Stats for Mr. Simmons, part II
Coach Substitution Patterns

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:

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"