{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b1639ce9",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "# Straight Shot Difficulty\n",
    "\n",
    "Consider a straight shot into a pocket where the cue ball (CB) is a total distance $D$ from the pocket. Which object ball (OB) position (distance $d$ from the CB) results in the most difficult pot?\n",
    "\n",
    "This question is posed by Dr. Dave Billiards in [this proof](https://billiards.colostate.edu/technical_proofs/TP_3-4.pdf) and based on the assumptions made, the answer is\n",
    "\n",
    "$$\n",
    "d = D/2\n",
    "$$\n",
    "\n",
    "In other words, the shot is made most difficult when the OB is placed equidistantly from both the pocket and the CB.\n",
    "\n",
    "In this example, we will directly simulate straight shots and determine under what circumstances this theory holds up."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d36cdb8d",
   "metadata": {},
   "source": [
    "## Setting up a system\n",
    "\n",
    "Let's set up a system where the OB is shot into a corner pocket _straight on_ (at an angle of 45 degrees from both the long cushion and short cushion).\n",
    "\n",
    "We'll begin by creating a big square [Table](../autoapi/pooltool/index.rst#pooltool.Table) that gives us plenty of space. There are many different parameters that can be passed to [PocketTableSpecs](../autoapi/pooltool/objects/index.rst#pooltool.objects.PocketTableSpecs) that influence the shape of the pockets (you can get a visual explanation of each parameter [here](../resources/table_specs.md)), but here we will keep the default values, which are modelled after my old 7-foot Showood table with pretty wide 5 inch pockets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e936c90f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:01.999331Z",
     "iopub.status.busy": "2025-06-02T02:35:01.998945Z",
     "iopub.status.idle": "2025-06-02T02:35:02.789524Z",
     "shell.execute_reply": "2025-06-02T02:35:02.788689Z"
    }
   },
   "outputs": [],
   "source": [
    "import pooltool as pt\n",
    "\n",
    "table_specs = pt.objects.PocketTableSpecs(l=10, w=10)\n",
    "table = pt.Table.from_table_specs(table_specs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "800e6f5e",
   "metadata": {},
   "source": [
    "As a reminder, $D$ represents the distance of the CB to the pocket, but let's be a little more precise with what that means. From the CB, we will measure from the ball's center, and from the pocket we will measure from pocket's edge that's closest to the CB. So when $D$ is 0, the CB is teetering on the edge of the pocket.\n",
    "\n",
    "With that in mind, let's pick the bottom-left corner [Pocket](../autoapi/pooltool/objects/index.rst#pooltool.objects.Pocket) as our target and place a CB a distance $D$ away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1aff3ee3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:02.793592Z",
     "iopub.status.busy": "2025-06-02T02:35:02.792866Z",
     "iopub.status.idle": "2025-06-02T02:35:02.798416Z",
     "shell.execute_reply": "2025-06-02T02:35:02.797681Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The pocket point is [0.0595383909759073 0.0595383909759073]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# lb stands for left-bottom\n",
    "pocket = table.pockets[\"lb\"]\n",
    "\n",
    "# The pocket's center is defined with 3D coordinates, but we'll just use X and Y\n",
    "center = pocket.center[:2]\n",
    "\n",
    "pocket_point = center + pocket.radius * np.sqrt(2)\n",
    "\n",
    "print(f\"The pocket point is {pocket_point}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ce62613",
   "metadata": {},
   "source": [
    "Now let's create a cue ball a distance $D$ away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "15884154",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:02.801238Z",
     "iopub.status.busy": "2025-06-02T02:35:02.800995Z",
     "iopub.status.idle": "2025-06-02T02:35:03.152126Z",
     "shell.execute_reply": "2025-06-02T02:35:03.151320Z"
    }
   },
   "outputs": [],
   "source": [
    "D = 1.0\n",
    "\n",
    "def create_cue_ball(pocket_point, D):\n",
    "    cue_point = pocket_point + D * np.sqrt(2)\n",
    "    return pt.Ball.create(\"CB\", xy=cue_point)\n",
    "\n",
    "cue_ball = create_cue_ball(pocket_point, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "704f82e8",
   "metadata": {},
   "source": [
    "Let's create an object ball a distance $d$ from the cue ball. In order for the object ball to be between the cue and the pocket, $d$ is constrained by\n",
    "\n",
    "$$\n",
    "2 R \\lt d \\lt D\n",
    "$$\n",
    "\n",
    "where $R$ is the radius of the balls."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9587ae3e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.155477Z",
