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Stats for Mr. Simmons, part II
Coach Substitution Patterns

Bill Simmons Sports Guy A response to Bill Simmons,
ESPN's "The Sports Guy"


Last time round, Bill had asked for some stats on how often each team had blown 4th quarter leads in an attempt to support his argument that that Boston would be better served by getting a new coach than trading away their best player Paul Pierce.

This time Bill has a new theory on ways to evaluate coaching ability:

"I am convinced that Doc makes more substitutions per game and uses more lineups per game than any other coach in the league except possibly the Knicks. Is there any way to figure this out? And is there a correlation between a team's success and the frequency/infrequency of substitutions during a game? It just seems like the smarter coach figure out their five best players, play them as much as possible, spell them when they get tired with bench guys, then make sure those same five guys are playing the last 7-8 minutes of the game. I don't think this is rocket science. But Doc shuttles guys in and out like an NHL coach. Lemme know if this can be figured out."

As it happens we've been sitting on a "coach substitution" article concept for a while, and yes indeed there are ways to figure some of this stuff out...

1) Lineups used
Let's begin with the easiest of all, simply how many different 5-man units a team has utilized over the course of the season. We'll track this year to Feb. 5th and last year.

2005-06 Season (thru Feb. 5th)
Team
Units
W
L
 Detroit 101 39 7
 Phoenix 154 31 16
 Toronto 173 17 31
 New Orleans 188 24 22
 Atlanta 193 14 32
 Miami 206 29 19
 Cleveland 209 27 19
 Sacramento 210 20 27
 Milwaukee 226 24 22
 Washington 230 22 23
 New Jersey 241 24 21
 Denver 242 26 23
 Seattle 243 19 28
 L.A. Lakers 246 24 23
 Golden State 257 21 25
 Memphis 257 26 20
 Dallas 259 37 10
 Philadelphia 259 24 23
 Minnesota 264 21 25
 San Antonio 269 37 10
 Chicago 270 20 26
 Indiana 275 23 22
 Utah 279 23 25
 Orlando 289 19 26
 L.A. Clippers 292 28 17
 Houston 293 18 29
 Portland 337 17 29
 Boston 347 18 30
 New York 407 14 32
 Charlotte 479 12 36
2004-05 Season
Team
Units
W
L
 Minnesota 231 44 38
 Phoenix 255 62 20
 Seattle 267 52 30
 Cleveland 297 42 40
 Toronto 308 33 49
 Philadelphia 330 43 39
 Miami 346 59 23
 Boston 358 45 37
 L.A. Lakers 369 34 48
 Milwaukee 369 30 52
 Sacramento 369 50 32
 Detroit 383 54 28
 Memphis 392 45 37
 Chicago 398 47 35
 L.A. Clippers 400 37 45
 Portland 416 27 55
 Dallas 433 58 24
 Golden State 440 34 48
 San Antonio 442 59 23
 New York 444 33 49
 Washington 444 45 37
 Houston 452 51 31
 Denver 453 49 33
 New Orleans 460 18 64
 Indiana 483 44 38
 Orlando 496 36 46
 Utah 505 26 56
 Atlanta 591 13 69
 New Jersey 594 42 40
 Charlotte 709 18 64

So first of all it's only fair to point out some obvious things: teams that make trades or have serious injury issues are much more likely to use lots of different 5-man units. Likewise, teams with lots of depth or bad teams trying to figure out a winning lineup with what they've got on the roster will experiment more often. Still when you check the units used against winning percentage, you'll find a -.39 correlation, which is a reasonably strong way of saying that more successful teams tend to use fewer different units.

This season the Celtics have used the third most array of 5-man units, and almost as many as they did in the entire 2004-05 season, so maybe there's something to Bill's argument that Doc tends to be a little quick with the substitution, even realizing the recent trade has a big impact on these numbers. Of course it's hard not to notice that the league leading Pistons have by far the fewest units used to this point.

Let's look next at the raw substitution numbers.

2) Number of substitutions
We'll count the number of substitutions per game with one minor note: at the start of the third quarter, we'll assume the initial starting lineup will return again, and only count diversions from this for subs, regardless of who was in the game at the end of the first half.

