Elo ranking scheme

elo.ipynb

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    "import typing, math"
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   "source": [
    "class Elo(typing.NamedTuple):\n",
    "  ratings: dict[typing.Any, float]\n",
    "  K: float = 30.\n",
    "\n",
    "  def log(self, winner, loser):\n",
    "    \"log a game returning a new Elo object\"\n",
    "    # compute win/lose probabilities\n",
    "    p1 = (1 / (1 + 10 ** ((self.ratings[winner] - self.ratings[loser]) / 400)))\n",
    "    p2 = (1 / (1 + 10 ** ((self.ratings[loser] - self.ratings[winner]) / 400)))\n",
    "    \n",
    "    # update probabilities\n",
    "    update = {winner: self.ratings[winner] + self.K * (1 - p2),\n",
    "              loser: self.ratings[loser] + self.K * (0 - p1)}\n",
    "\n",
    "    # construct result\n",
    "    res = dict(self.ratings) # copy existing dict\n",
    "    res.update(update)\n",
    "    return Elo(res, K=self.K)"
   ]
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      "text/plain": [
       "Elo(ratings={'A': 1200, 'B': 1000, 'C': 800}, K=30.0)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env = Elo({\"A\": 1200, \"B\": 1000, \"C\": 800})\n",
    "env"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "86ca1bea-a211-4538-84f7-8f5409de4989",
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   "source": [
    "winner, loser = \"B\", \"A\""
   ]
  },
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    {
     "data": {
      "text/plain": [
       "{'B': 1022.7924077994387, 'A': 1177.2075922005613}"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute win/lose probabilities\n",
    "p1 = (1 / (1 + 10 ** ((env.ratings[winner] - env.ratings[loser]) / 400)))\n",
    "p2 = (1 / (1 + 10 ** ((env.ratings[loser] - env.ratings[winner]) / 400)))\n",
    "\n",
    "# update probabilities\n",
    "{winner: env.ratings[winner] + env.K * (1 - p2),\n",
    " loser: env.ratings[loser] + env.K * (0 - p1)}"
   ]
  },
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   "execution_count": 81,
   "id": "06eb7747-2010-4355-8ad5-0e035b9ee40e",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Elo(ratings={'A': 1110.060653079418, 'B': 1063.7227544923412, 'C': 826.2165924282407}, K=30.0)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "env.log(winner, loser).log(winner, loser).log(winner, loser).log(\"C\", \"A\")"
   ]
  }
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