# Plus/minus - Cal vs. ASU

While the author passed up the opportunity to attend this past weekend's basketball games in favor of attending several automobile races, the plus/minus for the Cal-Arizona State has finally arrived, limping in four days after the game's conclusion. For those that are new to this, a brief explanation of the plus/minus has been included, as well as a chart showing how well the starting lineup has been performing compared to the other lineups.

For those that are relatively new to plus/minus charts, here are a few things to keep in mind.

1.  Calculated similarly to hockey's plus/minus, it is a measure of a player's effectiveness, but not the measure.

The plus/minus measures how many points a team scores and gives up when a particular player is on the court. It generally does a better job of indicating the effectiveness of role players than it will for starters.  If a player plays 38 minutes of a 40 minute game that a team wins by five, it's likely that player's plus/minus will be very close to a +5. A reserve who comes in and makes a key contribution during a run, could see a number quite a bit higher than that. For example, during Cal's 58-55 loss to Arizona earlier this year, the starters all had plus/minus numbers between 0 and -8. Theo Robertson came off the bench and had an astonishing +8 during 20 minutes of play.   There is no single statistical measure that determines how well someone played; not points, not free-throw percentage, not steals and not plus/minus.  If over time, a player continually shows up in the top two or three in plus/minus, it's a good indication that player is doing something to help the team play more efficiently.

2.  Yes, a player can be effective without scoring.

Earlier in conference play, the Bears were fortunate to get a couple of strong peformances from a reserve who generally sees extended minutes only if somebody happens to get in foul trouble. During these two games (which were not consecutive), the player played a total of 25 minutes, scored 0 points, had 5 rebounds and 2 assists; numbers one would normally associate with someone who's playing just to keep things from falling apart.

 With Player Without Player Net. Diff. Opponent Min. Plus Minus Difference Min. Plus. Minus. Diff. Stanford 11 18 13 +5 29 43 62 -19 24 WSU 14 23 15 +8 26 32 38 -6 14 Total 25 41 28 +13 55 75 100 -25 38

The net difference for this player was far greater than it was for anybody else on the team during these two games. It's safe to say that this player was providing something of value to the team during those 25 minutes; something one might not conclude by looking at his scoring and rebounding totals during these two games.

3.  Offense/defense substitutions can skew the numbers.

While California head coach Ben Braun has used the offense-for-defense substitution pattern less this year than he has in previous years, it's something that can be useful depending on what matchups are the floor, what the foul situation is, and the need to keep better free throw shooters on the floor.  However they can cause considerable wreckage to a player's plus/minus numbers.  Take for example Leon Powe and DeVon Hardin's numbers from last Saturday's Cal/Arizona State game.

 Player Min +Pts -Pts Pts Reb Ast Diff Leon Powe 44 62 54 23 10 0 +8 DeVon Hardin 39 46 52 13 10 0 -6

One would gather that the team did considerably better with Powe than it did with Hardin. But let's compare the players after regulation when the score was tied at 51.

 Player +Pts -Pts Diff Leon Powe 49 46 +3 DeVon Hardin 38 39 -1

There's a slight difference between the two players at this point.   During the final 2:20 of the first overtime, Powe and Harden were swapped out on offense/defense substitutions, with Powe in for offense and Hardin in for defense.   This meant that barring turnovers and fast breaks, Powe would rarely be oncourt when the team was playing defense and Hardin would rarely be on court when the team was on offense.  After the first overtime, the numbers looked like this:

 Player +Pts -Pts Diff Leon Powe 56 49 +7 DeVon Hardin 40 45 -5

The tiny four-point difference between the two players has now mushroomed into a twelve-point difference. It didn't mean that Powe played significantly more inspired basketball or that Hardin all of a sudden lost his way, it's just an effect of the offense for defense substitution.

Anytime an offense/defense substitution has a pronounced effect on plus/minus numbers, it will usually be pointed out.  While it's usually not been practice to do any sort of adjustment for the plus/minus, an adjustment where Powe/Harden split the net effect of the offense/defense substitution would have resulted in something like this.

 Player +Pts -Pts Diff Leon Powe 60 56 +4 DeVon Hardin 48 50 -2

The adjustment is very slight, but a 14-point difference between the two players has now been whittled to six.

4.  Keep an eye on the starting lineup.

(This doesn't have much to do with interpreting the plus/minus, but should prove interesting for people who like looking at charts.)

