{"id":146,"date":"2011-01-14T16:12:27","date_gmt":"2011-01-14T22:12:27","guid":{"rendered":"http:\/\/godismyjudgeok.com\/DStats\/?p=146"},"modified":"2013-01-04T10:25:48","modified_gmt":"2013-01-04T16:25:48","slug":"nba-adjusted-efficiency-rankings-1-13-2011","status":"publish","type":"post","link":"https:\/\/godismyjudgeok.com\/DStats\/2011\/nba-rankings\/nba-adjusted-efficiency-rankings-1-13-2011\/","title":{"rendered":"NBA Adjusted Efficiency Rankings 1-13-2011"},"content":{"rendered":"

Last week, I unveiled my NBA Adjusted Efficiency rating system<\/a>. This week, I’ll explore some of the decisions I made with that system, per the request of Ben<\/a>.<\/p>\n

The first question is how much the ranking are effected by using rest-days adjustments.\u00a0 See my original research on APBRmetrics<\/a> for where this comes from.\u00a0 Here’s a table comparing the effect on each team:\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Team<\/th>Rest-Adjusted<\/th>Not Rest-Adjusted<\/th>Difference<\/th>\n<\/tr>\n<\/thead>\n
ATL<\/td>2.88<\/td>2.46<\/td>0.42<\/td>\n<\/tr>\n
BOS<\/td>7.99<\/td>7.32<\/td>0.67<\/td>\n<\/tr>\n
CHA<\/td>-3.72<\/td>-3.59<\/td>-0.13<\/td>\n<\/tr>\n
CHI<\/td>4.63<\/td>4.16<\/td>0.47<\/td>\n<\/tr>\n
CLE<\/td>-10.81<\/td>-10.85<\/td>0.04<\/td>\n<\/tr>\n
DAL<\/td>4.17<\/td>4.58<\/td>-0.41<\/td>\n<\/tr>\n
DEN<\/td>2.55<\/td>2.39<\/td>0.16<\/td>\n<\/tr>\n
DET<\/td>-5.83<\/td>-5.55<\/td>-0.28<\/td>\n<\/tr>\n
GSW<\/td>-2.77<\/td>-2.75<\/td>-0.02<\/td>\n<\/tr>\n
HOU<\/td>-0.11<\/td>0.07<\/td>-0.18<\/td>\n<\/tr>\n
IND<\/td>-1.42<\/td>-1.31<\/td>-0.11<\/td>\n<\/tr>\n
LAC<\/td>-2.96<\/td>-3.56<\/td>0.61<\/td>\n<\/tr>\n
LAL<\/td>7.13<\/td>6.34<\/td>0.79<\/td>\n<\/tr>\n
MEM<\/td>1.26<\/td>0.64<\/td>0.63<\/td>\n<\/tr>\n
MIA<\/td>8.33<\/td>8.55<\/td>-0.22<\/td>\n<\/tr>\n
MIL<\/td>-1.49<\/td>-1.39<\/td>-0.10<\/td>\n<\/tr>\n
MIN<\/td>-4.71<\/td>-4.55<\/td>-0.16<\/td>\n<\/tr>\n
NJN<\/td>-6.38<\/td>-6.54<\/td>0.16<\/td>\n<\/tr>\n
NOH<\/td>2.27<\/td>2.96<\/td>-0.70<\/td>\n<\/tr>\n
NYK<\/td>2.22<\/td>2.12<\/td>0.10<\/td>\n<\/tr>\n
OKC<\/td>2.48<\/td>2.95<\/td>-0.46<\/td>\n<\/tr>\n
ORL<\/td>4.84<\/td>4.98<\/td>-0.14<\/td>\n<\/tr>\n
PHI<\/td>0.36<\/td>0.10<\/td>0.26<\/td>\n<\/tr>\n
PHO<\/td>-2.33<\/td>-2.33<\/td>0.00<\/td>\n<\/tr>\n
POR<\/td>1.40<\/td>1.74<\/td>-0.34<\/td>\n<\/tr>\n
SAC<\/td>-8.79<\/td>-8.48<\/td>-0.31<\/td>\n<\/tr>\n
SAS<\/td>7.40<\/td>8.01<\/td>-0.61<\/td>\n<\/tr>\n
TOR<\/td>-4.78<\/td>-4.77<\/td>-0.01<\/td>\n<\/tr>\n
UTA<\/td>3.26<\/td>3.05<\/td>0.21<\/td>\n<\/tr>\n
WAS<\/td>-7.09<\/td>-6.76<\/td>-0.33<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\n

