Latrinsorm
03-15-2014, 03:55 PM
Games decided by 5 points or less are basically a 50/50 shot, as I demonstrated long (http://forum.gsplayers.com/showthread.php?68943-NBA-Winning-Ugly-and-2012) ago (http://forum.gsplayers.com/showthread.php?86809-NBA-Winning-Ugly-and-1984)... but how basically is basically? I selected 5 points for close because in 2011 the Heat were excoriated for losing so many games of that margin or less, but as was demonstrated by the Heat never once being praised for winning so many such games in 2013 that margin was totally arbitrary.
Let's take the last ten years for every NBA team (Charlotte only has nine), find their record in games decided by exactly 1, 2, 3 ... 9, and 10 points, and see how they compare with random chance. One concise way of looking at that is using z-scores:
1. Calculate standard deviation by sqrt(win% * (1 - win%) * games).
2. Calculate the number of standard deviations away from the model by (win% - 50%) / (standard deviation).
The normal distribution (http://en.wikipedia.org/wiki/Standard_deviation) predicts that in a 30 team league we should get about 20.5 teams within 1 standard deviation, 8.2 within 2, 1.3 within 3, and the remaining .08 outside of 3. Empirically, we find:
margin 1 2 3 4 5 6 7
10 10 7 5 3 3 1 1
9 10 10 3 2 4 0 1
8 10 10 3 4 2 1 0
7 11 11 2 4 2 0 0
6 16 5 6 2 1 0 0
5 16 9 4 1 0 0 0
4 17 9 3 1 0 0 0
3 18 8 3 1 0 0 0
2 19 10 1 0 0 0 0
1 21 6 3 0 0 0 0
model 20.5 8.2 1.3 0.1
Thus, games decided by 1 or 2 points are absolutely indistinguishable from luck. Games decided by 3-5 points show a bit of evidence for a skill component, games decided by 6-7 a bit more, and games decided by 8-10 are almost if not entirely skill. The 3 outliers for 3-5 are Minnesota in 3 point games (-3.3), Minnesota in 4 point games (-3.4), Dallas in 5 point games (+3.5).
The average z-score is going to be clustered around 0 for all margins, because every game that one team wins another team has to lose, but we can get interesting information by taking the standard deviations of the z-scores, which look like this:
http://img.photobucket.com/albums/v456/johnnyoldschool/NBAWhatsLuckGottoDo_zpsa84a922f.png
There is a potentially interesting hump at 1 point games, but this is probably just because they are the smallest samples and therefore the noisiest data. As anyone would expect, there is no discontinuous cutoff for luck. It factors into every game inversely proportional to margin, the surprise is how neatly linear the relationship is.
.
Full data, where the numbers are 1 point higher than the margin:
no okc den uta por min lac gs lal sac pho sa mem hou dal no NYK BRO BOS PHI tor ind chi mil det cle mia atl was cha orl
Team W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L
11 238 237 233 234 254 187 247 201 242 235 186 279 206 233 222 256 280 191 206 265 247 208 267 165 238 249 249 240 303 169 238 237 218 274 215 227 255 237 220 266 195 272 238 231 254 217 231 275 255 213 245 229 246 201 236 238 188 267 170 260 214 242
10 226 216 210 210 225 173 217 182 223 214 169 261 184 211 198 237 263 170 194 243 224 190 237 152 211 219 230 220 272 153 226 216 202 244 198 197 233 222 202 239 177 253 211 213 237 196 216 254 226 199 229 204 226 179 212 221 166 245 155 242 198 212
9 203 191 189 188 198 154 187 161 202 189 152 237 166 186 178 213 238 148 171 215 194 173 199 143 190 197 203 193 232 136 203 191 189 220 180 167 211 200 184 215 161 228 194 188 210 173 196 226 202 188 207 181 202 163 182 205 152 216 142 210 170 180
8 181 158 153 166 173 142 160 138 174 170 130 198 137 165 151 181 203 131 154 185 149 154 183 127 168 171 174 162 207 124 181 158 164 183 157 144 184 169 158 185 144 202 165 169 185 150 178 196 173 166 175 152 179 142 154 179 135 181 121 180 154 153
7 148 134 131 142 142 129 132 110 150 141 111 166 115 137 117 158 169 118 132 148 130 126 148 104 142 142 151 135 174 106 148 134 139 156 133 121 159 146 137 153 124 160 131 148 150 120 154 168 141 142 146 126 152 113 136 151 116 157 102 147 127 135
6 121 108 108 117 115 106 108 89 123 117 90 130 89 109 96 131 137 94 115 118 104 104 117 90 110 118 128 105 142 90 121 108 112 123 110 99 137 122 114 125 101 120 103 132 117 103 119 132 114 117 119 103 116 92 110 124 105 124 88 120 99 105
5 98 85 85 89 93 87 82 67 101 88 66 110 72 82 79 103 103 77 90 88 74 71 97 66 77 91 100 79 105 73 98 85 90 87 86 79 108 94 80 96 77 98 72 103 87 79 85 98 89 91 88 78 94 73 79 88 86 94 66 89 76 82
4 72 56 64 68 73 64 57 49 78 48 48 84 49 61 54 74 77 61 65 69 51 49 75 52 59 74 70 59 85 54 72 56 60 61 60 56 78 73 58 67 55 70 56 70 64 59 60 71 57 65 63 61 68 58 56 68 71 67 53 62 55 61
3 46 33 40 45 48 37 37 37 50 29 34 47 34 39 33 43 46 40 40 42 36 29 46 31 39 40 44 33 51 38 46 33 38 45 41 32 49 52 36 39 39 43 40 49 37 38 32 48 37 40 38 36 39 38 31 47 42 42 33 38 30 36
2 21 17 18 20 26 12 13 17 22 15 13 18 16 17 11 21 23 18 18 11 11 9 21 9 17 18 16 10 15 15 21 17 17 14 13 14 16 19 16 17 17 20 21 16 17 23 11 23 18 20 23 21 15 12 17 26 17 16 14 18 11 18
Let's take the last ten years for every NBA team (Charlotte only has nine), find their record in games decided by exactly 1, 2, 3 ... 9, and 10 points, and see how they compare with random chance. One concise way of looking at that is using z-scores:
