Towards a Notation System for Foosball

30 August, 2010

This entry documents the fourth of my projects for this summer's ITP 4-in-4. 4-in-4s are occasional events entailing the execution of one complete project each day for four consecutive days. They're a great opportunity to finally do a daydream project you've been talking about for ages or to play with a new technology or technique you'd be meaning to try out.

Foosball is the national pastime of ITP. An old, beaten-up, much beloved table is a fixture on the floor and during semesters a game is almost always in progress, from busy daytime hours when the clunk of the ball adds to the overall noise of the floor to late night procrastination sessions when students round up whoever's around to play intense games meant to block out any thought of a looming deadline or mountainous pile of work.

I'd played some foos before coming to ITP — most notably at UC Riverside with my cousins after a series of summer softball games — but, in my first year at ITP, I've become predictably obsessed: trying my best to learn from the masterful 2nd year players who, at the start of the year at least, routinely routed me.

In the course of this foosball education, I began to come up with certain theories. For example, I noticed that players were divided into those who moved both hands between the handles (advancing to the 5-man and the 3-man when on offense, for example) and those who kept their left hand anchored at the goalie, only advancing with their right. I instinctually favored the latter approach, feeling that scoring opportunities were created for the other player whenever hands moved: a left hand-anchored approach minimized movement and hand-off-handle scoring opportunities. Similarly, I started to see that a lot of the best players shared a certain style of passing and shooting from the outside players of the 5- and 3-man rows that was especially effective. Also, a few players (most notably Jeremiah Johnson) used their lightning quick reflexes to play an aggressive kind of defense where, instead of simply blocking an opponent's attempt to move the ball forward, they'd slap it back at full speed, as if hitting it from their own possession (an especially deadly move against the opponent's defense where it frequently results in a goal).

I started to wish for a formal vocabulary to describe these trends and ideas I was seeing and some structured way to test my hypotheses, a procedure that would allow me to transcribe and keep statistics on games in order to better understand them and discuss them. I realized that I needed a notation system like exists for chess or baseball, something analogous to the "1-6-3 double play" or " Bxd7+" (bishop to D7, check). And, on Scott Wayne Indiana's suggestion, I sought a system that could be represented visually (like a baseball scorecard) to enhance transcription.

So, for my final 4-in-4 project, I set out to design such a system.

Foosball scorecard with annotations

Starting from Scott's suggestion about the baseball scorecard, I started by designing a simple graphical representation of the foosball table. I then labeled each handle with a "B" or "W" (for Black or White) representing each side (at ITP, at least, the actual players can be nearly any color, having been repaired, replaced, and becostumed so frequently) and a number corresponding to how many players were attached to that row. Hence: B5 would be black's 5-man row and W1, white's goalie. Then, for the multi-man rows, I added letters for each man so that the notation system could also capture which specific man hit the ball. For example: "W3a" would mean that white hit the ball with the man furthest from them on their 3-man row.

I also included the handles in the diagram because I knew that the position of the players' hands at the time of each contact with the ball was important data for exploring my theories about handle strategy. It also, when you have a series of events in sequence, turns out to give a really nice feeling of the momentum or drama of a moment of play. I didn't try to include the hand-on-handle positions in the written notation system as I wanted to make it easy and intuitively understandable. I'll present some real examples in a minute, but if I said: "W3a to W3c for the goal", you'd easily be able to picture a lateral pass between the two outside players on white's 3-man row followed by a scoring shot. All the extra cascade of notation that would be required to capture hand position would only water down that flavorful little bit of drama.

Now: an example of the notation in action! I printed out a handful of sheets of paper filled with a grid of scorecards and recruited Mike Cohen and Jeff Howard to play.


I told them that, after each goal, I'd interrupt them to transcribe the events that led from from the last coherent possession to the goal. In theory, it would be great to transcribe an entire game and to do statistical analysis on the resulting data, but that would require adding sensors or a camera tracking rig to the foosball table (not that it hasn't had both of those things applied to it before, the thing bristles with the leavings of old class projects) and spending inordinate amounts of time getting the technology working rather than focusing on the notation which was the point of this project. I would love it if someone constructed a system for machine-generating this notation automatically at some point, but it was beyond the scope of this one-day project. With that in mind, I figured incidents of scoring were the most interesting thing to transcribe and also imminently doable.

I designated Mike "Black" and Jeff "White" and had them kick things off. Before too long, Jeff scored the first goal. I had the players pause and reconstructed it thusly:

Jeff vs. Mike G1

See the larger size on Flickr.

This diagram might appear dense at first glance; let's break it down. First, look at the notations on the handles. White has his hands on W3 (the 3-man) and W5 (the 5-man), a position I soon dubbed "classic offense". Black is on B1 (the goalie) and B2 (the 2-man): "classic defense". Their hands stay in those positions for all four events of this play. Now, look at the red 'x' that moves between the four diagrams: at first between two of white's players and then into the goal. That's a fancy bit of passing on Jeff's part before the shot that scored; he knocked the ball laterally from the middle 3-man (W3b) to the one closest to him (W3c) and then back to take the shot. So, in the final notation, this play reads as: "W3b W3c W3b W!" (where "W!" reads as "White goal").

You should be able to start to picture it in your head now: Jeff starts with control of the ball at the middle of his 3-man. Mike is back in defensive position. Jeff passes the ball to the side; Mike adjusts his defensemen to follow. Then Jeff passes it back to the middle, where he slaps it directly into the goal before Mike can recover. A classic bit of foosball strategy: using lateral passing between the 3-man to shake the defenders and create an opening for a goal.

