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@arfon
Created July 21, 2015 12:59
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Stitch Fix, Jupyter, GitHub, and the Long Tail\n",
"==\n",
"\n",
"At Stitch Fix we are avid users of Jupyter for research at both the personal and team scales. At the personal level, Jupyter is a great interface to research the question at hand. It captures the workflow of the research where we can take detailed notes on the code and explain models with written content and mathematical equations. \n",
"\n",
"At the team level, Jupyter is a great tool for communication. Notebooks allow one to fluidly mix text, code, equations, data, and plots in whatever way makes the most sense to explain something. You can organize your explanation around your thought process rather than around the artificial lines determined by the tools you’re using. You have a single Jupyter notebook instead of a bunch of disconnected files, one containing SQL code, another Python, a third LaTeX to typeset equations.\n",
"\n",
"When the analysis is finished, the Jupyter notebook remains a “living” interactive research notebook. Re-doing the analysis using new data or different assumptions is simple.\n",
"\n",
"Stitch Fix provides clothing to its clients based on their style preferences. We send a client five pieces of clothing we predict they’ll like, and the client chooses what to keep. Inevitably, some pieces of clothing will be more popular than others. In some cases, a few select items may be unpopular. \n",
"\n",
"The largest benefit from adding a single style of clothing to our line of inventory comes from the most popular one. Each of the less popular styles, by itself, contributes less. However, there are *many* of the less popular ones, reflecting the fact that our clients are unique in their fashion preferences. Together, the value in the \"long tail\" can match or exceed the value of the few products in the \"head.\" Catering to the long tail allows us to save our clients the time they would otherwise spend searching through many retail stores to find clothing that’s unique to their tastes.\n",
"\n",
"But, where do we draw the line on how far into the long tail we should support? Below we investigate this question using the Jupyter Notebook. The portability and flexibility of the Notebooks allows us to easily share the analysis with others. GitHub integration allows a great new possibility: other researches can fork the notebook to extend or alter the analysis according to their own particular interests!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Is the value in the head or the tail?\n",
"--\n",
"\n",
"We will approximate the number of each style of clothing sold as a power law of the rank $r$ by sales volume. The most popular style has $r=1$, the second most popular $r=2$, and the least popular has $r=N$. Consumer preferences dictate the shape of the curve. \n",
"\n",
"Even though we may want to carry an infinite number of styles of clothing, it's important to keep $N$ finite so that the integrals converge! For the moment we will consider a scaled-down version of Stitch Fix that only carrys 100 styles of clothing and sells a volume of $V=5,000$ units per year.\n",
"\n",
"The volume of each style sold is\n",
"\\begin{equation}\n",
"v(r) = \\frac{A}{r^n}\n",
"\\end{equation}\n",
"where $A$ is a normalization constant and $n$ is the index of the power law. The value of $n$ will determine how much value is in the head versus the tail.\n",
"\n",
"Approximating the product distribution as continuous so it can be written as an integral, the normalization constant is set by the constraint\n",
"\\begin{equation}\n",
"\\int_1^N \\frac{A\\,dr}{r^n} = V\n",
"\\end{equation}\n",
"so\n",
"\\begin{equation}\n",
"A = \\frac{(n-1) V}{1-N^{1-n}} \n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"\n",
"%matplotlib inline\n",
"sns.set_context('talk')\n",
"sns.set_style('darkgrid')"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 100)"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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A+TDw76XDWmQwEzPM9G/gCUwwOsNv8UTrdCU3YT78X8SsdLwPE4z6a90T0dbOAf73XoGZ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wl397Td6f7tUL9OJbULNgl1rUmoC6CtPDB5nsfJY1f52pdOMTdjemLq4e6eF++Vt1KswXb9YmkE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\nQogOIKFOCCGEEKIDSKgTQgghhOgA/x8/FDWWkr4mxQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cb2e210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"inventory = 100.0\n",
"volume = 5000.0\n",
"\n",
"rr = np.linspace(1,inventory,100)\n",
"ns = [0.25, 0.75, 1.25, 1.75]\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
"for nn in ns:\n",
" norm = (nn-1)*volume/(1-inventory**(1-nn))\n",
" ax.plot(rr, norm/rr**nn, label='$n=%g$' % nn)\n",
"\n",
"ax.legend()\n",
"ax.set_xlabel('Rank by Sales Volume $r$')\n",
"ax.set_ylabel('Units Sold')\n",
"ax.set_title('Sales volume of each product by rank')\n",
"ax.set_ylim(0,100)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"All of these distributions have the same area under the curve, so they represent the same total number of units sold. Smaller values of $n$ give flatter distributions (less head, more tail) and larger values of $n$ give more head-heavy distributions.\n",
"\n",