The average difference is 0.30.\u00a0 As the season goes on, the difference should decrease as the rest situations equalize over time.\u00a0 Over the whole year, though, there are certainly still advantages and disadvantages based on scheduling.\u00a0 I haven’t tabulated them based on my updated estimate of\u00a0 rest day impact, but earlier, with older estimates, I used rest-days adjustments in my prediction of wins<\/a> for this season.<\/p>\n

Question 2 is based on my choice of 1.5 as the exponent of residuals to minimize.\u00a0 EDIT: (That’s formulated (abs(residual))^1.5, Ryan<\/a>.)<\/em> A true arithmetic mean is effectively minimizing residuals^2.\u00a0 I chose 1.5.\u00a0 Why?\u00a0 Well, just gut feeling mostly, but I will eventually investigate what exponent is the best.\u00a0 The question, though, is best for what?\u00a0 What is the objective?\u00a0 With residuals^2, outliers like the Lakers’ pounding of Cleveland 112 to 57<\/a> have a huge effect.\u00a0 On the other hand, minimizing residuals alone under-weights the outliers–in fact, minimizing pure residuals gives you the median of the set!\u00a0 Here’s an example:<\/p>\n

Take a distribution of 5 numbers: -2, -1, 0, 3, 11.\u00a0 What is the result of minimizing residuals, residuals^1.5, or residuals^2?\u00a0 Let’s throw this in Excel and look at the results\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Exponent:<\/th>1<\/th>1.25<\/th>1.5<\/th>1.75<\/th>2<\/th>2.25<\/th>2.5<\/th>\n<\/tr>\n<\/thead>\n
Cald'd Mean<\/td>0.00<\/td>0.35<\/td>1.27<\/td>1.80<\/td>2.20<\/td>2.55<\/td>2.87<\/td>\n<\/tr>\n
Value<\/td>Err<\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n
-2<\/td>2.0<\/td>2.9<\/td>5.9<\/td>10.3<\/td>17.6<\/td>30.3<\/td>52.3<\/td>\n<\/tr>\n
-1<\/td>1.0<\/td>1.5<\/td>3.4<\/td>6.0<\/td>10.2<\/td>17.3<\/td>29.5<\/td>\n<\/tr>\n
0<\/td>0.0<\/td>0.3<\/td>1.4<\/td>2.8<\/td>4.8<\/td>8.2<\/td>14.0<\/td>\n<\/tr>\n
3<\/td>3.0<\/td>3.4<\/td>2.3<\/td>1.4<\/td>0.6<\/td>0.2<\/td>0.0<\/td>\n<\/tr>\n
11<\/td>11.0<\/td>19.2<\/td>30.4<\/td>48.6<\/td>77.4<\/td>121.6<\/td>188.4<\/td>\n<\/tr>\n
<\/td><\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n
Sum Error<\/td>17.0<\/td>27.3<\/td>43.4<\/td>69.2<\/td>110.8<\/td>177.7<\/td>284.2<\/td>\n<\/tr>\n
<\/td><\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n
Mean<\/td>2.20<\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n
Median<\/td>0<\/td><\/td><\/td><\/td><\/td><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\n

