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Translating WS/48 to PER
Posted: Sat Feb 16, 2013 3:16 pm
by AYC
The average WS/48 is .100 and the all-time single-season high is .340
The average PER is 15.0 and the all-time single-season high is 31.8
Based on those ranges, I came up with the following simple formula for translating WS/48 to PER:
WS/48^(1+WS/48) * 200^(1 - (WS/48)/5)
Here are the general results the formula produces:
0.010 1.89
0.020 3.62
0.030 5.23
0.040 6.74
0.050 8.16
0.060 9.51
0.070 10.79
0.080 12.01
0.090 13.17
0.100 14.29
0.110 15.36
0.120 16.39
0.130 17.38
0.140 18.33
0.150 19.25
0.160 20.15
0.170 21.01
0.180 21.85
0.190 22.66
0.200 23.45
0.210 24.23
0.220 24.98
0.230 25.71
0.240 26.43
0.250 27.13
0.260 27.81
0.270 28.48
0.280 29.14
0.290 29.79
0.300 30.42
0.310 31.05
0.320 31.66
0.330 32.27
0.340 32.87
I'm pretty happy with those results, except the formula doesn't work well if a player's WS/48 is negative. Any thoughts or suggestions?
Re: Translating WS/48 to PER
Posted: Sat Feb 16, 2013 3:26 pm
by v-zero
Why not run a linear-regression between PER and WS/48?
Re: Translating WS/48 to PER
Posted: Sat Feb 16, 2013 3:37 pm
by AYC
Because I'm an amateur! I just ran across this earlier post on the subject and it inspired me:
viewtopic.php?f=2&t=299
Re: Translating WS/48 to PER
Posted: Sat Feb 16, 2013 3:44 pm
by AYC
Let's call it WinPER. I calculated it for the following 30 players (ages 21-32). You can see that it's pretty close to actual PER for most players.
Code: Select all
WS/48 WinPER PER AVG DIFF/AVG
01 MJ 0.276 28.9 29.6 29.2 -0.025
02 LBJ 0.264 28.1 29.0 28.5 -0.032
03 KAJ 0.262 27.9 26.8 27.4 0.042
04 DR 0.261 27.9 27.8 27.8 0.003
05 WC 0.259 27.7 28.1 27.9 -0.013
06 CP3 0.254 27.4 26.1 26.8 0.049
07 SO 0.234 26.0 28.5 27.2 -0.092
08 EJ 0.231 25.8 24.5 25.1 0.051
09 OR 0.220 25.0 24.5 24.7 0.019
10 CB 0.219 24.9 25.1 25.0 -0.008
11 TD 0.219 24.9 25.0 25.0 -0.004
12 DN 0.218 24.8 24.0 24.4 0.034
13 LB 0.216 24.7 24.1 24.4 0.024
14 JW 0.215 24.6 22.9 23.8 0.072
15 BP 0.213 24.5 25.3 24.9 -0.034
16 JS 0.207 24.0 21.8 22.9 0.096
17 KG 0.205 23.8 24.8 24.3 -0.039
18 BR 0.201 23.5 19.4 21.5 0.193
19 JE 0.199 23.4 23.2 23.3 0.008
20 DH 0.198 23.3 23.5 23.4 -0.009
21 KB 0.196 23.1 24.4 23.8 -0.053
22 KML 0.196 23.1 23.3 23.2 -0.007
23 DWD 0.195 23.1 25.6 24.3 -0.104
24 AD 0.195 23.1 22.1 22.6 0.043
25 HO 0.191 22.7 24.5 23.6 -0.074
26 MM 0.188 22.5 23.2 22.9 -0.031
27 CD 0.178 21.7 21.3 21.5 0.018
28 PE 0.165 20.6 22.1 21.3 -0.071
29 EB 0.151 19.3 23.4 21.4 -0.190
30 IT 0.114 15.8 18.4 17.1 -0.154
Re: Translating WS/48 to PER
Posted: Sat Feb 16, 2013 4:28 pm
by v-zero
The Linear line would be something like: PER = 95*WS/48 + 3
This isn't perfect, but can handle negative guys.
However, the more useful equation is the one which converts PER to WS/48, because WS/48 is a useful number, approximating wins added, whilst PER is an abstraction that has to be explained with examples.
Re: Translating WS/48 to PER
Posted: Sat Feb 16, 2013 6:52 pm
by talkingpractice
AYC wrote:Any thoughts or suggestions?
You might want to look at translating just Offensive win shares to PER, as PER only looks at offense (and imo does a pretty ok job at it).
Re: Translating WS/48 to PER
Posted: Sun Feb 17, 2013 3:02 pm
by AYC
I wasn't trying to predict anything. I just wanted to match one to the other as closely as I could. I think my formula does that pretty well. For my purposes it's OK to just ignore the rare players who have negative WS/48.
