - last_update > 0.1:\n", 300 | " percentage = 100 * (slot+1) / slots_per_year\n", 301 | " elapsed = timedelta(seconds=int(t - start_time))\n", 302 | " print(f\"{percentage:.2f}% / {elapsed} elapsed\", end='\\r')\n", 303 | " last_update = t\n", 304 | "\n", 305 | "annual_full_rtn = pd.Series([100 * v / 32 for v in validators])\n", 306 | "annual_full_ecdf = Ecdf(annual_full_rtn)" 307 | ], 308 | "metadata": { 309 | "colab": { 310 | "base_uri": "https://localhost:8080/" 311 | }, 312 | "id": "J4wcmXWS2fhO", 313 | "outputId": "1d9d91ba-d510-4f98-9661-8cc088b3330a" 314 | }, 315 | "execution_count": 18, 316 | "outputs": [ 317 | { 318 | "output_type": "stream", 319 | "name": "stdout", 320 | "text": [] 321 | } 322 | ] 323 | }, 324 | { 325 | "cell_type": "code", 326 | "source": [ 327 | "fig, (ax1, ax2) = plt.subplots(2, figsize=(10, 10))\n", 328 | "\n", 329 | "bins = [e/5 for e in range(176)]\n", 330 | "annual_full_rtn.hist(ax=ax1, bins=bins, density=True, grid=False)\n", 331 | "ax1.set_title(\n", 332 | " 'Histogram of Simulated Validator Rate of Return (420k validators, 1 year)'\n", 333 | ")\n", 334 | "ax1.set_xlim(0, 35)\n", 335 | "ax1.set_ylabel('Frequency density')\n", 336 | "\n", 337 | "quantiles = [0, .01, .1, .25, .5, .75, .9, .99, .999, 1]\n", 338 | "\n", 339 | "table = pd.DataFrame({\n", 340 | " 'quantile': quantiles,\n", 341 | " 'centile': [100 * q for q in quantiles],\n", 342 | " 'all': [annual_full_ecdf.get_quantile(q) for q in quantiles],\n", 343 | "})\n", 344 | "table.set_index('quantile', inplace=True, drop=False)\n", 345 | "table.plot('all', 'quantile', kind='scatter', ax=ax2)\n", 346 | "\n", 347 | "annual_full_ecdf.plot(ax=ax2, label=\"whole dataset\")\n", 348 | "\n", 349 | " \n", 350 | "c1 = table['all'].loc[0.01]\n", 351 | "ax2.annotate(f'1st centile: {c1:.2f}% APR', (c1 + 0.7, 0.02))\n", 352 | "d1 = table['all'].loc[0.1]\n", 353 | "ax2.annotate(f'10th centile: {d1:.2f}% APR', (d1 + 0.7, 0.075))\n", 354 | "lq = table['all'].loc[0.25]\n", 355 | "ax2.annotate(f'25th centile (lower quartile): {lq:.2f}% APR', (lq + 1, 0.225))\n", 356 | "med = table['all'].loc[0.5]\n", 357 | "ax2.annotate(f'50th centile (median): {med:.2f}% APR', (med + 1, 0.475))\n", 358 | "uq = table['all'].loc[0.75]\n", 359 | "ax2.annotate(f'75th centile (upper quartile): {uq:.2f}% APR', (uq + 1.3, 0.725))\n", 360 | "d9 = table['all'].loc[0.9]\n", 361 | "ax2.annotate(f'90th centile: {d9:.2f}% APR', (d9 + 1.8, 0.875))\n", 362 | "c99 = table['all'].loc[0.99]\n", 363 | "ax2.annotate(f'99th centile: {c99:.2f}% APR', (c99 - 6, 0.925))\n", 364 | "\n", 365 | "ax2.set_title('Simulated Validator Rate of Return (420k validators, 1 year)')\n", 366 | "ax2.set_xlabel('Rate of return (% APR)')\n", 367 | "ax2.set_xlim(0, 35)\n", 368 | "ax2.set_ylabel('Cumulative frequency density')\n", 369 | "ax2.set_ylim(0, 1)\n", 370 | "ax2.legend(title='MEV distribution based on:', loc='lower right')\n", 371 | "\n", 372 | "plt.show()\n", 373 | "\n", 374 | "table.drop('quantile', axis=1, inplace=True)\n", 375 | "cols = [\n", 376 | " ('','Centile
(%)'),\n", 377 | " ('Rate of return (% APR)
based on data from:','Sep 2021
to Aug 2022'),\n", 378 | "]\n", 379 | "\n", 380 | "fmts = ['{:.1f}'] + ['{:.2f}'] * 3\n", 381 | "col_formats = {c: f for c, f in zip(cols, fmts)}\n", 382 | "table.columns = pd.MultiIndex.from_tuples(cols)" 383 | ], 384 | "metadata": { 385 | "colab": { 386 | "base_uri": "https://localhost:8080/", 387 | "height": 621 388 | }, 389 | "id": "-EA9bzBx6xGd", 390 | "outputId": "b1d3c7a1-dee2-4958-ea16-04cc72d5c037" 391 | }, 392 | "execution_count": 19, 393 | "outputs": [ 394 | { 395 | "output_type": "display_data", 396 | "data": { 397 | "text/plain": [ 398 | "
" 399 | ], 400 | "image/png": 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\n" 401 | }, 402 | "metadata": { 403 | "needs_background": "light" 404 | } 405 | } 406 | ] 407 | }, 408 | { 409 | "cell_type": "markdown", 410 | "source": [ 411 | "# Some thoughts/implications from the simulation\n", 412 | "Based on our full year historical MEV dataset, scaled to account for decreased mean block interval, we arrive at a simulated rate of return between around 5.7% and 8.5% for the \"middle 50%\" of validators. Meanwhile the \"luckiest 1%\" receive 30% APR, and the \"unluckiest 1%\" only 4.2%. The least profitable validator in the whole set still made a return of 3.8%, whilst the most profitable managed over 4500% (i.e. 45x) for the year. Bear in mind that the rates of return in this model are not compounded — in practice, operators earning such large returns may will choose to spin up new validators and therefore will begin earning a return on those too." 413 | ], 414 | "metadata": { 415 | "id": "gQrGOj8t9uL2" 416 | } 417 | } 418 | ] 419 | } --------------------------------------------------------------------------------