Introducing Plus-Minus to Cal Hoops

Sports fans are pretty familiar with the metrics we use to judge our basketball players. Points, rebounds, assists have been around for decades, and I can't really imagine them going anywhere.

What people don't recognize is that some of these stats don't necessarily tell us that much about a player. Other than maybe points and shooting percentage, all the other stats have a significant degree of uncertainty to them. The definition of an assist has changed quite a bit from when we were kids (and the arbitrary method in which they are assigned leaves much to be desired).

Take a steal, for instance. Dwyane Wade just had a spectacular season where he recorded 100 blocks and 200 steals (the first time a guard has done that since MJ's peak). However, what it doesn't tell you is how many times Wade gambled for the steal, resulting in leaving his man open for the wide open 3 (we have other stats for that, but that's a different story for a different time), or how many blocks ended up going back to the opposing team, giving them another possession. It's similar in football; although an interception and a fumble arguably have greater impact on the game, it isn't necessarily a sign of great one-on-one defense or good tackling form. These are actions that are being measured, not the effort in between the lines.

Hence the need for new stats. One of the most prominent is the plus-minus (otherwise known as +/-), which will be the focus of this article.

+/- measures pure point differential. Let's say Kobe and the Lakers start off the game on a 27-17 run. He gets a +10 for this contribution. Let's say Kobe comes back and his team loses a net 3 points during his duration on the floor. He gets a -3. We keep on doing this for the rest of the game, measuring how well the team performs with Kobe on the floor, and then sum up all these figures at the end. That's the basic form of +/- you see on those Yahoo Sports box scores.

Let's examine Cal basketball's first Pac-10 game this season versus Arizona. The boxes represent who was playing and the score differential during that particular game. Final boxes have the basic +/- for each player.

Cal-Arizona +/- Statsheet
Boykin	Theo	Wilkes	Randle	Patrick.	D.J.	Jorge	Nikola	Amoke	Kamp	Score
-1	-1	-1	-1	-1						A 14-13
		-1	-1	-1		-1			-1	A 17-15
-2			-2	-2		-2			-2	A 19-15
0	0		0			0			0	A 23-19
	2		2	2				2	2	A 23-21
				5	5		5	5	5	C 28-25
		-1	-1	-1	-1				-1	C 30-28
		2	2	2		2			2	C 32-28
		0		0		0	0		0	C 34-30
		2	2	2		2			2	C 36-30
4	4	4	4	4						C 48-38
	-3	-3	-3	-3					-3	C 51-44
	-3					-3	-3	-3	-3	C 53-49
	2			2			2	2	2	C 57-51
	9		9	9				9	9	C 69-54
	-1					-1	-1	-1	-1	C 69-55
1	9	2	11	18	4	-3	3	14	11	ON +/-

The starting unit started off slow. This was not an isolated occurrence (and something we'll talk about in later posts), although they had a much better start in the second half. It was only when Cal unleashed our reserves (not a normal strength for us) that we broke away from the Wildcats.

Does the data match up with the individual performances? In the most prominent case, yes. Patrick Christopher ended up with the best metric overall, and probably had the best overall game of the night for the casual observer (TedfordIsGod did attest that he destroyed Chase Budinger).

However, he wasn't the biggest swing player. Omondi Amoke and Harper Kamp were involved in the two biggest spurts of the game and would end up having the highest +/-s off the bench. More interestingly, Christopherwas involved in those stretches as well! Turns out that's supported by eye-witness observation, as indicated by CBKWit's post back in January.

Harper Kamp received the ball in the high post, occupying the middle of the 3 baseline defenders. He then gave a bounce pass to a cutting wing (generally Patrick Christopher, who matched his uniform with 23 points) who found the basket unobstructed, with the post defender occupied at the top of the key and the baseline wing defender late to leave his perimeter responsibilities. Kamp had a career high 5 assists using this play, all in the second half.

So it does seem that not only did Kamp help out in this particular game, but he helped Christopher's game as well with his passes from the high post. These are the type of cool observations you can make with plus-minus.

Finally, for the stat geeks like me, I did a few further calculations to factor in how much playing time factored into the +/-, by seeing how much the team was impacted when the player was NOT on the floor. I know some NBA statisticians use these types of formulas, although far more refined.

Here are the simplified formulas

ON +/- = That last row of the first table.

OFF +/- = Margin of victory - ON +/-

ON % = Minutes played/Minutes in the game

OFF% = 1 - ON %

Adjusted ON +/- = (ON +/-) * (ON%)

Adjusted OFF +/- = (OFF +/-) * (OFF%)

Net Adjusted +/-, or Net= (Adjusted ON plus minus) - (Adjusted OFF plus minus)

Bold indicates inconclusive results; not enough PT to figure out their value to the game (generally you have to play more than 30% of the given minutes.