Minimizing residuals^1.5 yields a result in between the mean and the median, obviously.\u00a0 I’ll revisit this another time… but first, a table comparing the ratings using residuals, residuals^1.5, and residuals^2 to get the results:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Team<\/th>Residuals^1<\/th>Residuals^1.5<\/th>Residuals^2<\/th>Skew<\/th>\n<\/tr>\n<\/thead>\n
MIA<\/td>8.02<\/td>8.33<\/td>8.36<\/td>0.34<\/td>\n<\/tr>\n
BOS<\/td>8.15<\/td>7.99<\/td>7.99<\/td>-0.16<\/td>\n<\/tr>\n
SAS<\/td>7.69<\/td>7.40<\/td>7.23<\/td>-0.46<\/td>\n<\/tr>\n
LAL<\/td>7.23<\/td>7.13<\/td>7.01<\/td>-0.22<\/td>\n<\/tr>\n
ORL<\/td>4.86<\/td>4.84<\/td>5.11<\/td>0.25<\/td>\n<\/tr>\n
CHI<\/td>4.17<\/td>4.63<\/td>4.95<\/td>0.78<\/td>\n<\/tr>\n
DAL<\/td>4.93<\/td>4.17<\/td>4.06<\/td>-0.87<\/td>\n<\/tr>\n
UTA<\/td>5.68<\/td>3.26<\/td>2.35<\/td>-3.33<\/td>\n<\/tr>\n
ATL<\/td>2.01<\/td>2.88<\/td>2.84<\/td>0.83<\/td>\n<\/tr>\n
DEN<\/td>1.31<\/td>2.55<\/td>3.21<\/td>1.90<\/td>\n<\/tr>\n
OKC<\/td>2.82<\/td>2.48<\/td>1.74<\/td>-1.08<\/td>\n<\/tr>\n
NOH<\/td>2.87<\/td>2.27<\/td>2.17<\/td>-0.70<\/td>\n<\/tr>\n
NYK<\/td>2.57<\/td>2.22<\/td>1.86<\/td>-0.71<\/td>\n<\/tr>\n
POR<\/td>1.39<\/td>1.40<\/td>1.34<\/td>-0.05<\/td>\n<\/tr>\n
MEM<\/td>1.17<\/td>1.26<\/td>0.90<\/td>-0.27<\/td>\n<\/tr>\n
PHI<\/td>0.47<\/td>0.36<\/td>0.13<\/td>-0.34<\/td>\n<\/tr>\n
HOU<\/td>-1.25<\/td>-0.11<\/td>0.35<\/td>1.60<\/td>\n<\/tr>\n
IND<\/td>-2.13<\/td>-1.42<\/td>-0.72<\/td>1.41<\/td>\n<\/tr>\n
MIL<\/td>-2.18<\/td>-1.49<\/td>-0.65<\/td>1.53<\/td>\n<\/tr>\n
PHO<\/td>-1.76<\/td>-2.33<\/td>-2.44<\/td>-0.68<\/td>\n<\/tr>\n
GSW<\/td>-3.92<\/td>-2.77<\/td>-2.95<\/td>0.97<\/td>\n<\/tr>\n
LAC<\/td>-3.17<\/td>-2.96<\/td>-2.67<\/td>0.50<\/td>\n<\/tr>\n
CHA<\/td>-2.31<\/td>-3.72<\/td>-4.63<\/td>-2.31<\/td>\n<\/tr>\n
MIN<\/td>-2.62<\/td>-4.71<\/td>-5.16<\/td>-2.53<\/td>\n<\/tr>\n
TOR<\/td>-5.86<\/td>-4.78<\/td>-4.17<\/td>1.69<\/td>\n<\/tr>\n
DET<\/td>-6.61<\/td>-5.83<\/td>-5.21<\/td>1.40<\/td>\n<\/tr>\n
NJN<\/td>-6.22<\/td>-6.38<\/td>-6.77<\/td>-0.55<\/td>\n<\/tr>\n
WAS<\/td>-7.64<\/td>-7.09<\/td>-6.87<\/td>0.78<\/td>\n<\/tr>\n
SAC<\/td>-8.99<\/td>-8.79<\/td>-8.46<\/td>0.53<\/td>\n<\/tr>\n
CLE<\/td>-10.66<\/td>-10.81<\/td>-10.89<\/td>-0.23<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

What can we interpret these to mean?\u00a0 If a team has a higher ^1 and a lower ^2, the have had a bunch of better performances and a few really bad clunkers.\u00a0 On the other hand, if the ^1 is lower and the ^2 is higher, they’ve had a bunch of lesser performances and a few really dominant ones.\u00a0 Basically, the difference reflects the skew of the distribution.\u00a0 Utah has generally been quite solid (median +5.68) but has had some awful clunkers (mean +2.35).\u00a0 On the other hand, Denver has typically played mediocre but every once in a while plays a great game.<\/p>\n

Okay, on to the actual rankings.\u00a0 The last time I did these was 8 days ago, so the “previous” data is from that point.\u00a0 As usual, these are adjusted for rest days, location, and opponent, all according to the residuals^2.\u00a0 First the pretty image:<\/p>\n

