This morning at 6 a.m. jiu-jitsu class, I talked about iterated algorithms. Let me apologize here to all of the students that I hit with that number before daybreak or coffee, and thank the one person who nodded vigorously when I asked “does anyone know what an iterated algorithm is?” (An algorithm that’s been iterated. Duh).

I’ll get back to math-nerdiness in a moment, but let’s start with peer-reviewed study nerdiness. Why should you keep reading? Because this post is about a very simple way that you can improve competition performance — with minimal effort and no risk of injury. You can even do it if your time at jiu-jitsu class is limited. That simple method is visualization.

When I say visualization, here is what I mean: you use your mind to visualize the way you want your match to go. When I’m preparing for competitions, I do this a lot during my off-the-mat time. In fact, I’ll be doing visualization constantly all the way up to my time in the bullpen preparing for tournament matches. I’ll visualize myself doing all the techniques that I’d do if the match goes exactly the way I want it to: single leg takedown, knee cut pass, knee drive to mount, mounted collar choke. In my mind’s eye, I guide myself through all of these steps.

To name one benefit, it helps me be calm and focus in that nerve-wracking time before I step on the mat. But there are more benefits, and study after scientific study has shown that using visualization techniques has myriad benefits, including improving sport-specific skills, improving strength and coordination. Bluntly, visualizing a guard pass will help you pass the guard more effectively. 

Skeptical? A host of studies bear this out, on topics as widely varied as strength training, golf, judo and other skills-based competitive activities. While I’m hardly an expert on this research, I’ve read more than a few studies on the topic. There is a broad general agreement on the fact that visualization has benefits, although the theories about why these benefits exist vary. But you don’t care overmuch about the why, do you? You want to pass the guard better. You want better results.

So let’s get you there. First, I’m going to review some of the visualization studies I’ve read. That’ll hopefully convince you that this is a thing you should be doing, because this is rigorous, peer-reviewed research. Second, I’m going to tell you my method of visualization, which hasn’t been tested by anybody, but seems to work for me. Then we’ll get back to iterated algorithms. How can you not stay to the end after that teaser?

Here’s the big picture: many, many different studies have been done on this, trying to establish whether we can prove that visualization effects are real. I’ll get into the specific studies in a second, but sometimes the most convincing evidence is a review that takes into account a bunch of research. Let’s say, for example, someone did a meta-study that examined more than 20 research projects into visualization’s effects. If they found a general trend toward major benefits, that would tell us something, no? Check this out:

Empirical research suggests that mental practice may enhance the performance of motor skills. Many variables have been shown to mediate the size and direction of the mental practice effects. The purpose of the present study is to provide an overview of research examining the role played by these variables in mediating the effectiveness of mental practice. In order to integrate the findings in the literature and to further analyze the relative contributions of each of these variables, a meta-analysis was performed according to the procedure outlined by Smith, Glass, and Miller. Twenty-one studies that met the criteria of having both an adequate control and a mental practice alone group were included in the meta-analysis. The forty-four separate effect sizes resulted in an overall average effect size of .68, (SD = .11) indicating that there is a significant benefit to performance of using mental practice over no practice. (emphasis added)

In summary, scientists picked 21 of the best studies they could find, and those studies had to have a way of determining whether mental practice alone could be shown to have a benefit. In those studies, there were 44 “effects” shown from visualization. And while these effect sizes varied, they were found to show clear and significant benefits to performance across the board.

Whenever I read a single study, my inner skeptic tells me to be cautious of the conclusions. You can find one study that says virtually anything you want it to. When it’s a couple of dozen well-designed studies across decades, you get on much more solid ground.

If groups of studies are more convincing, specific studies are more fascinating and evocative. Just check out the narrative from this guy’s thesis, describing a couple of important research projects and their conclusions.

In addition, Eddy & Mellalieu (2003) elaborated that the use of imagery techniques to imagine performing a specific sports skill has been shown to improve the physical performance of that. Using the mind, an athlete can register positive images over and over, enhancing the skill through repetition or rehearsal, similar to physical practice. Therefore, with mental rehearsal, minds and bodies become trained to actually perform the skill imagined. Imagery and visualization is the development of creating a mental image or goal of what he/she wants to happen or feel. Research by Newmark (2012) supports visualization was first applied to sports performance after the 1984 Olympics, when Russian researchers studying Olympic athletes found that Olympians who had employed visualization techniques experienced a positive impact on their biological outcomes and performance. (emphasis added)

To a certain extent, this is intuitive. Our brains run on electrical impulses, and using our brains to visualize, say, a sweep, seems like it should get the right patterns set in our brains. Besides, most of us spend an all-too-brief time actually on the mats during the week. The knowledge that thinking about the motion of shrimping while you’re sitting at your desk might improve your jiu-jitsu is powerful. While there’s certainly no substitute for hard physical training, it’s helpful to know that mental training — which you can do anywhere — can afford additional benefits.

