2012-13 starter-sub comparisons

[Mike G]

Ed Davis of Toronto started 1 of his first 23 games, and then moved into the starting lineup for the last 12 games. Here are his unadjusted per-36 minute rates

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Ed Davis             per 36 minutes, unadjusted                           
.61    mpg   TS%   FTA    TSA   ORb   DRb   Ast   Stl   Blk    PF    Pts    X
start  31   .579   2.6   11.6   2.2   6.2   1.8    .9   1.2   2.6   13.4   24.3
sub    15   .574   4.7   12.4   4.8   8.1   1.6   1.2   1.6   5.2   14.2   30.0

TSA = 'true shot attempts' = FGA + .44*FTA
X = sum of Pts, Reb, Ast, Stl, Blk, -TO, per36
As a starter, he gets half as many FTA and PF, less than half the OReb.

[Crow]

It is either the right time to do this (making Davis a starter) and stick with it or too slow.

Valanciunas with an ok winshares per 48 but in bottom 25 in the league on xRAPM so far and has the lowest team win % while on the court.

[Mike G]

I'm going to do this for players with at least 300 minutes as a starter and 300 off the bench.
The Spurs' Tiago Splitter started 2 of their first 24 games, and the last 12.

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Tiago Splitter         per 36 minutes, unadjusted                      
.62   mpg   TS%    FGA   FTA   ORb   DRb   Blk    TO    PF    Pts    X
start 25   .587    9.8   5.6   2.1   6.4   1.4   1.8   3.0   14.5   26.1
sub   18   .655   10.8   6.0   3.0   5.7   1.2   2.2   3.6   17.6   28.8

Off the bench he got more shots and hit a better percentage.
More OReb off the bench is partly offset by fewer DReb.


Ryan Anderson started for Orlando for a couple of years, and this year he's come off the bench in 16 of 33 games. Because he plays almost as many minutes off the bench, his stats are gotten with and against similar players.

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Ryan Anderson         per 36 minutes, unadjusted                
.67   mpg   TS%    FGA   FTA   ORb   DRb   Stl   PF    Pts    X
start 35   .591   15.5   1.4   2.5   5.5   .7   3.0   19.1   28.4
sub   30   .554   17.3   2.3   2.7   4.6   .5   2.4   20.3   28.9

As a starter, he's shot better but not as often. He bucks the trend of fouling more off the bench.
I'm not showing categories that are virtually the same as starter and as sub.

EDIT: Atop the 'start/sub' column is the estimated fraction of opponents and teammates who have been starters in the player's minutes.

[kjb]

Mike: Can you post your "minutes against starters" estimator?

[Mike G]

For starters and subs, the estimated avg % of starters on the court:

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mpg  start   sub
48    .67    .66
42    .71    .62
36    .75    .58
30    .79    .54
24    .84    .50
18    .88    .46
12    .92    .42
6     .96    .37
0    1.00    .33

It's assumed that starters average 32 mpg -- 2/3 of a game. Actually I've assumed 48.4 minutes in the avg game.
A starter who plays just a few seconds has played entirely (100%) with other starters on the court.
A guy who comes off the bench after just a few seconds and stays on the floor the rest of the game is playing against 2/3 starters, on avg.

Leading the league in estimated Sta% are Willie Green and Andrew Bogut (4 G), who have started every game but average just 18 minutes.
Warriors' rookie Kent Bazemore has been in 17 games, no starts, avg 2.1 mpg. His est Sta% is .35, the league low.

[v-zero]

How did you derive this data, if you don't mind sharing?

[Mike G]

It's a straight line deduction, from correct values at the extremes of zero and 48 minutes.
It does not account for quirks of coaching or player specialization.
For example, a backup center may specialize in fouling Dwight Howard early in the game. He plays relatively few minutes, but they aren't garbage minutes against other backups.

If other starters leave and re-enter the game at random points in time, and they average 32 minutes, you get this distribution.
The general equation is:
Sta% = (GS/G)*(1-.333*mpg/48.4) + (1-GS/G)*.333*(1+mpg/48.4)

The first half is for games started, and the 2nd half is games not started.

[Mike G]

Cavs' rookie Tyler Zeller became a starter 10 games ago; not so much from merit, but because Anderson Varejao has been injured.

