摘要：本文意在創(chuàng)建一個(gè)得分圖，該圖同時(shí)描繪了從場上不同位置投籃得分的百分比和投籃次數(shù)，這和個(gè)人網(wǎng)站上的帖子類似。接下來，我們需要繪制一個(gè)包含得分圖的籃球場圖。球員照片會出現(xiàn)在得分圖的右下角。的解決辦法是將命中率與聯(lián)賽平均分關(guān)聯(lián)。

本文意在創(chuàng)建一個(gè)得分圖，該圖同時(shí)描繪了從場上不同位置投籃得分的百分比和投籃次數(shù)，這和 Austin Clemen 個(gè)人網(wǎng)站上的帖子 http://www.austinclemens.com/shotcharts/ 類似 。

為了實(shí)現(xiàn)這個(gè)得分圖，筆者參考了 Savvas Tjortjoglou 的帖子 http://savvastjortjoglou.com/nba-shot-sharts.html。這篇帖子很棒，但是他只描述了從不同位置投籃的次數(shù)。而筆者對在不同位置的投籃次數(shù)和進(jìn)球百分比都很感興趣，所以還需要進(jìn)一步的工作，在原有基礎(chǔ)上添加些東西，下面是實(shí)現(xiàn)過程。

#import some libraries and tell ipython we want inline figures rather than interactive figures. 
%matplotlib inline
import matplotlib.pyplot as plt, pandas as pd, numpy as np, matplotlib as mpl

首先，我們需要獲得每個(gè)球員的投籃數(shù)據(jù)。利用 Savvas Tjortjoglou 貼出的代碼，筆者從 NBA.com 網(wǎng)站 API 上獲取了數(shù)據(jù)。在此不會貼出這個(gè)函數(shù)的結(jié)果。如果你感興趣，推薦你去看看 Savvas Tjortjoglou 的博客。

def aqcuire_shootingData(PlayerID,Season):
    import requests
    shot_chart_url = "http://stats.nba.com/stats/shotchartdetail?CFID=33&CFPARAMS="+Season+"&ContextFilter="
                    "&ContextMeasure=FGA&DateFrom=&DateTo=&GameID=&GameSegment=&LastNGames=0&LeagueID="
                    "00&Location=&MeasureType=Base&Month=0&OpponentTeamID=0&Outcome=&PaceAdjust="
                    "N&PerMode=PerGame&Period=0&PlayerID="+PlayerID+"&PlusMinus=N&Position=&Rank="
                    "N&RookieYear=&Season="+Season+"&SeasonSegment=&SeasonType=Regular+Season&TeamID="
                    "0&VsConference=&VsDivision=&mode=Advanced&showDetails=0&showShots=1&showZones=0"
    response = requests.get(shot_chart_url)
    headers = response.json()["resultSets"][0]["headers"]
    shots = response.json()["resultSets"][0]["rowSet"]
    shot_df = pd.DataFrame(shots, columns=headers)
    return shot_df

接下來，我們需要繪制一個(gè)包含得分圖的籃球場圖。該籃球場圖例必須使用與NBA.com API 相同的坐標(biāo)系統(tǒng)。例如，3分位置的投籃距籃筐必須為 X 單位，上籃距離籃筐則是 Y 單位。同樣，筆者再次使用了 Savvas Tjortjoglou 的代碼（哈哈，否則的話，搞明白 NBA.com 網(wǎng)站的坐標(biāo)系統(tǒng)肯定會耗費(fèi)不少的時(shí)間）。

def draw_court(ax=None, color="black", lw=2, outer_lines=False):
    from matplotlib.patches import Circle, Rectangle, Arc
    if ax is None:
        ax = plt.gca()
    hoop = Circle((0, 0), radius=7.5, linewidth=lw, color=color, fill=False)
    backboard = Rectangle((-30, -7.5), 60, -1, linewidth=lw, color=color)
    outer_box = Rectangle((-80, -47.5), 160, 190, linewidth=lw, color=color,
                          fill=False)
    inner_box = Rectangle((-60, -47.5), 120, 190, linewidth=lw, color=color,
                          fill=False)
    top_free_throw = Arc((0, 142.5), 120, 120, theta1=0, theta2=180,
                         linewidth=lw, color=color, fill=False)
    bottom_free_throw = Arc((0, 142.5), 120, 120, theta1=180, theta2=0,
                            linewidth=lw, color=color, linestyle="dashed")
    restricted = Arc((0, 0), 80, 80, theta1=0, theta2=180, linewidth=lw,
                     color=color)
    corner_three_a = Rectangle((-220, -47.5), 0, 140, linewidth=lw,
                               color=color)
    corner_three_b = Rectangle((220, -47.5), 0, 140, linewidth=lw, color=color)
    three_arc = Arc((0, 0), 475, 475, theta1=22, theta2=158, linewidth=lw,
                    color=color)
    center_outer_arc = Arc((0, 422.5), 120, 120, theta1=180, theta2=0,
                           linewidth=lw, color=color)
    center_inner_arc = Arc((0, 422.5), 40, 40, theta1=180, theta2=0,
                           linewidth=lw, color=color)
    court_elements = [hoop, backboard, outer_box, inner_box, top_free_throw,
                      bottom_free_throw, restricted, corner_three_a,
                      corner_three_b, three_arc, center_outer_arc,
                      center_inner_arc]
    if outer_lines:
        outer_lines = Rectangle((-250, -47.5), 500, 470, linewidth=lw,
                                color=color, fill=False)
        court_elements.append(outer_lines)