Substitutions per game (2005-06 Season thru Feb 5th)
Team
Subs/Game
1st
Qtr
2nd
Qtr
3rd
Qtr
4th
Qtr+
 San Antonio
27.7
4.7
8.5
5.1
9.3
 New York
26.9
4.8
8.1
6.0
8.1
 Indiana
26.0
5.4
7.4
5.3
7.9
 Boston
25.5
5.0
7.1
4.6
8.7
 Charlotte
25.5
4.6
8.4
5.5
7.0
 Dallas
25.1
4.7
8.0
5.0
7.5
 Chicago
24.7
5.3
7.5
5.1
6.7
 Cleveland
24.2
4.2
8.0
4.5
7.5
 Portland
24.2
4.8
6.9
4.4
8.0
 Denver
22.4
3.7
7.4
3.9
7.5
 Milwaukee
22.4
3.5
7.3
3.7
7.8
 Atlanta
22.1
4.6
7.1
4.7
5.7
 New Jersey
22.1
3.8
7.0
4.0
7.4
 Philadelphia
22.1
3.3
8.4
3.2
7.3
 Miami
21.8
3.4
7.2
3.7
7.5
 Houston
21.6
3.2
7.2
4.0
7.3
 Seattle
21.6
3.5
7.4
4.1
6.6
 L.A. Clippers
21.1
2.8
7.2
3.0
8.0
 L.A. Lakers
21.1
2.6
8.0
3.2
7.3
 Golden State
21.0
3.3
7.6
3.9
6.3
 Memphis
20.6
3.7
6.8
3.8
6.3
 Orlando
19.9
3.1
7.4
3.4
6.0
 Utah
19.1
3.3
6.5
3.8
5.5
 Washington
18.8
2.7
6.6
4.0
5.4
 Toronto
18.7
3.6
6.1
3.8
5.1
 Minnesota
18.5
2.5
7.4
3.2
5.5
 New Orleans
18.5
3.1
6.6
2.9
5.9
 Detroit
18.0
2.5
7.0
2.4
6.1
 Sacramento
16.8
2.1
6.9
2.0
5.7
 Phoenix
16.6
3.5
5.9
3.1
4.2

So Doc's Celtics have indeed made heavy use of substitutions, ranking 4th overall in most subs, and 3rd in first quarter subs, and 2nd in 4th quarter/overtime subs. Of course you can't conclude that it's a bad thing to be active on in game maneuvers, especially since none other than the defending champion Spurs lead the league. In fact, the correlations between pure number of substitutions and winning percentage is practically zero over the past two seasons.

So given the number alone may not tell the full story, how do we measure the effectiveness of a coach's "matchup maneuvering" in the course of games? You could look at the sub numbers for a team against its opponents, and indeed we did, but that wasn't very revealing. Instead we'd propose a couple of additional tweaks:

- team performance and % of game time with 0-5 starters on the floor
- team performance based on subs versus opponent subs at a given time

3) Starters on the floor
A team starts the game with five starters on the floor and then substitutes in and out from there. Not all teams necessarily use the "best five start" approach, with many teams using a different 5-man combo down the stretch of a close game than in the opening minutes. Still, most coaches try and keep at least a few starters out there at all times as opposed to a wholescale first unit/second unit approach (but maybe there is something to trying to build compatible "lines" like they do in hockey).

It's an easy matter for us to count up the minutes and results with each various numbers of starters in the game:

Starters on the floor:
4 to 5
2 to 3
0 to 1
Team
Time
+/-
Time
+/-
Time
+/-
 Atlanta 36%  -106  50%  -122  11%  -27 
 Boston 52%  +1  26%  -51  19%  -72 
 Charlotte 43%  -166  39%  -73  14%  -11 
 Chicago 34%  +15  53%  -78  10%  +29 
 Cleveland 45%  +76  45%  +132  8%  -60 
 Dallas 45%  +141  43%  +165  9%  -4 
 Denver 44%  -3  43%  +37  10%  -4 
 Detroit 60%  +342  30%  +150  7%  -94 
 Golden State 51%  +3  37%  +9  8%  -13 
 Houston 50%  -107  40%  +21  7%  +8 
 Indiana 42%  +30  42%  +67  13%  -9 
 L.A. Clippers 57%  +140  35%  +32  5%  -43 
 L.A. Lakers 53%  +28  34%  +33  9%  +0 
 Memphis 56%  +125  30%  -23  11%  +23 
 Miami 50%  +136  39%  +67  8%  -6 
 Milwaukee 56%  +47  30%  -56  10%  -78 
 Minnesota 51%  +33  35%  -12  11%  -44 
 New Jersey 58%  +133  26%  -53  13%  -75 
 New Orleans 47%  -128  39%  +120  10%  -32 
 New York 36%  -205  41%  -104  21%  +72 
 Orlando 52%  -29  38%  -83  7%  +6 
 Philadelphia 65%  +13  26%  -19  6%  -31 
 Phoenix 58%  +248  34%  +17  5%  +23 
 Portland 43%  -73  31%  -99  23%  -117 
 Sacramento 62%  +10  27%  -45  7%  -5 
 San Antonio 41%  +196  45%  +122  11%  +0 
 Seattle 48%  -70  35%  -138  15%  -10 
 Toronto 40%  -120  43%  -8  14%  -33 
 Utah 40%  -41  38%  -80  20%  -19 
 Washington 48%  +50  40%  +6  9%  -27 

How to read this table: We measured how often during each game the team had a certain number of starters on the floor, tallied this up into percentages, along with the unadjusted plus/minus. For example Atlanta has had 4 or 5 starters on the floor during 36% of their total minutes, with a -106 plus/minus under these conditions. [Keep in mind that moments when a team has "zero starters" in the game are often essentially garbage time when games are already decided.]

