巫师融合法杖

游戏内描述

巫师融合法杖是深蓝工坊引擎产物

巫师融合法杖图标

巫师融合法杖的文本描述如下

描述文本

实测

实际测试中，左键攻击周期5gt，魔力消耗功率40mana/s，DPS 60，有效射程16m

右键技能实测与描述有较大出入，结论为

射弹预期每2gt生成一次，客户端在网络状况一般的情况下可能会看到N(2gt,1gt)的生成间隔

射弹持续生成4s，会生成41个，总计伤害4100，总周期21s，占空比19.0%

射弹CEP为2.39m——有50%的射弹会掉进以触发点为圆心半径2.39m的圆内，约2000点伤害

一个0.8x0.8m的区域，4s的预期伤害仅有71.3

使用python的数据分析流程如下，以供勘误：

通过录制一次完整的施法视频，放入视频编辑软件中逐帧读取，获取了原始数据：

vegas pro中的标记点，为粒子出现的第一帧

将测得数据输入jupyter notebook

import numpy as np

import matplotlib.pyplot as plt

#raw data

proj = np.array([[-0.5,-0.5],[-2.5,1.5],[-0.25,1.5],[1.9,-2],[-1,2],[2.2,2.1],[2.5,3.2],[0,-2],

[0,-1.5],[-1,-2],[-2.2,-0.5],[1,2],[1,2],[0.2,3],[-1.1,-1],[-1,0.5],

[-3,-0.1],[-1.5,0.5],[3,2.5],[0.25,-2.5],[-1,0.4],[ -1.5, -0.6],[2.4,0.6],[2.5,0],

[-0.5,-2.5],[1,0.5],[0.6,-1.2],[0.2,0],[2,-2.5],[3,-2.5],[-0.7,-0.5],[-0.3,1.5],

[-1,2.5],[2.5,-2.5],[-1.8,-2.4],[1.9,-0.9],[2.1,-0.6],[0.4,-1],[2.7,-2.2],[1.5,-1.4],[2.7,0.2]])

dt_in_frame = np.array([1,1,3,8,5,0,0,4,2,2,3,5,1,3,3,3,3,3,4,2,3,3,3,3,3,3,3,3,4,2,4,3,2,5,1,3,3,3,4,2,3])

print(proj.shape,dt_in_frame.size)

终端给出：(41, 2) 41，正确无误，接下来进行数据可视化，分别绘制弹着点散点图和射弹生成间隔直方图

t_array = 1/30.0*np.cumsum(dt_in_frame)

plt.figure(figsize=(10, 4))

plt.subplot(1, 2, 1)

plt.scatter(proj[:,0],proj[:,1],c="red",alpha=0.4)

plt.xlabel('rel x in m')

plt.ylabel('rel y in m')

plt.title('proj target pos scat')

plt.subplot(1, 2, 2)

plt.hist(dt_in_frame, bins=10, range=(0,10),alpha=0.7, color='blue', edgecolor='black', align='left')

plt.xlabel('dt in frame')

plt.ylabel('num')

plt.title('proj freq hist')

plt.show()

输出图像

分离各个射弹落点的x坐标和y坐标，分别绘制直方图，查看概率分布的关系，发现并非十分正态

projx = proj[:,0]

projy = proj[:,1]

plt.figure(figsize=(10, 4))

plt.subplot(1, 2, 1)

plt.hist(projx, bins=16, range=(-4,4),alpha=0.7, color='red', edgecolor='black', align='left')

plt.xlabel('proj x')

plt.ylabel('num')

plt.title('proj x hist')

plt.subplot(1, 2, 2)

plt.hist(projy, bins=16, range=(-4,4),alpha=0.7, color='green', edgecolor='black', align='left')

plt.xlabel('proj y')

plt.ylabel('num')

plt.title('proj y hist')

plt.show()

x，y直方图

尝试强行拟合为正态分布概率计算射弹落点的圆公算偏差，事实证明norm.fit方法没有考虑到样本的自由度减少，所以通过统计学方法计算样本方差的CEP会大一些

#norm fit and CEP

from scipy.stats import norm

from scipy.optimize import curve_fit

def N(x,mean,sig):

   return norm.pdf(x,mean,sig)

projx_cen = projx-np.mean(projx)

projy_cen = projy-np.mean(projy)

meanx, sigmax = norm.fit(projx_cen)

meany, sigmay = norm.fit(projy_cen)

#print(meanx,meany)

plt.figure(figsize=(10, 4))

plt.subplot(1, 2, 1)

plt.hist(projx_cen, bins=16, range=(-4,4),alpha=0.7, color='red', edgecolor='black', align='left',density = True)

x_lin = np.linspace(-4, 4, 100)

norm_curve_x = N(x_lin, meanx, sigmax)

plt.plot(x_lin, norm_curve_x, 'b--', label='fitted norm')

plt.xlabel('proj x')

plt.ylabel('num')

plt.title('proj x hist')

plt.subplot(1, 2, 2)

plt.hist(projy_cen, bins=16, range=(-4,4),alpha=0.7, color='green', edgecolor='black', align='left',density = True)

y_lin = np.linspace(-4, 4, 100)

norm_curve_y = N(y_lin, meany, sigmay)

plt.plot(y_lin, norm_curve_y, 'b--', label='fitted norm')

plt.xlabel('proj y')

plt.ylabel('num')

plt.title('proj y hist')

plt.show()