Cal-Arizona Adjusted +/-
	ON +/-	ON %	OFF +/-	OFF %	Adj ON +/-	Adj OFF +/-	Net	Min
Boykin	1	0.4	13	0.6	0.4	7.8	-7.4	16
Theo	9	0.73	5	0.28	6.53	1.38	5.15	29
Wilkes	2	0.58	12	0.43	1.15	5.1	-3.95	23
Randle	11	0.8	3	0.2	8.8	0.6	8.2	32
Patrick	18	0.85	-4	0.15	15.3	-0.6	15.9	34
DJ	4	0.13	10	0.88	0.5	8.75	-8.25	5
Jorge	-3	0.3	17	0.7	-0.9	11.9	-7.2	12
Nikola	3	0.2	11	0.8	0.6	8.8	-1.8	8
Amoke	14	0.35	0	0.65	4.9	0	10.1	14
Kamp	11	0.65	3	0.35	7.15	1.05	8.9	26

You'll see that Jordan Wilkes had a pretty weak adjusted +/- for an eleven point victory (also not an isolated occurence), but did see plenty of minutes. Interestingly, the team didn't do much with him on the floor, but seemed to thrive with him off of it. Monty wasn't quite as leninent with Boykin (16 minutes to Wilkes's 29), and it made his adjusted +/- look worse as California performed better against Arizona with him off the floor in long stretches.

So that's a basic run down of what the plus minus is all about. In future posts on this topic, I'll be tackling certain things that stood out from these stats, particular games that really stood out, strengths and weaknesses of plus minus, etc. Feel free to discuss your thoughts on all this fancy data and the plus minus in the comments.

NOTE: If any of our commenters here are really good at data/Excel stuff like the tables above (or, even better, data visualization), drop a line at bearsnecessities at gmail! I have a few more parts in this series and could really use your help to spruce up this dry dissertation.

Poll

What do you think about the +/- stat?

Highly insightful.

24 votes

Interesting, not sure about its use.

23 votes

Fun to look at, lots of flaws though.

19 votes

Total waste.

10 votes

76 votes | Poll has closed

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Comments

Like all stats

The real key is to look at the context and not just in isolation. I know Darryl Morey (Houston Rockets GM) and his staff look at some very advanced stuff, but they also keep lots of basketball guys on their staff to gain a more organic look at the game – qualitative and quantiative together. One of the really interesting things I heard someone on the Rockets staff mention is they really like to look at college tempo-free rebounding stats.
I really like the tempo-free stats for looking at how good a player is against a common background.

In general, I really like a lot of what Tom Ziller from SacTown Royalty has written.

by LeonPowe on Jun 4, 2009 3:32 AM PDT reply actions

Yeah, I definitely want to examine tempo-free stats. Plus-minus is just the easiest to start with. The rest of the stuff may take a lot longer because it requires going through all the play-by-plays, counting the number of possessions. I know Ken Pomeroy has good aggregate stats though.

Could you link me to the Ziller articles you’re talking about?

by Avinash Kunnath on Jun 4, 2009 9:10 AM PDT up reply actions

In general the biggest problem with using +/- is multicollinearity, in which it’s difficult to isolate that player’s own impact from those that he plays with. A guy who plays on a team almost exclusively with strong (or even halfway decent) starters that has weak backups across the board will have a +/- that overstates his contribution to the team because the starters can come in and blow away the other team’s starters, but once you go to the second units, they’ll give that lead right back.

I think that’s exactly why the Michael Smith article that discussed Shane Battier mentioned that Vince Carter had such a strong +/-. Now, I love Vince to death, but I suspect that his +/- last year had more to do with the fact that the Nets had the likes of Antoine Wright, Darrell Armstrong, Jamaal Magloire, and Bostjan Nachbar coming off the bench to spell him, Jason Kidd, and Richard Jefferson. You’ll end up with Vince averaging a +/- of 6 and Wright averaging a +/- of -8…which isn’t great for the team.

Still holding out hope that Ryan Anderson will capitulate and grant him that interview he's been asking for for months now.

by yellow fever on Jun 4, 2009 6:04 AM PDT reply actions

Yeah, that’s a big weakness of this stat, and something I’ll probably address in a future post on the topic.

by Avinash Kunnath on Jun 4, 2009 9:10 AM PDT up reply actions

I think it’s why stat geeks prefer mixing in not only pure +/- but also production value (a variation of Hollinger’s PER) to measure players to get a more accurate list, but you’re right, still heavily based on who you’re playing with.

What do you think of On Court/Off Court stats?

by Avinash Kunnath on Jun 4, 2009 9:14 AM PDT up reply actions

This

is definitely the biggest issue. The nature of +/- is also a comparison of the player to his backup – so the player who’s replacing the original player matters to it just as much as the original player. As yellow fever stated it’s also hugely reflective of teammates, and both teams substitution patterns, as well as matchups. Not really a huge fan of it, myself.

by HyphyBearsFan on Jun 4, 2009 10:06 AM PDT up reply actions

I feel for plus/minus to be an effective tool it needs a large sample size. The variables within the plus/minus for one game are so great that the credibility of any conclusions comes in question. Variables include:

Strength of Your Teammates
Strength of the Opposing Team (at the time of play)
Match-ups
Situation – Playing from ahead or behind, early vrs late in the game
Coaching Competency – the ability to utilize the roster effectively, and placing the players in a situation to succeed.
Intangibles – essentially, all the flukey little things that happen, bad bounces, long rebounds, cold shooting spells, hot shooting spells, etc.