So, looking back at the Celtics you'll notice that as long as they have 4 or 5 starters on the court they've been okay -- a +1 plus/minus in 52% of minutes -- but when Doc has gone deeper into the bench for a five man unit, it's started to hurt: -51 in 26% of minutes with 2/5 or 3/5 starters, and -72 in 19% of minutes when he's down to one or zero starters on the floor. The Celtics do lead the league in "percentage of minutes played with exactly one starter on the floor."

Again, interpretation of these numbers is no simple thing, and can't just be pinned as cause and effect of the coach... we'll let Mr. Simmons reach his own conclusions.

The other side of the matchup is how your opponents play against you with the various levels of starters on the court:

OPPONENT unit distribution and results (how the opponents have done AGAINST a team)
Opposing Starters on the floor:
4 to 5
2 to 3
0 to 1
 Team
Time
+/-
Time
+/-
Time
+/-
 vs Atlanta 48%  +203  37%  +114  13%  -62 
 vs Boston 51%  -2  37%  +80  8%  +44 
 vs Charlotte 48%  +272  37%  +81  12%  -103 
 vs Chicago 49%  +99  38%  +1  11%  -66 
 vs Cleveland 48%  -55  37%  -43  11%  -50 
 vs Dallas 51%  -169  33%  -87  14%  -46 
 vs Denver 47%  +44  39%  -63  11%  -11 
 vs Detroit 47%  -237  37%  -199  12%  +38 
 vs Golden State 49%  +61  34%  -20  15%  -40 
 vs Houston 49%  +88  38%  +41  10%  -51 
 vs Indiana 48%  -59  39%  -6  10%  -23 
 vs L.A. Clippers 51%  -71  36%  -27  10%  -31 
 vs L.A. Lakers 47%  +15  40%  -115  11%  +39 
 vs Memphis 51%  -97  36%  -33  10%  +5 
 vs Miami 49%  -75  38%  -76  10%  -46 
 vs Milwaukee 49%  +8  40%  +104  8%  -25 
 vs Minnesota 49%  +76  35%  -91  12%  +38 
 vs New Jersey 45%  +29  38%  -6  14%  -28 
 vs New Orleans 49%  +86  37%  -7  12%  -39 
 vs New York 52%  +306  36%  +42  10%  -111 
 vs Orlando 48%  -8  36%  +124  12%  -10 
 vs Philadelphia 50%  +93  38%  -8  9%  -48 
 vs Phoenix 47%  -140  43%  -133  8%  -15 
 vs Portland 50%  +145  36%  +84  11%  +60 
 vs Sacramento 49%  -45  38%  +114  10%  -29 
 vs San Antonio 47%  -214  38%  -31  11%  -73 
 vs Seattle 50%  +144  36%  +54  10%  +20 
 vs Toronto 48%  +167  38%  -14  11%  +8 
 vs Utah 48%  +58  34%  +100  15%  -18 
 vs Washington 47%  -3  38%  -46  13%  +20 

This look perhaps leaves a little less wiggle room for Doc: the Celtics have been about even against opposing teams' when four or five of the opponent starters on the floor, but when the Boston adversaries have gone with lineups with three of less starters, they've outscored the Celtics by 124 points.

If you're getting creamed by lineups with 4/5ths or more of the opposing starters, you can make a case it's primarily a talent discrepancy (or your team going with the wrong starting five), but when you're getting clobbered by the opposing bench, then it's harder to shake the notion that you are getting beat in part from the other team winning the in-game substitution matchups.

The Pistons for instance pummel the opposition regardless of what the foes throw at them, excepting the 0/1 starter garbage time minutes. Phil Jackson's Lakers as another example have been barely above even facing opponents units with four or more starters, but once the opponent goes deeper into the bench, then the Lakers strike, outscoring their opponents by 115 against 2/3 starter lineups.

The next logical place to go with this analysis is to break down the actual substitutions and counter-moves as they happen, with ensuing results, and adjustments for how the game was going to that point. This however becomes increasingly complex (picture 6x6 grids), and while fascinating for us uber-stats freaks, perhaps a little more than is warranted here -- in other words we'll save it for another time.

Also see:
Stats for Mr. Simmons: blown 4th quarter leads, comebacks and team stats "in the clutch"


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