     "iopub.status.busy": "2025-06-02T02:35:03.155105Z",
     "iopub.status.idle": "2025-06-02T02:35:03.159459Z",
     "shell.execute_reply": "2025-06-02T02:35:03.158788Z"
    }
   },
   "outputs": [],
   "source": [
    "def create_object_ball(cue_ball, d):\n",
    "    obj_point = cue_ball.xyz[:2] - d * np.sqrt(2)\n",
    "    return pt.Ball.create(\"OB\", xy=obj_point)\n",
    "\n",
    "d = 0.3\n",
    "\n",
    "obj_ball = create_object_ball(cue_ball, d)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95351ff2",
   "metadata": {},
   "source": [
    "Let's go ahead and turn everything we've done into a function that takes $d$ and $D$ as parameters and returns a [System](../autoapi/pooltool/index.rst#pooltool.System)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d6e40365",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.162651Z",
     "iopub.status.busy": "2025-06-02T02:35:03.162358Z",
     "iopub.status.idle": "2025-06-02T02:35:03.166447Z",
     "shell.execute_reply": "2025-06-02T02:35:03.165932Z"
    }
   },
   "outputs": [],
   "source": [
    "def create_system(d, D):\n",
    "    table_specs = pt.objects.PocketTableSpecs(l=10, w=10)\n",
    "    table = pt.Table.from_table_specs(table_specs)       \n",
    "    pocket = table.pockets[\"lb\"]\n",
    "    pocket_point = pocket.center[:2] + pocket.radius * np.sqrt(2)\n",
    "\n",
    "    cue_ball = create_cue_ball(pocket_point, D)\n",
    "    obj_ball = create_object_ball(cue_ball, d)\n",
    "\n",
    "    return pt.System(\n",
    "        cue=pt.Cue(cue_ball_id=\"CB\"),\n",
    "        balls=(cue_ball, obj_ball),\n",
    "        table=table,\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a0670b",
   "metadata": {},
   "source": [
    "With this function, we can create a system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "404172c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.169250Z",
     "iopub.status.busy": "2025-06-02T02:35:03.168941Z",
     "iopub.status.idle": "2025-06-02T02:35:03.172905Z",
     "shell.execute_reply": "2025-06-02T02:35:03.172349Z"
    }
   },
   "outputs": [],
   "source": [
    "system = create_system(d, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42e69fe",
   "metadata": {},
   "source": [
    "If you have a graphics card, you can visualize the system in 3D with\n",
    "\n",
    "```python\n",
    "pt.show(system)\n",
    "```\n",
    "\n",
    "## Simulating a shot\n",
    "\n",
    "No energy has been imparted into the system so it's currently rather dull. Let's change that by striking the CB in the direction of the OB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "58e960a9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.176029Z",
     "iopub.status.busy": "2025-06-02T02:35:03.175682Z",
     "iopub.status.idle": "2025-06-02T02:35:03.254751Z",
     "shell.execute_reply": "2025-06-02T02:35:03.253926Z"
    }
   },
   "outputs": [],
   "source": [
    "# phi is the aiming direction\n",
    "phi = pt.aim.at_ball(cue_ball=system.balls[\"CB\"], object_ball=system.balls[\"OB\"], cut=0)\n",
    "\n",
    "# Based on the geometry, we know that phi is 225 degrees (towards the bottom-left pocket)\n",
    "assert phi == 225.0\n",
    "\n",
    "system.cue.set_state(V0=1, phi=phi, cue_ball_id=\"CB\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29da653d",
   "metadata": {},
   "source": [
    "Since the pocket, OB, and CB are all lined up, this should lead to a successful pot. Let's check by simulating and filtering the system events according to our criteria."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dd1cd57e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.258288Z",
     "iopub.status.busy": "2025-06-02T02:35:03.257996Z",
     "iopub.status.idle": "2025-06-02T02:35:03.466738Z",
     "shell.execute_reply": "2025-06-02T02:35:03.466200Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pt.simulate(system, inplace=True)\n",
    "\n",
    "def successful_pot(system) -> bool:\n",
    "    # Find events that are ball-pocket events and involve the object ball\n",
    "    pocket_events = pt.events.filter_events(\n",
    "        system.events,\n",
    "        pt.events.by_type(pt.EventType.BALL_POCKET),\n",
    "        pt.events.by_ball(\"OB\"),\n",
    "    )\n",
    "    return bool(len(pocket_events))    \n",
    "\n",
    "successful_pot(system)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60ec5314",
   "metadata": {},
   "source": [
    "Great! As expected, it went straight in."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d31587ee",
   "metadata": {},
   "source": [
    "## Modeling imprecision\n",
    "\n",
    "Real pool players don't have perfect precision and we are going to emulate this by introducing uncertainty into the aiming angle $\\phi$. We'll call this uncertainty $d\\phi$.\n",