CEP_norm_fit = (sigmax**2+sigmay**2)**0.5

print("CEP from norm fit is",CEP_norm_fit)

# 1/n-1sum((x-xmean)^2)

sx = np.std(projx, ddof=1)

sy = np.std(projy, ddof=1)

CEP_from_raw = np.sqrt(sx**2 + sy**2)

print("CEP from norm raw is",CEP_from_raw)

终端输出：

CEP from norm fit is 2.3728843233284

CEP from norm raw is 2.4023622774667275

norm.fit的预测值与直方图

这个落点甚至有可能是均匀分布的，所以额外计算了均匀分布的CEP，同时绘制了三幅图像：正态拟合CEP与实际落点，统计学方差CEP与实际落点、均匀分布CEP与实际落点

#uniform reg

rangex = projx_cen.max()-projx_cen.min()

rangey = projy_cen.max()-projy_cen.min()

print(rangex,rangey)

#6x6 square uniform prob CEP:

CEP_uniform = (18/np.pi)**0.5

print("CEP form uniform is",CEP_uniform)

fig, axs = plt.subplots(1, 3, figsize=(12, 4))

plt.subplot(1, 3, 1)

plt.xlim(-4, 4)

plt.ylim(-4, 4)

axs[0].set_aspect('equal')

plt.scatter(projx_cen,projy_cen,c="blue",alpha=0.4)

circle = plt.Circle((0, 0), CEP_norm_fit, edgecolor='red', facecolor='none', linestyle='--', linewidth=2, label='CEP')

plt.gca().add_patch(circle)

plt.xlabel('rel x in m')

plt.ylabel('rel y in m')

plt.title(f'using CEP = {np.round(CEP_norm_fit,3)} norm fit, dof = 0')

plt.subplot(1, 3, 2)

plt.xlim(-4, 4)

plt.ylim(-4, 4)

axs[1].set_aspect('equal')

plt.scatter(projx_cen,projy_cen,c="blue",alpha=0.4)

circle = plt.Circle((0, 0), CEP_from_raw, edgecolor='red', facecolor='none', linestyle='--', linewidth=2, label='CEP')

plt.gca().add_patch(circle)

plt.xlabel('rel x in m')

plt.ylabel('rel y in m')

plt.title(f'using CEP = {np.round(CEP_from_raw,3)} sample var, dof = 1')

plt.subplot(1, 3, 3)

plt.xlim(-4, 4)

plt.ylim(-4, 4)

axs[2].set_aspect('equal')

plt.scatter(projx_cen,projy_cen,c="blue",alpha=0.4)

circle = plt.Circle((0, 0), CEP_uniform, edgecolor='red', facecolor='none', linestyle='--', linewidth=2, label='CEP')

plt.gca().add_patch(circle)

plt.xlabel('rel x in m')

plt.ylabel('rel y in m')

plt.title(f'using CEP = {np.round(CEP_uniform,3)} from U 6x6 dist')

plt.show()

CEP与实际落点

对dt进行线性回归，受限于网络，射弹在客户端看来并非平均生成，好在也没有non-constant variance现象发生

from sklearn.linear_model import LinearRegression

lm = LinearRegression()

x = np.arange(0, t_array.size).reshape(-1, 1)

lm.fit(x, t_array.reshape(-1, 1))

t_pred = lm.predict(x)

fig, axs = plt.subplots(1, 2, figsize=(8, 3))

plt.subplot(1, 2, 1)

plt.scatter(x, t_array, label='time data',alpha=0.5)

plt.plot(x, t_pred, 'r--', label='lm',alpha = 0.8)

plt.xlabel('# proj')

plt.ylabel('time in s')

plt.title("cum t - pred t")

plt.legend()

plt.subplot(1, 2, 2)

plt.plot(dt_in_frame/30.0,"rx",alpha = 0.7)

x_temp = np.arange(0,41)

y_temp = np.ones(41)*lm.coef_[0][0]

plt.plot(x_temp,y_temp,"b--",alpha = 0.5,label = "avg dt")

plt.legend()

plt.xlabel('# proj')

plt.ylabel('sec')

plt.title("dt - pred dt")

plt.show()

射弹生成间隔分析

打印射弹生成时长的分析：

print("Intercept:", lm.intercept_[0])

print("coef / avg proj dealta t:", lm.coef_[0][0])

print("std of dt is",np.std(dt_in_frame/30.0,ddof=1))

rpm = 1/lm.coef_[0][0] * 60

print("rpm =",rpm)

终端给出：

Intercept: 0.026248548199767185

coef / avg proj dealta t: 0.098281068524971

std of dt is 0.04761236886961931

rpm = 610.4939730560149