1. Calculate standard deviation by sqrt(win% * (1 - win%) * games).
2. Calculate the number of standard deviations away from the model by (win% - 50%) / (standard deviation).
The normal distribution (http://en.wikipedia.org/wiki/Standard_deviation) predicts that in a 30 team league we should get about 20.5 teams within 1 standard deviation, 8.2 within 2, 1.3 within 3, and the remaining .08 outside of 3. Empirically, we find:
margin 1 2 3 4 5 6 7
10 10 7 5 3 3 1 1
9 10 10 3 2 4 0 1
8 10 10 3 4 2 1 0
7 11 11 2 4 2 0 0
6 16 5 6 2 1 0 0
5 16 9 4 1 0 0 0
4 17 9 3 1 0 0 0
3 18 8 3 1 0 0 0
2 19 10 1 0 0 0 0
1 21 6 3 0 0 0 0
model 20.5 8.2 1.3 0.1
Thus, games decided by 1 or 2 points are absolutely indistinguishable from luck. Games decided by 3-5 points show a bit of evidence for a skill component, games decided by 6-7 a bit more, and games decided by 8-10 are almost if not entirely skill. The 3 outliers for 3-5 are Minnesota in 3 point games (-3.3), Minnesota in 4 point games (-3.4), Dallas in 5 point games (+3.5).
The average z-score is going to be clustered around 0 for all margins, because every game that one team wins another team has to lose, but we can get interesting information by taking the standard deviations of the z-scores, which look like this:
http://img.photobucket.com/albums/v456/johnnyoldschool/NBAWhatsLuckGottoDo_zpsa84a922f.png
There is a potentially interesting hump at 1 point games, but this is probably just because they are the smallest samples and therefore the noisiest data. As anyone would expect, there is no discontinuous cutoff for luck. It factors into every game inversely proportional to margin, the surprise is how neatly linear the relationship is.
.
Full data, where the numbers are 1 point higher than the margin:
no okc den uta por min lac gs lal sac pho sa mem hou dal no NYK BRO BOS PHI tor ind chi mil det cle mia atl was cha orl
Team W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L W L
11 238 237 233 234 254 187 247 201 242 235 186 279 206 233 222 256 280 191 206 265 247 208 267 165 238 249 249 240 303 169 238 237 218 274 215 227 255 237 220 266 195 272 238 231 254 217 231 275 255 213 245 229 246 201 236 238 188 267 170 260 214 242
10 226 216 210 210 225 173 217 182 223 214 169 261 184 211 198 237 263 170 194 243 224 190 237 152 211 219 230 220 272 153 226 216 202 244 198 197 233 222 202 239 177 253 211 213 237 196 216 254 226 199 229 204 226 179 212 221 166 245 155 242 198 212
9 203 191 189 188 198 154 187 161 202 189 152 237 166 186 178 213 238 148 171 215 194 173 199 143 190 197 203 193 232 136 203 191 189 220 180 167 211 200 184 215 161 228 194 188 210 173 196 226 202 188 207 181 202 163 182 205 152 216 142 210 170 180
8 181 158 153 166 173 142 160 138 174 170 130 198 137 165 151 181 203 131 154 185 149 154 183 127 168 171 174 162 207 124 181 158 164 183 157 144 184 169 158 185 144 202 165 169 185 150 178 196 173 166 175 152 179 142 154 179 135 181 121 180 154 153
7 148 134 131 142 142 129 132 110 150 141 111 166 115 137 117 158 169 118 132 148 130 126 148 104 142 142 151 135 174 106 148 134 139 156 133 121 159 146 137 153 124 160 131 148 150 120 154 168 141 142 146 126 152 113 136 151 116 157 102 147 127 135
6 121 108 108 117 115 106 108 89 123 117 90 130 89 109 96 131 137 94 115 118 104 104 117 90 110 118 128 105 142 90 121 108 112 123 110 99 137 122 114 125 101 120 103 132 117 103 119 132 114 117 119 103 116 92 110 124 105 124 88 120 99 105
5 98 85 85 89 93 87 82 67 101 88 66 110 72 82 79 103 103 77 90 88 74 71 97 66 77 91 100 79 105 73 98 85 90 87 86 79 108 94 80 96 77 98 72 103 87 79 85 98 89 91 88 78 94 73 79 88 86 94 66 89 76 82
4 72 56 64 68 73 64 57 49 78 48 48 84 49 61 54 74 77 61 65 69 51 49 75 52 59 74 70 59 85 54 72 56 60 61 60 56 78 73 58 67 55 70 56 70 64 59 60 71 57 65 63 61 68 58 56 68 71 67 53 62 55 61
3 46 33 40 45 48 37 37 37 50 29 34 47 34 39 33 43 46 40 40 42 36 29 46 31 39 40 44 33 51 38 46 33 38 45 41 32 49 52 36 39 39 43 40 49 37 38 32 48 37 40 38 36 39 38 31 47 42 42 33 38 30 36
2 21 17 18 20 26 12 13 17 22 15 13 18 16 17 11 21 23 18 18 11 11 9 21 9 17 18 16 10 15 15 21 17 17 14 13 14 16 19 16 17 17 20 21 16 17 23 11 23 18 20 23 21 15 12 17 26 17 16 14 18 11 18