Looking at the last 12 conference games, notice the difference between how the team plays when the starting lineup is intact versus when all other combinations are used. The difference was negligble during the first seven games due to early foul trouble that kept the starting lineup from playing together very long.

Up until the second Stanford game, the Bears went with a starting lineup of Ubaka, Omar Wilkes, Midgley, Hardin, and Powe. Starting with the second Stanford game, Theo Robertson replaced an injured Wilkes in the starting lineup.

During the past five games, the starting lineup has been a +40 in 98 minutes of play, while all other combinations have been -10 in 112 minutes of play. What's encouraging is that the starting lineup has been able to stay intact longer; due primarily to Powe, Hardin, and to a lesser extent Midgley staying out of early foul trouble.

 With Starting Lineup Without Starting Lineup Net. Diff. Opponent Min. Plus Minus Difference Min. Plus. Minus. Diff. Oregon 18:10 38 29 +9 21:50 39 37 +2 7 Oregon St. 15:13 18 24 -6 24:47 46 48 -2 -4 Stanford 14:43 23 25 -2 25:17 38 50 -12 10 Arizona St. 11:40 25 22 +3 28:20 63 36 +27 -24 Arizona 10:06 13 12 +1 29:54 42 46 -4 5 Washington 9:05 19 10 +9 30:55 52 59 -7 16 Washington St. 7:30 12 13 -1 32:30 43 40 +3 -4 Oregon St. 15:20 30 17 +13 24:40 39 35 +4 9 Oregon 15:20 25 20 +5 24:40 37 40 -3 8 Stanford 20:42 40 34 +6 19:18 25 28 -3 9 Arizona 23:32 51 43 +8 16:28 24 23 +1 7 Arizona St. 23:20 36 28 +8 26:40 28 37 -9 17 Home 117:32 214 181 +33 172:28 257 272 -15 48 Road 67:09 116 96 +20 132:51 219 207 +12 8 Last Five 98:14 182 142 +40 111:46 153 163 -10 50 Total 184:41 330 278 +52 305:19 476 479 -3 55

Onto the plus/minus numbers for the Cal/Arizona State game.

 Player Min +Pts -Pts Pts Reb Ast Diff Leon Powe 44 62 54 23 10 0 +8 Theo Robertson 34 48 45 3 1 3 +3 Richard Midgley 45 61 58 3 3 5 +3 Ayinde Ubaka 46 62 61 12 3 4 +1 Jordan Wilkes 4 6 7 3 0 0 -1 Nikola Knezevic 5 2 4 2 1 0 -2 Omar Wilkes 21 25 27 3 0 0 -2 Alex Pribble 4 3 7 2 0 0 -4 Rod Benson 8 5 10 0 1 0 -5 DeVon Hardin 39 46 52 13 10 0 -6

First vs. Second Half (minimum 2 minutes)

First Half Top - Ayinde Ubaka, 25-17, +8
Second Half Top - Omar Wilkes, 12-11, +1
Overtime Top - Leon Powe, 13-8, +5

First Half Bottom - Nikola Knezevic, 2-4, -2
Second Half Bottom - DeVon Hardin, 17-25, -8
Overtime Bottom - DeVon Hardin, 8-13, -5

Difference Makers

With Leon Powe in 44 minutes - 62-54, +8
Without Powe in 6 minutes - 2-11, -9

With Theo Robertson in 34 minutes - 48-45, +3
Without Robertson in 11 minutes - 16-20, -4

With Richard Midgley in 45 minutes - 61-58, +3
Without Midgley in 5 minutes - 3-7, -4

Starting Five

Ubaka, Wilkes, Midgley, Hardin, Powe in 23:20 - 36-28, +8
All other lineups in 26:40 - 28-37, -9

The starting unit averaged 1.69 points/minute (67 points/40 minutes) on offense when intact; all other lineups averaged 1.04 points/minute (42 points/40 minutes), which is a significant dropoff.  The Bears struggled when Knezevic was in the game; Cal scored just two points during the five minutes that he played. Likewise a four-minute stretch with Alex Pribble when Cal only scored three points was similarly productive.