    for element in court_elements:
        ax.add_patch(element)

    ax.set_xticklabels([])
    ax.set_yticklabels([])
    ax.set_xticks([])
    ax.set_yticks([])
    return ax

我想創(chuàng)造一個(gè)不同位置的投籃百分比數(shù)組，因此決定利用 matplot 的 Hexbin 函數(shù) http://matplotlib.org/api/pyplot_api.html 將投籃位置均勻地分組到六邊形中。該函數(shù)會對每個(gè)六邊形中每一個(gè)位置的投籃次數(shù)進(jìn)行計(jì)數(shù)。

六邊形是均勻的分布在 XY 網(wǎng)格中。「gridsize」變量控制六邊形的數(shù)目?！竐xtent」變量控制第一個(gè)和最后一個(gè)六邊形的繪制位置（一般來說第一個(gè)六邊形的位置基于第一個(gè)投籃的位置）。

計(jì)算命中率則需要對每個(gè)六邊形中投籃的次數(shù)和投籃得分次數(shù)進(jìn)行計(jì)數(shù)，因此筆者對同一位置的投籃和得分?jǐn)?shù)分別運(yùn)行 hexbin 函數(shù)。然后，只需用每個(gè)位置的進(jìn)球數(shù)除以投籃數(shù)。

def find_shootingPcts(shot_df, gridNum):
    x = shot_df.LOC_X[shot_df["LOC_Y"]<425.1] #i want to make sure to only include shots I can draw
    y = shot_df.LOC_Y[shot_df["LOC_Y"]<425.1]

    x_made = shot_df.LOC_X[(shot_df["SHOT_MADE_FLAG"]==1) & (shot_df["LOC_Y"]<425.1)]
    y_made = shot_df.LOC_Y[(shot_df["SHOT_MADE_FLAG"]==1) & (shot_df["LOC_Y"]<425.1)]

    #compute number of shots made and taken from each hexbin location
    hb_shot = plt.hexbin(x, y, gridsize=gridNum, extent=(-250,250,425,-50));
    plt.close() #don"t want to show this figure!
    hb_made = plt.hexbin(x_made, y_made, gridsize=gridNum, extent=(-250,250,425,-50),cmap=plt.cm.Reds);
    plt.close()

    #compute shooting percentage
    ShootingPctLocs = hb_made.get_array() / hb_shot.get_array()
    ShootingPctLocs[np.isnan(ShootingPctLocs)] = 0 #makes 0/0s=0
    return (ShootingPctLocs, hb_shot)

筆者非常喜歡 Savvas Tjortjoglou 在他的得分圖中加入了球員頭像的做法，因此也順道用了他的這部分代碼。球員照片會出現(xiàn)在得分圖的右下角。

def acquire_playerPic(PlayerID, zoom, offset=(250,400)):
    from matplotlib import  offsetbox as osb
    import urllib
    pic = urllib.urlretrieve("http://stats.nba.com/media/players/230x185/"+PlayerID+".png",PlayerID+".png")
    player_pic = plt.imread(pic[0])
    img = osb.OffsetImage(player_pic, zoom)
    #img.set_offset(offset)
    img = osb.AnnotationBbox(img, offset,xycoords="data",pad=0.0, box_alignment=(1,0), frameon=False)
    return img

筆者想用連續(xù)的顏色圖來描述投籃進(jìn)球百分比，紅圈越多代表著更高的進(jìn)球百分比。雖然「紅」顏色圖示效果不錯(cuò)，但是它會將0%的投籃進(jìn)球百分比顯示為白色http://matplotlib.org/users/colormaps.html，而這樣顯示就會不明顯，所以筆者用淡粉紅色代表0%的命中率，因此對紅顏色圖做了下面的修改。