We all dream of being a child again, even the worst of us, the worst... perhaps... most of all.

by chowder on Jun 4, 2009 9:02 AM PDT reply actions

We've had some similar discussions on CougCenter

Also I’ve read discussions on a few of the NBA blogs I look at, and essentially even season-long +/-‘s don’t really tell you anything you wouldn’t know from watching the games. The real “large sample size” you’d need is a large number of players on a given team, not as much a large number of games. If you had fifteen players getting significant minutes (in an alternate universe obviously) then you could single out one player’s contributions much better.

I’ve found that I enjoy looking at various +/- stats as a way of remembering the flow of the game, not just the high points. Like “oh, this player played poorly during the first part of the second half.”

Also it can be helpful for analyzing the strength of a given unit of five players. Obviously many of the same weaknesses that you’ve pointed out still apply, but over time (especially in a more even league like the NBA) you can figure out which five guys work the best together. Putting the five best +/- guys together may not be your best lineup.

by johnnycougar on Jun 4, 2009 3:24 PM PDT up reply actions

I refuse to believe that Jorge was bad in any game.

While the rides on the Pain Train and Brock Mansion Party Yacht have been fun, I think its time I hop on the BakBakcycle.

by rollonubears on Jun 4, 2009 4:54 PM PDT reply actions

You refuse to believe a lot of things.

by Avinash Kunnath on Jun 4, 2009 5:00 PM PDT up reply actions

Jorge is our best defensive player though (his offense on the other hand…). It seems unlikely he would have a bad +/-.

While the rides on the Pain Train and Brock Mansion Party Yacht have been fun, I think its time I hop on the BakBakcycle.

by rollonubears on Jun 4, 2009 5:10 PM PDT up reply actions

It was one game bro. Players have bad games.

by Avinash Kunnath on Jun 4, 2009 5:49 PM PDT up reply actions

I wasn’t being 100% reasonable with my argument.

While the rides on the Pain Train and Brock Mansion Party Yacht have been fun, I think its time I hop on the BakBakcycle.

by rollonubears on Jun 4, 2009 6:49 PM PDT up reply actions

Ummm... I liked the NYT article!

Other than that, I’m totally lost, so… I’ll just leave it at that.

I haven't seen that many tear-stained dollar bills since my dad hired a stripper for my uncle's funeral.

by BearStage on Jun 5, 2009 1:53 AM PDT reply actions

This is great stuff

Are you getting the stats from a site, or hand-calculating them? If it’s the first, I want to go there… if it’s the second, um, thanks for the hard work.

Linda's in the cold ground, won't see her anymore
Somewhere out on the highway tonight, the drunken engines roar
It's just one of those things, one of those things
-- Al Stewart, "Accident on 3rd St."
In memory of Nick Adenhart and all victims of drunk driving

by PaulThomas on Jun 6, 2009 1:51 AM PDT reply actions

Can’t really get those from a site; if they do I want to find it.

Hand calculation was my game here.

by Avinash Kunnath on Jun 6, 2009 1:16 PM PDT up reply actions

Comments For This Post Are Closed

Golden Bears Football Schedule

Fresno St.	Sat 09/03	W 36 - 21
@ Colorado The Ralphie Report	Sat 09/10	W 36 - 33
Presbyterian	Sat 09/17	W 63 - 12
@ Washington UW Dawg Pound	Sat 09/24	L 23 - 31
@ Oregon Addicted To Quack	Thu 10/06	L 15 - 43
USC Conquest Chronicles	Thu 10/13	L 9 - 30
Utah Block U	Sat 10/22	W 34 - 10
@ UCLA Bruins Nation	Sat 10/29	L 14 - 31
Washington St. CougCenter	Sat 11/05	W 30 - 7
Oregon St. Building The Dam	Sat 11/12	W 23 - 6
@ Stanford Rule Of Tree	Sat 11/19	L 28 - 31
@ Arizona St. House Of Sparky	Fri 11/25	W 47 - 38
@ Texas Burnt Orange Nation	Wed 12/28	L 10 - 21

Pacific-12 Conference Standings

(updated 1.2.2012 at 11:12 PM PST)

North	Conf		Overall
	W	L	W	L
Oregon Ducks Addicted To Quack	8	1	12	2
Stanford Cardinal Rule Of Tree	8	1	11	2
Washington Huskies UW Dawg Pound	5	4	7	6
California Golden Bears California Golden Blogs	4	5	7	6
Oregon St. Beavers Building The Dam	3	6	3	9
Washington St. Cougars CougCenter	2	7	4	8

South	Conf		Overall
	W	L	W	L
USC Trojans Conquest Chronicles	7	2	10	2
UCLA Bruins Bruins Nation	5	4	6	8
Utah Utes Block U	4	5	8	5
Arizona St. Sun Devils House Of Sparky	4	5	6	7
Arizona Wildcats Arizona Desert Swarm	2	7	4	8
Colorado Buffaloes The Ralphie Report	2	7	3	10