"What is the _total_ value in the head versus the tail? Define the head to be the 10% of styles with the largest sales volume, the tail to be the 50% of styles with the lowest sales volumes, and the middle to be those in between.\n",
"\n",
"That is, the head, tail, and middle look like this:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10ba6ba50>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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9jdQX1qVR2rnNsv8d6z45ZlB3tOt4wnJwQ93VWJNUdJslUysDKa4jhJjdCrdc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\nIYToA/8ftMGJXA/315QAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c06ba90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same plot as above\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
"for nn in ns:\n",
" norm = (nn-1)*volume/(1-inventory**(1-nn))\n",
" ax.plot(rr, norm/rr**nn, label='$n=%g$' % nn)\n",
"\n",
"ax.set_xlabel('Rank by Sales Volume $r$')\n",
"ax.set_ylabel('Units Sold')\n",
"ax.set_title('Sales volume of each product by rank')\n",
"ax.set_ylim(0,100)\n",
"\n",
"# Ask seaborn for some pleasing colors\n",
"c1, c2, c3 = sns.color_palette(n_colors=3)\n",
"\n",
"# Add transparent rectangles\n",
"head_patch = plt.matplotlib.patches.Rectangle((1,0), 9, 100, alpha=0.25, color=c1)\n",
"middle_patch = plt.matplotlib.patches.Rectangle((11,0), 39, 100, alpha=0.25, color=c2)\n",
"tail_patch = plt.matplotlib.patches.Rectangle((51,0), 48, 100, alpha=0.25, color=c3)\n",
"ax.add_patch(head_patch)\n",
"ax.add_patch(middle_patch)\n",
"ax.add_patch(tail_patch)\n",
"\n",
"# Add text annotations\n",
"ax.text(5,50,\"Head\", color=c1, fontsize=16, rotation=90)\n",
"ax.text(25,80,\"Middle\", color=c2, fontsize=16)\n",
"ax.text(75,80,\"Tail\", color=c3, fontsize=16)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How many units from the head, tail, and middle are sold? Integrate over the sales rank distribution to get the sales volume in the head:\n",
"\n",
"\\begin{equation}\n",
"V_H = \\int_1^{f_H N} \\frac{A\\, dr}{r^n} = \\frac{V(N^{n-1} - f_H^{1-n})}{N^{n-1} - 1}\n",
"\\end{equation}\n",
"where $f_H=0.1$\n",
"\n",
"The volume in the tail is\n",
"\n",
"\\begin{equation}\n",
"V_T = \\int_{f_T N}^N \\frac{A\\, dr}{r^n} = \\frac{V(f_T^{1-n}-1)}{N^{n-1}-1}\n",
"\\end{equation}\n",
"where $f_T=0.5$\n",
"\n",
"And the middle:\n",
"\n",
"\\begin{equation}\n",
"V_M = \\int_{f_H N}^{f_T N} \\frac{A\\, dr}{r^n} = \\frac{V(f_H^{1-n} - f_T^{1-n})}{N^{n-1}-1}\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10c06bf90>"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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zhK2mnObWYMc+t8vB9PG5XDFlKNPH55Csa/S6RUVfjOxgkEBVVVxey5OdjcP93v5r2pfV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\naGmLLKN21dR8PrpkIj6vJ6b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V+2lw1mE0yBXeVCKhT8RLQl/iJPSJuDyvY474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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c3125d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"f_head = 0.1\n",
"f_tail = 0.5\n",
"\n",
"ns = np.linspace(0,2,100)\n",
"nm1 = ns-1.0\n",
"\n",
"head = volume*(inventory**nm1 - f_head**-nm1)/(inventory**nm1-1)\n",
"middle = volume*(f_head**-nm1 - f_tail**-nm1)/(inventory**nm1-1)\n",
"tail = volume*(f_tail**-nm1 - 1)/(inventory**nm1-1)\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
"ax.plot(ns, head, label='Head')\n",
"ax.plot(ns, middle, label='Middle')\n",
"ax.plot(ns, tail, label='Tail')\n",
"ax.legend(loc='upper left')\n",
"ax.set_ylabel('Units Sold')\n",
"ax.set_xlabel('Power law index $n$')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For $n>1$, the head has most of value. As $n$ falls, the middle and tail become important."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How many styles of clothing should we carry?\n",
"--\n",
"\n",
"We can choose expand our inventory from $N$ to $N+1$ styles of clothing. How many additional units will we sell?\n",
"\n",
"This is just the sales volume distribution $n(r)$ evaluated at $r=N+1$\n",
"\n",
"\\begin{equation}\n",
"\\frac{d V}{d N} = \\frac{(n-1) V}{(1-N^{1-n})(N+1)^n} \n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10c0cc8d0>"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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6GRVvxYmJCVC/fi2qW65I6ShfxC/lioTCy5dSN7v5HuNmjLkQuBM3aSAOsMCz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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c91c190>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"marginal_benefit = ((ns-1)*volume)/((1-inventory**(1-ns))*(inventory+1)**ns)\n",
"\n",
"fig, ax = plt.subplots(figsize=(10, 6))\n",
"\n",
"ax.plot(ns, marginal_benefit)\n",
"ax.set_ylabel('Additional Units Sold')\n",
"ax.set_xlabel('Power law index $n$')\n",
"ax.set_title('Marginal Benefit of Expanding Inventory')"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"Our scaled down version of Stitch Fix can expect to sell an additional $\\simeq 40$ pieces of clothing per year if the sales distribution has $n=0.25$, or an additional $\\simeq 3$ units per year if $n=1.5$ Whether expanding the inventory is worth it to get those additional sales depends entirely on how much it costs to bring one additional product into the inventory.\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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