#cmap = plt.cm.Reds
#cdict = cmap._segmentdata
cdict = {
    "blue": [(0.0, 0.6313725709915161, 0.6313725709915161), (0.25, 0.4470588266849518, 0.4470588266849518), (0.5, 0.29019609093666077, 0.29019609093666077), (0.75, 0.11372549086809158, 0.11372549086809158), (1.0, 0.05098039284348488, 0.05098039284348488)],
    "green": [(0.0, 0.7333333492279053, 0.7333333492279053), (0.25, 0.572549045085907, 0.572549045085907), (0.5, 0.4156862795352936, 0.4156862795352936), (0.75, 0.0941176488995552, 0.0941176488995552), (1.0, 0.0, 0.0)],
    "red": [(0.0, 0.9882352948188782, 0.9882352948188782), (0.25, 0.9882352948188782, 0.9882352948188782), (0.5, 0.9843137264251709, 0.9843137264251709), (0.75, 0.7960784435272217, 0.7960784435272217), (1.0, 0.40392157435417175, 0.40392157435417175)]
}

mymap = mpl.colors.LinearSegmentedColormap("my_colormap", cdict, 1024)

好了，現(xiàn)在需要做的就是將它們合并到一塊兒。下面所示的較大函數(shù)會利用上文描述的函數(shù)來創(chuàng)建一個(gè)描述投籃命中率的得分圖，百分比由紅圈表示（紅色越深 = 更高的命中率），投籃次數(shù)則由圓圈的大小決定（圓圈越大 = 投籃次數(shù)越多）。需要注意的是，圓圈在交疊之前都能增大。一旦圓圈開始交疊，就無法繼續(xù)增大。

在這個(gè)函數(shù)中，計(jì)算了每個(gè)位置的投籃進(jìn)球百分比和投籃次數(shù)。然后畫出在該位置投籃的次數(shù)（圓圈大小）和進(jìn)球百分比（圓圈顏色深淺）。

def shooting_plot(shot_df, plot_size=(12,8),gridNum=30):
    from matplotlib.patches import Circle
    x = shot_df.LOC_X[shot_df["LOC_Y"]<425.1]
    y = shot_df.LOC_Y[shot_df["LOC_Y"]<425.1]

    #compute shooting percentage and # of shots
    (ShootingPctLocs, shotNumber) = find_shootingPcts(shot_df, gridNum)

    #draw figure and court
    fig = plt.figure(figsize=plot_size)#(12,7)
    cmap = mymap #my modified colormap
    ax = plt.axes([0.1, 0.1, 0.8, 0.8]) #where to place the plot within the figure
    draw_court(outer_lines=False)
    plt.xlim(-250,250)
    plt.ylim(400, -25)

    #draw player image
    zoom = np.float(plot_size[0])/(12.0*2) #how much to zoom the player"s pic. I have this hackily dependent on figure size
    img = acquire_playerPic(PlayerID, zoom)
    ax.add_artist(img)

    #draw circles
    for i, shots in enumerate(ShootingPctLocs):
        restricted = Circle(shotNumber.get_offsets()[i], radius=shotNumber.get_array()[i],
                            color=cmap(shots),alpha=0.8, fill=True)
        if restricted.radius > 240/gridNum: restricted.radius=240/gridNum
        ax.add_patch(restricted)

    #draw color bar
    ax2 = fig.add_axes([0.92, 0.1, 0.02, 0.8])
    cb = mpl.colorbar.ColorbarBase(ax2,cmap=cmap, orientation="vertical")
    cb.set_label("Shooting %")
    cb.set_ticks([0.0, 0.25, 0.5, 0.75, 1.0])
    cb.set_ticklabels(["0%","25%", "50%","75%", "100%"])

    plt.show()
    return ax

好了，大功告成！因?yàn)楣P者是森林狼隊(duì)的粉絲，在下面用幾分鐘跑出了森林狼隊(duì)前六甲的得分圖。

PlayerID = "203952" #andrew wiggins
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8));

PlayerID = "1626157" #karl anthony towns
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8));

PlayerID = "203897" #zach lavine
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8));

PlayerID = "203476" #gorgui deing
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8));

PlayerID = "2755" #kevin martin
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8));

PlayerID = "201937" #ricky rubio
shot_df = aqcuire_shootingData(PlayerID,"2015-16")
ax = shooting_plot(shot_df, plot_size=(12,8)); 

使用 hexbin 函數(shù)也是有隱患的，第一它并沒有解釋由于三分線而導(dǎo)致的非線性特性（一些 hexbin 函數(shù)同時(shí)包括了2分和3分的投籃）。它很好的限定了一些窗口來進(jìn)行3分投籃，但如果沒有這個(gè)位置的硬編碼就沒有辦法做到這一點(diǎn)。此外 hexbin 方法的一個(gè)優(yōu)點(diǎn)與是可以很容易地改變窗口的數(shù)量，但不確定是否可以同樣靈活的處理2分投籃和3分投籃。

另外一個(gè)隱患在于此圖將所有投籃都一視同仁，這相當(dāng)不公平。在禁區(qū)投籃命中40%和三分線后的投籃命中40%可是大不相同。Austin Clemens 的解決辦法是將命中率與聯(lián)賽平均分關(guān)聯(lián)。也許過幾天筆者也會實(shí)現(xiàn)與之類似的功能。

原文 Creating NBA Shot Charts 作者 Dan Vatterott ，本文由 OneAPM 工程師編譯整理。

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