    "\n",
    "While we're at it, let's make a function that adds uncertainty not just to $\\phi$, but to the other cue striking parameters as well, that you can read about [here](../autoapi/pooltool/index.rst#pooltool.Cue)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "cd733141",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.469959Z",
     "iopub.status.busy": "2025-06-02T02:35:03.469622Z",
     "iopub.status.idle": "2025-06-02T02:35:03.474137Z",
     "shell.execute_reply": "2025-06-02T02:35:03.473495Z"
    }
   },
   "outputs": [],
   "source": [
    "def perturb(x, dx):\n",
    "    return x + dx * (2*np.random.rand() - 1)\n",
    "\n",
    "def strike(system, V0, a, phi, theta, dV0=0, da=0, dphi=0, dtheta=0):\n",
    "    system.cue.set_state(\n",
    "        cue_ball_id=\"CB\",\n",
    "        V0=perturb(V0, dV0),\n",
    "        a=perturb(a, da),\n",
    "        phi=perturb(phi, dphi),\n",
    "        theta=perturb(theta, dtheta),\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1dad881",
   "metadata": {},
   "source": [
    "## Estimating Difficulty for a Given $d$\n",
    "\n",
    "To evaluate the difficulty level associated with shot where the OB is a distance $d$ from the CB, we will calculate the fraction of successful pots (successful shots) from a set of trials. In these trials, we will introduce random perturbations to the angle $\\phi$ for each shot. The perturbations are limited so that the angle $\\phi$ deviates by no more than a fixed amount $d\\phi$.\n",
    "\n",
    "This means that for each shot, the angle $\\phi$ is randomly adjusted within the range $[\\phi - d\\phi, \\phi + d\\phi]$. By observing how these perturbations affect the success rate, we can estimate the difficulty associated with the given $d$.\n",
    "\n",
    "Let's pick a $d\\phi$ and then simulate 100 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ee0d1e66",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:03.477157Z",
     "iopub.status.busy": "2025-06-02T02:35:03.476854Z",
     "iopub.status.idle": "2025-06-02T02:35:04.001083Z",
     "shell.execute_reply": "2025-06-02T02:35:04.000450Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The success rate is 44%.\n"
     ]
    }
   ],
   "source": [
    "dphi = 0.4  # Just 0.4 degrees!\n",
    "phi = 225.0\n",
    "V0 = 1.0  # 1 m/s cue-stick strike\n",
    "a = 0  # No sidespin\n",
    "theta = 0  # Level cue stick\n",
    "d = 0.3\n",
    "D = 1.0\n",
    "\n",
    "num_trials = 100\n",
    "successes = []\n",
    "for _ in range(num_trials):\n",
    "    system = create_system(d, D)\n",
    "    strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "    pt.simulate(system, inplace=True)\n",
    "    success = successful_pot(system)\n",
    "    successes.append(success)\n",
    "\n",
    "pot_fraction = sum(successes) / len(successes)\n",
    "print(f\"The success rate is {pot_fraction*100:.0f}%.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "315fd227",
   "metadata": {},
   "source": [
    "## Which $d$ yields the most difficult shot?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1df8f50a",
   "metadata": {},
   "source": [
    "Great. Now, we can run the same experiment, but vary $d$ to determine which yields the most difficult shot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3a989057",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:04.004227Z",
     "iopub.status.busy": "2025-06-02T02:35:04.003927Z",
     "iopub.status.idle": "2025-06-02T02:35:31.882395Z",
     "shell.execute_reply": "2025-06-02T02:35:31.881553Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.06 m, the success rate is 100%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.14 m, the success rate is 90%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.23 m, the success rate is 55%.\n",
      "For d = 0.31 m, the success rate is 46%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.40 m, the success rate is 33%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.49 m, the success rate is 36%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.57 m, the success rate is 33%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.66 m, the success rate is 36%.\n",
      "For d = 0.74 m, the success rate is 43%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.83 m, the success rate is 56%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 0.91 m, the success rate is 94%.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For d = 1.00 m, the success rate is 100%.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Vary from 1mm separation between CB and OB to 1mm from pocket's edge\n",
    "d_values = np.linspace(2.001*cue_ball.params.R, D-0.001, 12)\n",
    "\n",
    "num_trials = 400\n",
    "pot_fractions = []\n",
    "\n",
    "for d in d_values:\n",
