There seems to have been quite a bit of discussion lately about the value of various statistical evaluations of NBA teams, especially the Blazers. This most likely is due to the Blazers 2nd best point differential, despite their slow pace. This usually leads to observations about strength of schedule and general doubt about what the future holds.
正如许多人所观察到的那样，点差异是缺陷的指标。大多数其他指标都有类似的问题，或者在这种神秘（Hollinger）中笼罩，即不可能讲述发生的事情。作为数学上倾向的个人，我一直在努力设计符合几个标准的指标：
1) Predictive:评分很大，也是一种统计数据。但是，如果我们正在寻找一些单个号码，如果它允许我们允许我们预测未来的游戏是最好的。也就是说，如果给出了两支球队的评级，系统将计算预期的保证金。
2) Sensitivity To Games:一旦预测了游戏的余量，团队将超过这个边缘。如果它确实超过它，那么团队比预期更好，评级应该向上调整。同样的想法适用于不符合保证金。
3) Dependent on Strength of Schedule:这真的是这篇文章的全部。如果每个人knows that the metric needs to be viewed through a SOS lense, then why not just incorporate SOS into the metric in the first place. Note that if the 1st two characteristics are incorporated, this one should be taken care of as well.
4）节奏调整：几乎所有篮球统计数据都是如此。西装外套慢慢地播放，我们真的想知道一支球队如何在100多个财产上进行，而不是48分钟。
With these in mind, I proceeded to construct a theory of skill as relates to basketball. The metric encompasses the first 3, but没有节奏调整, as I was unable to find pace calculations for individual games (if you have any tips, please let me know). The basic idea is that each team has a given rating, and the expected margin is merely,
TeamOneRating-TeamTwoRating = Margin,
where, since this is time based, the margin would be the expected margin after 48 minutes. However, I noticed that, on average, home teams outscore visiting teams by a margin of about 3.8. Thus, the margin that the Home team is expected to win by, MarginExpected, is given by
MarginExpected = 3.8 + HomeRating-VisitingRating.
From this formula and the scores of the last 221 basketball games, I was able to compute the ratings for all 30 teams. This was done using a least squares approximation. For each game, there is an error given by
error = permandermargin-alutymargin。
最小二乘法找到额定值的值，使得误差的总和最小化。此外，因为所有值相对于彼此，您可以将它们限制为使得平均评级为0.然后在30个变量的二次中变为约束最小化问题，计算机软件可以很容易地解决。
下表显示了计算的额定值，无论是和没有国内法院的优势，都可以看到，这确实会移动一些团队，例如湖人队，湖人队，才能播放3场公路游戏，但它离开了一般的排序不变，和第2号的西装外套。
Team |
家庭优势排名 |
Home Advantage |
没有家庭优势Ranking |
没有家庭优势 |
1 |
6.442 |
3 |
6.383 |
|
2 |
6.372 |
2 |
6.458 |
|
3 |
6.035 |
1 |
6.584 |
|
4 |
5.965 |
6 |
5.67 |
|
5 |
5.964 |
7 |
5.256 |
|
6 |
5.574 |
4 |
6.1416 |
|
7 |
5.09 |
9 |
4.286 |
|
8 |
4.28 |
10 |
3.931 |
|
9 |
4.264 |
5 |
6.128 |
|
10 |
3.93 |
8 |
5.18 |
|
11 |
2.999. |
11 |
2.954 |
|
12 |
2.748 |
12 |
2.394 |
|
13 |
1.748 |
13 |
1.986 |
|
14 |
0.618788 |
16 |
0.682 |
|
15 |
0.223 |
14 |
1.1 |
|
16 |
-0.087 |
17 |
-0.958 |
|
17 |
-1.146 |
18 |
-1.164 |
|
18 |
-1.246 |
21 |
-2.167 |
|
19 |
-1.259 |
15 |
0.8966 |
|
20 |
-1.269 |
20 |
-1.783 |
|
21 |
-1.363 |
19 |
-1.429 |
|
22 |
-3.259 |
22 |
-2.399 |
|
23 |
-3.358 |
24 |
-4.296 |
|
24 |
-3.648 |
23 |
-3.906 |
|
25 |
-4.847 |
26 |
-5.34 |
|
26 |
-5.097 |
25 |
-4.648 |
|
27 |
-5.5607 |
27 |
-5.92 |
|
New York Knickerbockers |
28 |
-7.565 |
28 |
-7.1002 |
29 |
-9.752 |
29 |
-10.5322 |
|
30 |
-12.8 |
30 |
-12.689 |
如果you have any questions about methodology, math, thought-process or anything else please just post a response. This is my first post, so I will be watching it closely. Hope you enjoy it.
To read the table, just subtract the visiting team rating from the home team and add 3.8. Thus, we expect the Blazers to win by roughly 6.372-(-5.5607)+3.8 = 15.7 pts. Go Blazers.
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