5.2 动机模型与付费意愿分层

{
  "version": 1,
  "note": "示例分层：付费率与 ARPPU 均为整数假设参数（ARPPU 单位为分）；真实分布需真实业务环境，命令行不可复现（X）",
  "tiers": [
    { "id": "social-free", "name": "社交白嫖型", "sharePermille": 420, "payRatePct": 0,  "arppuFen": 0 },
    { "id": "collector",   "name": "收集完成型", "sharePermille": 240, "payRatePct": 9,  "arppuFen": 1500 },
    { "id": "accelerator", "name": "效率加速型", "sharePermille": 160, "payRatePct": 14, "arppuFen": 2200 },
    { "id": "decorator",   "name": "装扮展示型", "sharePermille": 120, "payRatePct": 11, "arppuFen": 1800 },
    { "id": "competitor",  "name": "竞技攀比型", "sharePermille": 60,  "payRatePct": 18, "arppuFen": 3000 }
  ]
}

#!/usr/bin/env python3
# file: sim/ch05_motivation.py
# tier: S
# verify: /opt/homebrew/bin/python3 sim/ch05_motivation.py --config config/ --out out/
"""动机 → 付费意愿分层模型：读 config/ch05_motivation.json 的示例分层，
每层给出「占比（千分比）+ 付费率（整数百分比）+ ARPPU（分）」，算出
总体付费率、总体 ARPPU 与总体 ARPDAU，产出 JSON + CSV + SVG。
全程整数地板除，无浮点。

注意：付费率与 ARPPU 均为假设参数，真实分布需真实业务环境，命令行不可复现（X）。
"""

import argparse
import json
import os
import xml.etree.ElementTree as ET


def load_config(config_dir, name):
    with open(os.path.join(config_dir, name), encoding="utf-8") as f:
        return json.load(f)


def analyze(cfg):
    rows = cfg["tiers"]
    share_sum = sum(r["sharePermille"] for r in rows)
    # 每层的「付费权重」= 占比(‰) × 付费率(%)，单位是「‰·%」，全体加总后 //10 得整体付费率(‰)
    pay_weight = sum(r["sharePermille"] * r["payRatePct"] for r in rows)
    # 每层的收入权重 = 占比(‰) × 付费率(%) × ARPPU(分)，单位是「‰·%·分」
    rev_weight = sum(r["sharePermille"] * r["payRatePct"] * r["arppuFen"] for r in rows)

    payer_share_permille = pay_weight // 10          # 整体付费率，千分比
    arppu_fen = rev_weight // pay_weight if pay_weight else 0  # 付费用户平均 ARPPU（分）
    arpdau_fen = rev_weight // (1000 * 100)          # 全体日活 ARPDAU（分）

    per_tier = []
    for r in rows:
        contrib = r["sharePermille"] * r["payRatePct"] * r["arppuFen"] // (1000 * 100)
        per_tier.append(
            {
                "id": r["id"],
                "name": r["name"],
                "sharePermille": r["sharePermille"],
                "payRatePct": r["payRatePct"],
                "arppuFen": r["arppuFen"],
                "contributionFen": contrib,
            }
        )
    contrib_sum = sum(t["contributionFen"] for t in per_tier)
    return {
        "version": 1,
        "shareSumPermille": share_sum,
        "payerSharePermille": payer_share_permille,
        "arppuFen": arppu_fen,
        "arpdauFen": arpdau_fen,
        "contributionSumFen": contrib_sum,
        "roundingGapFen": arpdau_fen - contrib_sum,
        "tiers": per_tier,
    }


def write_svg(path, rows, title):
    W, H, pl, pr, pt, pb = 640, 360, 72, 24, 32, 56
    labels = [r["name"] for r in rows]
    values = [r["arppuFen"] for r in rows]
    hi = max(values) or 1
    iw, ih, n = W - pl - pr, H - pt - pb, len(labels)
    svg = ET.Element(
        "svg",
        {"xmlns": "http://www.w3.org/2000/svg", "viewBox": f"0 0 {W} {H}", "width": str(W), "height": str(H)},
    )
    ET.SubElement(svg, "rect", {"x": "0", "y": "0", "width": str(W), "height": str(H), "fill": "#ffffff"})
    t = ET.SubElement(svg, "text", {"x": str(pl), "y": "22", "font-size": "14", "fill": "#111827"})
    t.text = title
    ET.SubElement(svg, "line", {"x1": str(pl), "y1": str(pt + ih), "x2": str(W - pr), "y2": str(pt + ih), "stroke": "#9ca3af"})
    slot = iw // n
    bw = (iw // n) * 2 // 3
    for i, r in enumerate(rows):
        cx = pl + slot * i + slot // 2
        h = ih * values[i] // hi
        ET.SubElement(svg, "rect", {"x": str(cx - bw // 2), "y": str(pt + ih - h), "width": str(bw), "height": str(h), "fill": "#059669"})
        v = ET.SubElement(svg, "text", {"x": str(cx), "y": str(pt + ih - h - 6), "font-size": "11", "text-anchor": "middle", "fill": "#111827"})
        v.text = str(values[i])
        lab = ET.SubElement(svg, "text", {"x": str(cx), "y": str(H - pb + 18), "font-size": "11", "text-anchor": "middle", "fill": "#374151"})
        lab.text = labels[i]
        sh = ET.SubElement(svg, "text", {"x": str(cx), "y": str(H - pb + 34), "font-size": "10", "text-anchor": "middle", "fill": "#6b7280"})
        sh.text = f"{r['payRatePct']}%"
    xml = ET.tostring(svg, encoding="unicode")
    with open(path, "w", encoding="utf-8") as f:
        f.write(xml)
    ET.fromstring(xml)
    return len(xml.encode())


def main():
    ap = argparse.ArgumentParser()
    ap.add_argument("--config", default="config/")
    ap.add_argument("--out", default="out/")
    args = ap.parse_args()
    os.makedirs(args.out, exist_ok=True)
    cfg = load_config(args.config, "ch05_motivation.json")
    res = analyze(cfg)

    with open(os.path.join(args.out, "ch05_motivation.json"), "w", encoding="utf-8") as f:
        json.dump(res, f, ensure_ascii=False, indent=2)

    with open(os.path.join(args.out, "ch05_motivation.csv"), "w", encoding="utf-8") as f:
        f.write("id,name,sharePermille,payRatePct,arppuFen,contributionFen\n")
        for t in res["tiers"]:
            f.write(
                f"{t['id']},{t['name']},{t['sharePermille']},{t['payRatePct']},"
                f"{t['arppuFen']},{t['contributionFen']}\n"
            )

    size = write_svg(os.path.join(args.out, "ch05_motivation.svg"), res["tiers"], "《合成小岛》示例分层 ARPPU（分）")
    summary = {k: res[k] for k in ("payerSharePermille", "arppuFen", "arpdauFen", "contributionSumFen", "roundingGapFen")}
    print(json.dumps(summary, ensure_ascii=False))
    print(f"# svg bytes={size}")


if __name__ == "__main__":
    main()

/opt/homebrew/bin/python3 sim/ch05_motivation.py --config config/ --out out/
{"payerSharePermille": 680, "arppuFen": 2027, "arpdauFen": 137, "contributionSumFen": 136, "roundingGapFen": 1}
# svg bytes=1929