1-2-3 Trios (+1)
Ubaka/Midgley/Robertson combos in 25:11 - 36-31, +5
Ubaka/O.Wilkes/Midgley combos in 10:12 - 14-16, -2
O.Wilkes/Knezevic/Midgley combos in 4:20 - 2-4, -2
Ubaka/Robertson/Pribble combos in 4:08 - 3-7, -4
Ubaka/O.Wilkes/Knezevic combos in 0:46 - 0-0, 0
All others in 5:23 - 9-7, +2

Frontcourt Duos
Hardin/Powe in 32:52 - 44-41, +3
Benson/Hardin n 4:32 - 2-5, -3
J. Wilkes/Powe in 4:19 - 6-7, -1
Benson/Powe in 2:54 - 3-5, -2
All others in 5:23 - 9-7, +2

Contribution Evaluation

 Player Minutes Expected Actual Difference Powe 44 -0.88 +8 +8.88 Midgley 45 -0.90 +3 +3.90 Robertson 34 -0.68 +3 +3.68 Ubaka 46 -0.92 +1 +1.92 J.Wilkes 4 -0.08 -1 -0.92 O.Wilkes 21 -0.42 -2 -1.58 Knezevic 5 -0.10 -2 -1.90 Pribble 4 -0.08 -4 -3.92 Benson 8 -0.16 -5 -4.84 Hardin 39 -0.78 -6 -5.22

Description: This stat measures the significance of a player's contribution to the team's effort. If a team wins by 10 points, and a player plays in half of the team's minutes, his expected contribution would be a +5. For example, when Cal defeated Grambling by 19 points. Brian Wethers played 28 minutes or 70% of the game. If we multiply 70% x +19, Wethers' expected contribution would be a +13.30. But for the game he was a +26, so his net for the game for a +12.70. In a perfect team situation, if everyone contributed equally, the difference column would consist of a row of zeros.

Updated Standings

 W L Home Away California 10 4 UCLA, USC WSU, Wash UCLA 10 4 OSU, Oregon Cal, Stanford Stanford 9 5 USC, UCLA Wash, WSU Washington 9 5 Stanford, Cal ASU, Arizona Arizona 9 6 ASU, Wash, WSU USC 7 7 Oregon, OSU Stanford, Cal Oregon 6 9 USC, UCLA, OSU Washington State 4 10 Cal, Stanford Arizona, ASU Oregon State 4 11 Oregon UCLA, USC Arizona State 4 11 Wash., WSU Arizona

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For those that are relatively new to plus/minus charts, here are a few things to keep in mind.

1.  Calculated similarly to hockey's plus/minus, it is a measure of a player's effectiveness, but not the measure.

The plus/minus measures how many points a team scores and gives up when a particular player is on the court. It generally does a better job of indicating the effectiveness of role players than it will for starters.  If a player plays 38 minutes of a 40 minute game that a team wins by five, it's likely that player's plus/minus will be very close to a +5. A reserve who comes in and makes a key contribution during a run, could see a number quite a bit higher than that. For example, during Cal's 58-55 loss to Arizona earlier this year, the starters all had plus/minus numbers between 0 and -8. Theo Robertson came off the bench and had an astonishing +8 during 20 minutes of play.   There is no single statistical measure that determines how well someone played; not points, not free-throw percentage, not steals and not plus/minus.  If over time, a player continually shows up in the top two or three in plus/minus, it's a good indication that player is doing something to help the team play more efficiently.

2.  Yes, a player can be effective without scoring.

Earlier in conference play, the Bears were fortunate to get a couple of strong peformances from a reserve who generally sees extended minutes only if somebody happens to get in foul trouble. During these two games (which were not consecutive), the player played a total of 25 minutes, scored 0 points, had 5 rebounds and 2 assists; numbers one would normally associate with someone who's playing just to keep things from falling apart.

The net difference for this player was far greater than it was for anybody else on the team during these two games. It's safe to say that this player was providing something of value to the team during those 25 minutes; something one might not conclude by looking at his scoring and rebounding totals during these two games.

3.  Offense/defense substitutions can skew the numbers.

While California head coach Ben Braun has used the offense-for-defense substitution pattern less this year than he has in previous years, it's something that can be useful depending on what matchups are the floor, what the foul situation is, and the need to keep better free throw shooters on the floor.  However they can cause considerable wreckage to a player's plus/minus numbers.  Take for example Leon Powe and DeVon Hardin's numbers from last Saturday's Cal/Arizona State game.

One would gather that the team did considerably better with Powe than it did with Hardin. But let's compare the players after regulation when the score was tied at 51.