    "    successes = []\n",
    "    for _ in range(num_trials):\n",
    "        system = create_system(d, D)\n",
    "        strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "        pt.simulate(system, inplace=True)\n",
    "        success = successful_pot(system)\n",
    "        successes.append(success)\n",
    "\n",
    "    pot_fraction = sum(successes) / len(successes)\n",
    "    pot_fractions.append(pot_fraction)\n",
    "    print(f\"For d = {d:.2f} m, the success rate is {pot_fraction*100:.0f}%.\")\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(d_values, pot_fractions, marker='o')\n",
    "plt.xlabel('Distance d (m)')\n",
    "plt.ylabel('Success Rate')\n",
    "plt.title('Success Rate vs. Distance d')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c9119af",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    }
   },
   "source": [
    "Reading left to right, shot success starts high because the OB is close to the CB. But as the OB moves further away from the CB, the success rate decreases, reaching a minimum at around $D/2$. Past this point, the success rate starts to go up again, since the OB is now getting closer and closer to the pocket.\n",
    "\n",
    "Since this data is generated from a small number of trials, there is some variance in the plot, but if you increase `num_trials` the curve smooths."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed7c0e05",
   "metadata": {},
   "source": [
    "## What about skill level?\n",
    "\n",
    "Since $d\\phi$ is a measure of how precise the shot is, it is a reasonable proxy for skill level. With that in mind, how should we expect the shot success trajectory to vary as a function of skill level? Let's repeat the experiment for 3 different skill levels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5d781ff9",
   "metadata": {
    "editable": true,
    "execution": {
     "iopub.execute_input": "2025-06-02T02:35:31.887904Z",
     "iopub.status.busy": "2025-06-02T02:35:31.887293Z",
     "iopub.status.idle": "2025-06-02T02:36:54.575632Z",
     "shell.execute_reply": "2025-06-02T02:36:54.574932Z"
    },
    "slideshow": {
     "slide_type": ""
    },
    "tags": [
     "nbsphinx-gallery"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.15\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.25\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Finished dphi=0.5\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the range of 'd' values you want to test\n",
    "d_values = np.linspace(2.001 * cue_ball.params.R, D - 0.001, 12)\n",
    "\n",
    "# Define the range of 'dphi' values (in degrees)\n",
    "dphi_values = [0.15, 0.25, 0.5]\n",
    "\n",
    "num_trials = 400\n",
    "results = {}\n",
    "\n",
    "for dphi in dphi_values:\n",
    "    pot_fractions = []\n",
    "    for d in d_values:\n",
    "        successes = []\n",
    "        for _ in range(num_trials):\n",
    "            system = create_system(d, D)\n",
    "            strike(system, V0, a, phi, theta, dphi=dphi)\n",
    "            pt.simulate(system, inplace=True)\n",
    "            success = successful_pot(system)\n",
    "            successes.append(success)\n",
    "\n",
    "        pot_fraction = sum(successes) / len(successes)\n",
    "        pot_fractions.append(pot_fraction)\n",
    "        \n",
    "    print(f\"Finished {dphi=}\")\n",
    "    results[dphi] = pot_fractions\n",
    "\n",
    "plt.figure(figsize=(8, 6))\n",
    "for dphi in dphi_values:\n",
    "    plt.plot(d_values, results[dphi], marker='o', label=f'dphi = {dphi}°')\n",
    "\n",
    "plt.xlabel('Distance d (m)')\n",
    "plt.ylabel('Success Rate')\n",
    "plt.title('Success Rate vs. Distance d for Different Skill (dphi) Values')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3a6acf6",
   "metadata": {},
   "source": [
    "Regardless of skill level, when $\\lim_{d \\rightarrow 2R^{+}}$ and $\\lim_{d \\rightarrow D^{-}}$, the success rate converges to $100\\%$. That's expected—when the object ball OB is practically touching the CB or hanging over the pocket, potting becomes nearly automatic for all skill levels. \n",
    "\n",
    "But what’s more interesting is observing the extent and sharpness with which success rate drops when the OB is at an intermediate distance $d$. The least skilled players experience the earliest, sharpest, and lowest plummet in sucess rate, whereas high skilled players maintain higher success rate for longer. Yet no matter the skill, the minimum seems to be right at around $d=D/2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "19c96b60",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "jupytext": {
   "notebook_metadata_filter": "all"
  },
  "kernelspec": {
   "display_name": "pooltool-dev",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}