One Percent Every Day

1PctEveryDay.ipynb

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    "# One Percent Improvement Every Day\n",
    "\n",
    "### I came across the above phrase, and wondered:\n",
    "\n",
    "Given a very small starting number, and incrementing it by 1% a day, how many days does it take to get to the 100% mark?\n",
    "\n",
    "I am setting out to create a chart that maps the increase.\n",
    "\n",
    "For more information on this concept see: [Marginal gains philosophy](https://en.wikipedia.org/wiki/Dave_Brailsford?wprov=srpw1_0#'Marginal_gains'_philosophy)"
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    "##### Python 3.11"
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    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_percentages(percent_start, figsize=(10, 8)):\n",
    "    countBreak = 0\n",
    "    # percent_start = 0.01 # starting out with 2 decimal places (or 1-e2)\n",
    "    percent = percent_start\n",
    "    percentList = []\n",
    "    maxCountBreak = 1000000\n",
    "    while(percent <= 100.0 and countBreak <= 1000000):\n",
    "        countBreak += 1\n",
    "        # increment percent by 1%\n",
    "        percent *= 1.01\n",
    "        percentList.append(percent)\n",
    "        # print(f'{countBreak}: {percent:.8f}')\n",
    "    # print(f'{countBreak} days have passed')\n",
    "    # print(f'This is equivalent to {countBreak//365:.0f} years and {countBreak%365} days')\n",
    "\n",
    "    # Normalize percentList to the range 0 to 1\n",
    "    # max(percentList) gives the maximum value in percentList\n",
    "    percentListNormalized = [x / max(percentList) for x in percentList]\n",
    "\n",
    "    # Create a list of days from 0 to 1\n",
    "    daysNormalised = [x / len(percentList) for x in range(len(percentList))]\n",
    "\n",
    "    # Create a list of normalised years from 0 to len()/365\n",
    "    maxYears = (len(percentList)//365)\n",
    "    if len(percentList) % 365 > 0:\n",
    "        # +1 because we want to include the last year\n",
    "        maxYears += 1\n",
    "    yearsNormalised = [x / maxYears for x in range(maxYears)]\n",
    "\n",
    "    # Create a figure with a specific background color\n",
    "    fig, ax = plt.subplots(figsize=figsize)\n",
    "    fig.patch.set_facecolor('lightgray')  # Set figure background color\n",
    "    ax.set_facecolor('whitesmoke')        # Set axes background color\n",
    "\n",
    "    # Plot the line\n",
    "    ax.plot(daysNormalised, percentListNormalized, linestyle='-', color='cyan', linewidth=0.52)\n",
    "\n",
    "    # Plot the markers\n",
    "    ax.plot(daysNormalised, percentListNormalized, marker='+', linestyle='', color=(.5, 0.2, 0.1), markersize=2.5, linewidth=0.52)\n",
    "\n",
    "    # Add titles and labels\n",
    "    ax.set_title(f'Percentage Values Over {len(percentList)} Days ({len(percentList) / 365:.2f} Years) Starting from {percent_start}%', \n",
    "                fontsize=14)\n",
    "    ax.set_xlabel('Day of the Year', fontsize=11)\n",
    "    ax.set_ylabel('Percentage Value', fontsize=11)\n",
    "\n",
    "    # Set custom x-axis tick labels\n",
    "    num_ticks = 10  # Number of ticks you want on the x-axis\n",
    "    ticks = [i / num_ticks for i in range(num_ticks + 1)]\n",
    "    tick_labels = [f'{tick:.1f}\\n({(tick * len(percentList)) / 365:.2f}yr)' for tick in ticks]\n",
    "    ax.set_xticks(ticks)\n",
    "    ax.set_xticklabels(tick_labels, rotation=0, ha='right', fontsize=8)\n",
    "\n",
    "    # Set custom y-axis tick labels manually\n",
    "    y_ticks = [i / num_ticks for i in range(num_ticks + 1)]\n",
    "    y_tick_labels = [f'{tick * 100:.0f}%' for tick in y_ticks]\n",
    "    ax.set_yticks(y_ticks)\n",
    "    ax.set_yticklabels(y_tick_labels, fontsize=8)\n",
    "\n",
    "    # Set grid color\n",
    "    ax.grid(True, color='gray', linestyle='--', linewidth=0.5)\n",
    "\n",
    "    # Create a secondary x-axis\n",
    "    secax = ax.twiny()\n",
    "\n",
    "    # Set the same x-axis limits\n",
    "    secax.set_xlim(ax.get_xlim())\n",
    "\n",
    "    # Set secondary x-axis tick labels\n",
    "    sec_ticks = [i / maxYears for i in range(len(yearsNormalised))]\n",
    "    sec_tick_labels = [f'Year {id:.0f}' for id, tick in enumerate(sec_ticks)]\n",
    "    secax.set_xticks(sec_ticks)\n",
    "    secax.set_xticklabels(sec_tick_labels, color='darkred', fontsize=10)  # Custom text color and font size\n",
    "\n",
    "    # Show the plot\n",
    "    plt.show()"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_percentages(.0001, (12,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_percentages(.001, (12,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_percentages(.01, (12,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_percentages(.1, (12,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_percentages(1, (12,8))"
   ]
  }
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README.md

One Percent Improvement Every Day

python 3.11

I came across the above phrase

Given a very small starting number, and incrementing it by 1% how many days does it take to get to the 100% mark? I am setting out to create an increment chart.

For more information on this concept see: Marginal gains philosophy

From the code, I generated 5 graphs, each with different starting values from 0.0001% to 1%.

Here are the charts in ascending order of starting values.

percentGraphs.png

percentGraphs.psd