\"Team<\/a>

Adjusted NBA Team Efficiencies, through 1-13-2011<\/p><\/div>\n

Miami and Dallas have hit rough patches, and Phoenix and Cleveland have continued to tumble.\u00a0 Cleveland is REALLY bad, now.\u00a0 The top 4 teams have continued to separate from the rest of the field, but a new contender is making an impressive run, as Orlando’s climb continues.\u00a0 Remember, these rankings weight the whole season equally–Orlando has been a different team<\/a> with the new lineup.<\/p>\n

And now something new– a new Google Motion Chart!\u00a0 This one tracks the day-by-day efficiency ranking of each team, since the ratings had fairly stabilized around December 20th.\u00a0 At that point, also, the trade occurred between Phoenix and Orlando.\u00a0 Check out their different trajectories since then!<\/p>\n

<\/div>\n

Finally, here is the data from this week in table form:
\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
Rank<\/th>Chg<\/th>Team<\/th>Off Eff<\/th>Def Eff<\/th>Eff. Margin<\/th>Change<\/th>Prev<\/th>SoS<\/th>Pace<\/th>\n<\/tr>\n<\/thead>\n
1<\/td><\/td>MIA<\/td>4.67<\/td>-3.66<\/td>8.33<\/td>-1.30<\/td>9.63<\/td>-0.57<\/td>90.7<\/td>\n<\/tr>\n
2<\/td><\/td>BOS<\/td>1.81<\/td>-6.18<\/td>7.99<\/td>-0.62<\/td>8.60<\/td>-0.31<\/td>89.8<\/td>\n<\/tr>\n
3<\/td><\/td>SAS<\/td>4.69<\/td>-2.71<\/td>7.40<\/td>0.01<\/td>7.39<\/td>-0.80<\/td>92.0<\/td>\n<\/tr>\n
4<\/td><\/td>LAL<\/td>6.09<\/td>-1.04<\/td>7.13<\/td>1.09<\/td>6.05<\/td>-1.07<\/td>91.7<\/td>\n<\/tr>\n
5<\/td>2<\/td>ORL<\/td>1.75<\/td>-3.10<\/td>4.84<\/td>0.61<\/td>4.24<\/td>-0.76<\/td>91.7<\/td>\n<\/tr>\n
6<\/td><\/td>CHI<\/td>-2.24<\/td>-6.87<\/td>4.63<\/td>0.23<\/td>4.41<\/td>-1.07<\/td>91.4<\/td>\n<\/tr>\n
7<\/td>-2<\/td>DAL<\/td>1.68<\/td>-2.49<\/td>4.17<\/td>-1.23<\/td>5.40<\/td>0.17<\/td>90.7<\/td>\n<\/tr>\n
8<\/td><\/td>UTA<\/td>3.87<\/td>0.61<\/td>3.26<\/td>-0.14<\/td>3.40<\/td>1.06<\/td>89.9<\/td>\n<\/tr>\n
9<\/td><\/td>ATL<\/td>1.53<\/td>-1.35<\/td>2.88<\/td>0.35<\/td>2.53<\/td>-0.42<\/td>90.1<\/td>\n<\/tr>\n
10<\/td><\/td>DEN<\/td>4.48<\/td>1.93<\/td>2.55<\/td>0.36<\/td>2.19<\/td>-0.45<\/td>95.4<\/td>\n<\/tr>\n
11<\/td>3<\/td>OKC<\/td>4.21<\/td>1.72<\/td>2.48<\/td>0.83<\/td>1.65<\/td>0.38<\/td>92.8<\/td>\n<\/tr>\n
12<\/td><\/td>NOH<\/td>-1.53<\/td>-3.80<\/td>2.27<\/td>0.52<\/td>1.74<\/td>0.37<\/td>89.2<\/td>\n<\/tr>\n
13<\/td><\/td>NYK<\/td>3.42<\/td>1.20<\/td>2.22<\/td>0.52<\/td>1.70<\/td>0.82<\/td>96.2<\/td>\n<\/tr>\n
14<\/td>-3<\/td>POR<\/td>0.65<\/td>-0.75<\/td>1.40<\/td>-0.51<\/td>1.91<\/td>1.30<\/td>87.4<\/td>\n<\/tr>\n
15<\/td><\/td>MEM<\/td>-1.99<\/td>-3.25<\/td>1.26<\/td>0.05<\/td>1.21<\/td>0.96<\/td>93.0<\/td>\n<\/tr>\n
16<\/td><\/td>PHI<\/td>-0.97<\/td>-1.33<\/td>0.36<\/td>-0.58<\/td>0.94<\/td>1.06<\/td>90.9<\/td>\n<\/tr>\n