There's a slight difference between the two players at this point.   During the final 2:20 of the first overtime, Powe and Harden were swapped out on offense/defense substitutions, with Powe in for offense and Hardin in for defense.   This meant that barring turnovers and fast breaks, Powe would rarely be oncourt when the team was playing defense and Hardin would rarely be on court when the team was on offense.  After the first overtime, the numbers looked like this:

The tiny four-point difference between the two players has now mushroomed into a twelve-point difference. It didn't mean that Powe played significantly more inspired basketball or that Hardin all of a sudden lost his way, it's just an effect of the offense for defense substitution.

Anytime an offense/defense substitution has a pronounced effect on plus/minus numbers, it will usually be pointed out.  While it's usually not been practice to do any sort of adjustment for the plus/minus, an adjustment where Powe/Harden split the net effect of the offense/defense substitution would have resulted in something like this.

The adjustment is very slight, but a 14-point difference between the two players has now been whittled to six.

4.  Keep an eye on the starting lineup.

(This doesn't have much to do with interpreting the plus/minus, but should prove interesting for people who like looking at charts.)

Looking at the last 12 conference games, notice the difference between how the team plays when the starting lineup is intact versus when all other combinations are used. The difference was negligble during the first seven games due to early foul trouble that kept the starting lineup from playing together very long.

Up until the second Stanford game, the Bears went with a starting lineup of Ubaka, Omar Wilkes, Midgley, Hardin, and Powe. Starting with the second Stanford game, Theo Robertson replaced an injured Wilkes in the starting lineup.

During the past five games, the starting lineup has been a +40 in 98 minutes of play, while all other combinations have been -10 in 112 minutes of play. What's encouraging is that the starting lineup has been able to stay intact longer; due primarily to Powe, Hardin, and to a lesser extent Midgley staying out of early foul trouble.

Onto the plus/minus numbers for the Cal/Arizona State game.

(minimum 2 minutes)

First Half Top - Ayinde Ubaka, 25-17, +8
Second Half Top - Omar Wilkes, 12-11, +1
Overtime Top - Leon Powe, 13-8, +5

First Half Bottom - Nikola Knezevic, 2-4, -2
Second Half Bottom - DeVon Hardin, 17-25, -8
Overtime Bottom - DeVon Hardin, 8-13, -5

With Leon Powe in 44 minutes - 62-54, +8
Without Powe in 6 minutes - 2-11, -9

With Theo Robertson in 34 minutes - 48-45, +3
Without Robertson in 11 minutes - 16-20, -4

With Richard Midgley in 45 minutes - 61-58, +3
Without Midgley in 5 minutes - 3-7, -4

Starting Five

Ubaka, Wilkes, Midgley, Hardin, Powe in 23:20 - 36-28, +8
All other lineups in 26:40 - 28-37, -9

The starting unit averaged 1.69 points/minute (67 points/40 minutes) on offense when intact; all other lineups averaged 1.04 points/minute (42 points/40 minutes), which is a significant dropoff.  The Bears struggled when Knezevic was in the game; Cal scored just two points during the five minutes that he played. Likewise a four-minute stretch with Alex Pribble when Cal only scored three points was similarly productive.

1-2-3 Trios (+1)
Ubaka/Midgley/Robertson combos in 25:11 - 36-31, +5
Ubaka/O.Wilkes/Midgley combos in 10:12 - 14-16, -2
O.Wilkes/Knezevic/Midgley combos in 4:20 - 2-4, -2
Ubaka/Robertson/Pribble combos in 4:08 - 3-7, -4
Ubaka/O.Wilkes/Knezevic combos in 0:46 - 0-0, 0
All others in 5:23 - 9-7, +2

Frontcourt Duos
Hardin/Powe in 32:52 - 44-41, +3
Benson/Hardin n 4:32 - 2-5, -3
J. Wilkes/Powe in 4:19 - 6-7, -1
Benson/Powe in 2:54 - 3-5, -2
All others in 5:23 - 9-7, +2

This stat measures the significance of a player's contribution to the team's effort. If a team wins by 10 points, and a player plays in half of the team's minutes, his expected contribution would be a +5. For example, when Cal defeated Grambling by 19 points. Brian Wethers played 28 minutes or 70% of the game. If we multiply 70% x +19, Wethers' expected contribution would be a +13.30. But for the game he was a +26, so his net for the game for a +12.70. In a perfect team situation, if everyone contributed equally, the difference column would consist of a row of zeros.

Updated Standings