The game continued looking much like a whipping administered by Jeff who got up to a 6-0 lead before Mike scored his first goal. I'll revisit some of those earlier goals in a minute, but first I wanted to show another, even simpler, goal: #5 of the match:

Jeff v. Mike G5

An incredibly straightforward goal: W3b W! with both players in "classic defense" and "classic offense" throughout. Jeff controlled the ball with the middle player of his 3-man handle and then shot it past Mike's goalie and 2-man and in.

The goal immediately before that was nearly as simple. At this point, you should be able to imagine the whole story just from the notation: W5c B1 W!:

Jeff v. Mike G4

Now, let's talk about some goals that relate to the theories that set me off on this project in the first place, for example #6: W5c W!:

Jeff v. Mike G6

At first glance, it looks nearly as simple as #5, just coming from W5 rather than W3. But look at the position of the handles in this exchange. Black starts off with his hands on B2 and B5. His goalie is untouched. White has control of the ball at W5. Black was caught in transition, right in the middle of trying to move his hands up towards "classic offense" when White got control of the ball at W5. The second position shows even more evidence of the chaos caused for Black by this reversed transition: he actually had only one hand on a handle at the time of W!: B5. His left hand was probably moving back towards B1, retreating in the face of White's sudden possession of the ball, but not yet having arrived to take charge of the goalie.

And look at White's hand position by contrast: he's on W5 and W1. Probably starting from classic defense a few seconds earlier, he advanced only his right hand, keeping his left anchored on the goalie, making for maximum stability and speed during the transition play, which let him pound the goal in from midfield in the midst of Black's chaotic transition.

Obviously, from the way I'm telling the story of this goal, I think it counts as evidence for my transition theory in favor of playing with a hand anchored at the goalie. And, in fact, the next goal in the match, Black's first, offers more evidence in support:

Jeff v. Mike G7

This time, Black is anchored with his left hand on the goalie when he shoots, only having advanced his right hand to B5b to take possession. White is on W5 and W2, one of the weakest positions on the field: back on defense but with no anchor on the goalie and no hand on it to prevent deflections or allow for quick reactions. And, what's worse, as we can see from the hand positions in the second frame of this goal, White is also in transition: both of his hands move between B5b and B!, meaning, while the ball was in travel, he was, in fact, touching no handles. Black's hands have both also moved, but this has no bearing on the result of the play as he does not touch the ball again. In fact, if White had been able to prevent the goal, Black might have been left quite vulnerable to the kind of quick reversal we saw in goal #6 due to being in transition himself.

This is a strong goal for Black and there's a reason it dramatically changed the momentum of the game. Up to this point, many of White's goals were scored in the position I've described as "classic offensive", i.e. with hands on W3 and W5. While this is an especially strong position for players (like Jeff) with lots of good fine shooting and passing skills (checkout White's goal at #11 for example) it is also especially vulnerable to transition scoring if the opponent can kick the ball up field: from classic offense, you inherently have to move both hands in order to retreat at all, creating lots of transition time for an anchored opponent to pass or shoot. After this first occasion, Mike seemed to get into a rhythm in exploiting this weakness in Jeff's style: advancing the ball aggressively out of a seemingly defensive position and then proceeding to score while Jeff was forced to transition both hands back (Goal #8 is another great example of this). Though Jeff would go on to win 10-5, Mike kept up goal-for-goal from this point, losing so badly only because of the nearly insurmountable lead Jeff had built up with those first series of goals.

In fact, the second half of the game is replete with bank shots from deep within Black territory (B2), shots from B2 while White is still in classic offense, and combinations of both of those effects.

You can see all of the goals for this game notated in this flickr set.

So, hopefully at this point I've demonstrated my notation system's virtues for recording and re-telling the story of a game as well as for making strategic and tactical arguments such as the one I've been rehearsing here about the importance of transition play and hand position.

Given all of that, I did discover a few downsides to the system in using it for the first time. For example, my graphic doesn't include the foosholes so, if a goal was scored directly on foos, or if a machine was to attempt to transcribe a full game, that's a lack that would need to be addressed.

Also, as you can see from this picture:

Foosball scorecard

The scoresheets that I printed out did not include the lettering and numbering key I've included in the graphics presented here. I was trying to keep things simple and minimal. The main problem with that decision was that there were no visual cues for reading the orientation of the sheet: a couple of times I got started notating only to realized that I had black and white reversed due to the symmetry of the sheet. So, when I print out further sheets, I think I'll use the notated version for clarity's sake.

Another problem with the system is that it can occasionally be difficult to reconstruct complex interactions. Take, for example, this goal: W3c wall B1 W!

Jeff v. Mike G2

Clearly, the ball bounced off the wall after White's shot in a manner that surprised and evaded Black's goalie. But, you don't quite get as vivid of a picture of the logic at play as you do with better structured goals. It's my suspicion (or at least my hope) that this kind of ambiguity would be greatest with goals resulting from "slop" — the disorganized caroming of the ball around the table and off random players without the meaningful intervention of human intention — which, I think, you could argue is actually a virtue of a notation system, which must inherently reduce, simplify, and structure the thing it describes.

There was also a sense amongst the players that my notation didn't capture certain subtleties of particular goals, the angle of a shot that slipped in behind the goalie, for instance. This is definitely true, but again, I don't have a clear sense of how to capture that without making the notation system unwieldy. My intention is not to eliminate the need for human commentary, only to augment it and enhance its concision and clarity.

Topics for future research. Speaking of printing out further sheets, I plan to print out a handful of them and attach them to the ITP table so they'll be to hand for anyone who wants to sketch down a particularly interesting play or series of goals they see happening. I also plan to transcribe some additional games and to try to make a bit of a catalogue of signature plays and tactics that I've come across. And, of course, there's always the grand dream of machine transcription, which I intend to push on any unsuspecting first year looking for a topic for a camera tracking project or pcomp midterm.