When I say “benefits,” I’m talking sport-specific benefits. Take golf, for example. Two different studies tracked golfers on their putting accuracy: one found “significant performance improvements” in putting from visualization, and the other found that “using positive imagery” (i.e., imagining a successful putt instead of a missed putt) had a “significant main effect on performance improvement.” We’re talking a very specific motor-skills task here, folks: visualizing yourself striking a putt and having that putt go in makes your putting more likely to be accurate.

It’s not just golf, of course. Martial artists will be thrilled (and hopefully unsurprised) to learn that visualization while training judo not only helps you learn judo techniques, it also helps your “imaging” knowledge, your ability to successfully visualize. Like any task, the more you do it, the better you get at it, and the more you think about it, the better you get at thinking about it. When you put it that way, it seems like common sense, right?

Finally, one study that really blew my mind — and, to some researchers, hints at the mechanism by which visualization works. It’s one thing to talk about visualization improving your body’s coordination. But research shows that it increases your actual muscle strength as well. Read that again. Visualizing muscle movement actually increases your muscle strength. You remember in the Matrix, how Keanu Reeves had never used his muscles before, but he still could, y’know, move? Turns out that’s not so unrealistic.

Researchers asked 30 young, healthy volunteers to participate in the study. Eight of them were trained to perform “mental contractions” of their little finger muscles, without actually moving the muscles. Eight other people did the same mental task, but with elbow movements. Six other volunteers actually did the finger muscle movements instead of thinking about them. Then the remaining eight weren’t trained at all, physically or mentally, and served as a control group.

After the 12 week study concluded, they found this:

At the end of training, we found that the [mental-only finger movement] group had increased their finger abduction strength by 35% (P < 0.005) and the [mental-only elbow flexion] group augmented their elbow flexion strength by 13.5% (P < 0.001). The physical training group increased the finger abduction strength by 53% (P < 0.01). The control group showed no significant changes in strength for either finger abduction or elbow flexion tasks. The improvement in muscle strength for trained groups was accompanied by significant increases in electroencephalogram-derived cortical potential, a measure previously shown to be directly related to control of voluntary muscle contractions. We conclude that the mental training employed by this study enhances the cortical output signal, which drives the muscles to a higher activation level and increases strength. (emphasis added)

This tells us that yes, physical exercise is best for building muscle — but mental training can build strength, too. The mind is powerful.

One caveat: the practice of visualization in these studies isn’t standardized, so there’s some variability in how people use terms like “visualizing” and “imaging.” This doesn’t mean you shouldn’t do it: in fact, if that judo study is to be believed, the more you do it, the more efficient you’ll be (just like jiujitsu itself).

Rather than take you through all the methods used in these studies, I’m going to tell you how I do it, why I do it that way, and what that has to do with an iterated algorithm. I haven’t been the subject of any research studies since I was a kid, so I can’t prove what I do works, but it makes me feel more prepared, and that’s valuable in and of itself.

Given that the research shows that positive imagine has a greater impact — and that Marcelo Garcia says “I don’t worry about what the other guy’s going to do” — I start out by visualizing my ideal match, where everything goes right. I see myself doing the techniques that I’d choose to do if everything works perfectly. For me, those techniques are:

Single leg takedown > Knee cut guard pass > Knee drive pass to mount > Mounted collar choke

What can I say? I’m a simple man who likes choking with his hands. This plan, given the techniques I know and do, is my optimal world. Obviously, you can change it up and insert your ideal match techniques as well. I run through these techniques in my mind over and over before my match.

As we all know, no plan survives engagement with the enemy. Often, people are pesky, and they don’t let you just dominate them from stem to stern. Plus, sometimes I just choose to pull guard. And finally, it’s boring to imagine the same match in the same order over and over.

An iterated algorithm is a concept from math. You start with a number (or point), then process it somehow to obtain a new number or point. When you integrate that new number/point into the process, you create a “feedback mechanism” — and after a while a pattern emerges.

You can think of how I do visualization as several iterations, or, if you prefer, a Choose Your Own Adventure book. I start from the ideal match (Single leg takedown > Knee cut guard pass > Knee drive pass to mount > Mounted collar choke). Then, I insert some changes into the system. What if I get taken down? Maybe it’s:

Get double legged > Recover guard > Tripod sweep > Knee cut guard pass > Knee drive pass to mount > Mounted collar choke

Or what if the process is disrupted in the middle? Maybe he recovers guard, and I have to pass again:

Single leg takedown > Knee cut guard pass > He recovers guard > Torreando pass > Back Take > Bow & Arrow Choke

You can see that the possibilities are infinite. But two commonalities remain: first, I always visualize finding a way to win the match; and second, I keep the visualizations to my A-game techniques, the most likely tactics that I’ll have to use. This keeps all my best options in the top of my mind. It also gives me something to do in the bullpen, which is nice.

In most competitive pursuits, the person who is able to impose their game on the other party wins. This is why drilling and rolling are both important: getting to your happy place quickly and efficiently is critical.

If you want both your mind and your body to get to that happy place more often, try visualization. No iterated algorithms required.