PS Aren't Win Shares more retrodictive than predictive?
Re: Translating WS/48 to PER
Posted: Sun Feb 17, 2013 3:04 pm
by AYC
PER includes blocks, steals and defensive rebounds, so I don't think you can say it's only a measure of offense.
Re: Translating WS/48 to PER
Posted: Sun Feb 17, 2013 3:23 pm
by v-zero
Win shares are probably the best commonly available box-score metric for prediction, certainly very superior to PER.
Re: Translating WS/48 to PER
Posted: Mon Feb 18, 2013 6:13 pm
by AYC
The following formula works for going from PER to WS/48:
PER/200^(1-PER/240)
Code: Select all
01.0 0.005
02.0 0.010
03.0 0.016
04.0 0.022
05.0 0.028
06.0 0.034
07.0 0.041
08.0 0.048
09.0 0.055
10.0 0.062
11.0 0.070
12.0 0.078
13.0 0.087
14.0 0.095
15.0 0.104
16.0 0.114
17.0 0.124
18.0 0.134
19.0 0.145
20.0 0.156
21.0 0.167
22.0 0.179
23.0 0.191
24.0 0.204
25.0 0.217
26.0 0.231
27.0 0.245
28.0 0.260
29.0 0.275
30.0 0.291
31.0 0.307
32.0 0.324
33.0 0.342
34.0 0.360
35.0 0.379
36.0 0.398
37.0 0.419
38.0 0.440
Re: Translating WS/48 to PER
Posted: Mon Feb 18, 2013 6:28 pm
by AYC
Code: Select all
WS/48 PER-WS PER AVG
01 MJ 0.276 0.284 29.6 0.280
02 LBJ 0.264 0.275 29.0 0.270
03 SO 0.234 0.267 28.5 0.251
04 WC 0.259 0.261 28.1 0.260
05 DR 0.261 0.257 27.8 0.259
06 KAJ 0.262 0.242 26.8 0.252
07 CP3 0.254 0.232 26.1 0.243
08 DWD 0.195 0.225 25.6 0.210
09 BP 0.213 0.221 25.3 0.217
10 CB 0.219 0.218 25.1 0.219
11 TD 0.219 0.217 25.0 0.218
12 KG 0.205 0.214 24.8 0.210
13 EJ 0.231 0.210 24.5 0.221
14 OR 0.220 0.210 24.5 0.215
15 HO 0.191 0.210 24.5 0.201
16 KB 0.196 0.209 24.4 0.203
17 LB 0.216 0.205 24.1 0.211
18 DN 0.218 0.204 24.0 0.211
19 DH 0.198 0.197 23.5 0.198
20 EB 0.151 0.196 23.4 0.174
21 KML 0.196 0.195 23.3 0.195
22 JE 0.199 0.194 23.2 0.196
23 MM 0.188 0.194 23.2 0.191
24 JW 0.215 0.190 22.9 0.202
25 AD 0.195 0.180 22.1 0.187
26 PE 0.165 0.180 22.1 0.172
27 JS 0.207 0.176 21.8 0.192
28 CD 0.178 0.170 21.3 0.174
29 BR 0.201 0.149 19.4 0.175
30 IT 0.114 0.138 18.4 0.126
Re: Translating WS/48 to PER
Posted: Mon Feb 18, 2013 10:10 pm
by Mike G
The following formula works for going from PER to WS/48:
PER/200^(1-PER/240)
The star players you listed (can't tell who most of them are) may fit by this formula pretty well.
But there's no "y intercept" in this formula, for PER equivalent to zero WS/48.
Hollinger actually has used a PER of 10 or 11 (depending on position) to indicate a zero win-producing level. But your formula requires a negative PER to yield a negative WS rate.
This season, of 114 players with PER between 0 and 10, 61 have WS/48 > zero, and 52 are < 0
http://bkref.com/tiny/vSnwH
You'll notice I used PER of 5 = 0 WS/48 in the 'conversion' I put out in the earlier thread.
WS/48 = (PER-5)/100
You still might get a better fit with some exponent, but I don't see a theoretical reason to expect so.
Re: Translating WS/48 to PER
Posted: Tue Feb 19, 2013 12:38 am
by AYC
"The star players you listed (can't tell who most of them are) may fit by this formula pretty well."
Really? It's an all-time list; I thought initials would be sufficient for any knowledgeable NBA fan. Anyway, as I said in my initial post, the formula is based on the range from the lg avg. to single-season best in both metrics; I wasn't focused on fitting it to specific players. I can only find 53 players in NBA history with a minimum of 100 games with a negative career WS/48, with the lowest one at -.080. Only one of those players played in over 400 career games, and only 2 averaged over 25 mpg.