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Tyler Zeller - Cle         per 36 minutes, unadjusted        
.59   mpg   TS%    FGA   FTA   ORb   DRb   Ast  Stl   Blk    PF
Start 34   .448   11.4   2.7   2.5   4.3   1.8   .7   1.4   4.0
sub   22   .486   10.1   3.1   3.3   4.8   1.3   .9   1.0   5.0

Now shooting more but worse, he scores at the same rate. Overall a wash.

[v-zero]

How did you get the value of 0.33 for subs playing for almost no minutes?

[Mike G]

I don't remember.
But the league adds up to .661 St%, which is 32/48.4

[v-zero]

Fair enough, I'll have to take a look at using that at some point. Thanks.

[Mike G]

Also .33 is midway between what a random 1 minute appearance would be (.66) and what garbage time would be (close to zero).

While mop-up time against other 5 mpg players may be the anecdotal norm for 5 mpg guys, there are also the last-second shot and FT% specialists, the fouling specialists, etc.

Regardless of the formula, there will be individual outliers. But a straight line is likely pretty close for the vast majority.

[v-zero]

I have given this some thought. I like the logic, but the problem is that the total starter minutes faced by each player in the team won't add up to the opposition starter minutes under those values. The logic for the line for starters makes sense (assuming 32 minutes per starter on both teams) but that logic also defines the intercept and slope of the equation for starter minutes faced by backups under the constraint that total starter minutes faced must equal total opponent starter minutes. The problem then becomes a quadratic sum in minutes played by each bench player.

In the case where each bench player plays 16 minutes and there are five bench players (contrived but good for illustration) we get an equation for bench players of:

% starters faced = -2*minutes played/135 + 92/135

This is the only equation which will satisfy the constraints.

Interestingly in the limit as bench player individual minutes tends to zero (i.e. if you could play infinitely many bench players momentarily) then the solution reduces to:

% starters faced = 4/9 (+ (2/9)*minutes played, but since minutes played ---> 0, this will disappear).

[Mike G]

Hmm, ok.
So a lineup whose starters play 40, 36, 32, 28, and 24 minutes sum to 160 (32*5) starter minutes, but my formula predicts the team's equivalent vs-starter minutes sum to 158.2

This doesn't seem too bad. In reality, starters play much wider range of minutes than that, so being off by another 1 or 2% seems inconsequential.

Another large uncertainty is: Who is really a "starter"? The player who started the game, or the injured "real" starter he has replaced?

And in playoffs, starters may avg around 36 minutes. But I don't adjust the estimator for that. Everyone is scaled to the same standard, so it still serves my purpose.

[Mike G]

A few more bigs.

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Bismack Biyombo - Cha       per 36 minutes, unadjusted      
.67   mpg   TS%   FGA   FTA   ORb   DRb   Blk    TO    PF    X
start 30   .465   5.7   3.9   3.8   7.1   1.6   1.3   3.0   18.9
sub   21   .492   6.2   2.1   2.9   6.3   2.9   1.6   4.0   18.4

Larry Sanders - Mil       per 36 minutes, unadjusted       
.66   mpg   TS%   FGA   FTA   ORb   Stl   Blk    TO    PF    Pts    X
start 26   .543   9.5   1.5   4.0   1.6   4.5   2.3   4.8   11.0   28.7
sub   23   .568   9.8   3.0   3.4   1.0   4.8   2.0   6.2   12.6   29.6

Marcus Morris - Hou         per 36 minutes, unadjusted                     
.62   mpg  TS%    FGA   ORb   DRb   Ast   Stl   Blk   TO    PF    Pts    X
start 28  .576   11.5   1.5   4.1   2.1    .6   .4   1.8   2.7   14.6   21.4
sub   20  .529   12.3   2.4   5.1   1.1   1.2   .7   1.1   4.2   14.1   23.6

Markieff Morris - Phx       per 36 minutes, unadjusted           
.60   mpg  TS%    FGA   FTA   ORb   DRb  Stl  Blk    TO    PF    Pts    X
start 26  .553   13.3   1.5   2.4   5.3   .8   .9   1.3   3.2   15.4   25.9
sub   18  .421   14.7   2.6   2.8   4.7  2.1  1.3   1.8   4.7   13.3   24.6

The assumption is that when bench players do well, they often move into the starting lineup. When starters struggle, they go to the bench. Therefore, we suppose their output while starting should be better. But it doesn't seem to be so. The conclusion is that it must be easier to get shots, rebounds, blocks, steals against subs.
Assists and shooting% seem to be better with more starters on the floor. And fewer fouls, at least for bigs.