Translating WS/48 to PER

[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?

[v-zero]

Why not run a linear-regression between PER and WS/48?

[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

[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
	

[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.

[talkingpractice]

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).

[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?

[AYC]

PER includes blocks, steals and defensive rebounds, so I don't think you can say it's only a measure of offense.

[v-zero]

Win shares are probably the best commonly available box-score metric for prediction, certainly very superior to PER.

[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

[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

[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.

[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.