17<\/td><\/td>HOU<\/td>2.80<\/td>2.92<\/td>-0.11<\/td>-0.24<\/td>0.13<\/td>-0.31<\/td>93.7<\/td>\n<\/tr>\n
18<\/td>1<\/td>IND<\/td>-4.75<\/td>-3.33<\/td>-1.42<\/td>0.84<\/td>-2.26<\/td>-0.82<\/td>93.7<\/td>\n<\/tr>\n
19<\/td>1<\/td>MIL<\/td>-6.81<\/td>-5.32<\/td>-1.49<\/td>0.82<\/td>-2.31<\/td>0.61<\/td>90.1<\/td>\n<\/tr>\n
20<\/td>-2<\/td>PHO<\/td>3.79<\/td>6.12<\/td>-2.33<\/td>-0.95<\/td>-1.38<\/td>0.77<\/td>94.3<\/td>\n<\/tr>\n
21<\/td><\/td>GSW<\/td>1.07<\/td>3.83<\/td>-2.77<\/td>-0.27<\/td>-2.50<\/td>1.63<\/td>94.6<\/td>\n<\/tr>\n
22<\/td><\/td>LAC<\/td>-2.13<\/td>0.82<\/td>-2.96<\/td>0.79<\/td>-3.75<\/td>-0.16<\/td>91.1<\/td>\n<\/tr>\n
23<\/td>1<\/td>CHA<\/td>-4.06<\/td>-0.34<\/td>-3.72<\/td>1.05<\/td>-4.77<\/td>0.08<\/td>89.6<\/td>\n<\/tr>\n
24<\/td>1<\/td>MIN<\/td>-1.13<\/td>3.58<\/td>-4.71<\/td>0.09<\/td>-4.80<\/td>0.89<\/td>96.4<\/td>\n<\/tr>\n
25<\/td>-2<\/td>TOR<\/td>0.67<\/td>5.46<\/td>-4.78<\/td>-0.62<\/td>-4.16<\/td>-0.38<\/td>93.5<\/td>\n<\/tr>\n
26<\/td>1<\/td>DET<\/td>-1.00<\/td>4.83<\/td>-5.83<\/td>-0.30<\/td>-5.53<\/td>-0.13<\/td>88.5<\/td>\n<\/tr>\n
27<\/td>-1<\/td>NJN<\/td>-4.69<\/td>1.69<\/td>-6.38<\/td>-0.89<\/td>-5.49<\/td>0.92<\/td>89.2<\/td>\n<\/tr>\n
28<\/td><\/td>WAS<\/td>-4.54<\/td>2.54<\/td>-7.09<\/td>-0.31<\/td>-6.77<\/td>-0.69<\/td>92.8<\/td>\n<\/tr>\n
29<\/td><\/td>SAC<\/td>-4.80<\/td>3.99<\/td>-8.79<\/td>0.81<\/td>-9.60<\/td>-2.09<\/td>92.9<\/td>\n<\/tr>\n
30<\/td><\/td>CLE<\/td>-6.55<\/td>4.26<\/td>-10.81<\/td>-1.01<\/td>-9.80<\/td>0.59<\/td>92.3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/p>\n","protected":false},"excerpt":{"rendered":"

Last week, I unveiled my . This week, I’ll explore some of the decisions I made with that system, per the request of . The first question is how much the ranking are effected by using rest-days adjustments.\u00a0 See my original research on APBRmetrics for where this comes from.\u00a0 Here’s a table comparing the effect … [Read more…]<\/a><\/span><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[11,10,5,12],"tags":[57,54,22,24],"_links":{"self":[{"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/posts\/146"}],"collection":[{"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/comments?post=146"}],"version-history":[{"count":27,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/posts\/146\/revisions"}],"predecessor-version":[{"id":899,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/posts\/146\/revisions\/899"}],"wp:attachment":[{"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/media?parent=146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/categories?post=146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/godismyjudgeok.com\/DStats\/wp-json\/wp\/v2\/tags?post=146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}