Does Plinketto Work?

As your friendly neighborhood cinephile, I sometimes pass the time by watching a couple of YouTube channels that discuss movies. My favorite is Red Letter Media and their terrific series Best of the Worst in which they select random movies and VHS tapes, watch them, discuss, and rank them, selecting a winner—i.e. a best of the worst. One method they use to select movies is a game called Plinketto, which is similar but legally distinct from the Price is Right’s game Plinko. A player drops a ball down a board with pins on it, and the pins cause the ball to bounce around as it falls, creating the illusion that the player has some control over the film selected.

Not only am I a cinephile, I’m also a math nerd and I wanted to know how much choice the player actually has in the selection process by choosing which column to drop the ball down. Can the trajectory be predicted with any accuracy, or is the selection completely random regardless of where the player drops the ball?

To find out, I decided to watch every episode of Best of the Worst in which they play Plinketto and record the starting and ending positions, then perform a statistical analysis on the resulting population of games.

For the sake of consistency, I only included in this analysis episodes in which they play Plinketto with a ball. When they first made the game, they dropped a puck down the board, much like on The Price is Right, but quickly switched to a rubber ball, my guess is that it bounced around the pins more and made the selection process more random than the heavy puck did. I also excluded the Christmas episode in which Santa drops a piece of coal—the coal was smaller than the ball and more prone to falling straight down.

Now onto the analysis. Below you will find the histogram of the starting positions that the players at Red Letter Media choose when they drop the ball. As you will see, this distribution looks surprisingly Normal—that’s Normal with a capital N, as in it has a bell curve shape. Players seem particularly partial to starting position 3, and no one has ever chosen 2, but position 6 is by far the favorite place to drop the ball. This frequency of position 6 also makes the histogram look like it’s giving you the finger.

A histogram of the starting positions from which the ball is dropped

This tendency to select position 6 as a starting point has a couple of explanations. First, the player has to climb a ladder to play Plinketto, and I do not believe that there is a platform or anything that would make it easy to walk to positions on the ends. For safety, players may choose positions closest to the ladder, thus eliminating the edges of the board from frequent play. The other explanation is that the middle ending point of the Plinketto board (ending position 6) is called Player’s Choice, meaning the player can select any film to watch, including sometimes those not even on the board. Perhaps a hope that the ball will fall straight down to player’s choice encourages position 6 as a starting point.

The histogram of the ending positions, however, tells us a different story regarding the selection process.

A histogram of the ending positions where the ball lands

The ball has never selected the VHS tapes located on the ends of the Plinketto board (positions 1 and 11), and the frequency with which position 6 is selected as a starting point does not lead to a higher frequency of the selection of the player’s choice spot. If the pins on the board had absolutely no impact on the selection process, we would expect the ending histogram to mirror the beginning histogram. If the process was purely random, the ending distribution would be uniform, each spot being just as likely as any other to be chosen. What we see instead is spikes not in the same ending positions as starting positions, but rather spikes on either side of the most common starting positions. Column 6 is chosen the most frequently, but we see spikes in the ending histogram in spots 5, 7, and 8. Column 3 is the second most frequently chosen start, and we see a large spike at ending spot 2, a small spike at 3, and the same spike at 5, indicating that balls dropped in columns 3 and 6 are both feeding into ending spot 5.

These beginning and ending histograms are helpful, but we also need some information about the path that the ball takes. See below the chart of starting positions vs ending positions.

A bubble chart of the starting and ending positions. Darker bubbles indicate a higher frequency of the starting/ending position combination.

This tells us a little more about the strategy a player might choose when selecting where to drop the ball. Earlier I mentioned that the desire to hit the player’s choice spot may be behind the frequency with which starting position 6 is chosen, but we can see from the Y-axis that ending position 6 (Player’s Choice) is only ever selected when the player drops the ball in column 6. Because column 6 is so frequently chosen, it also has the largest sample size and therefore the largest distribution of ending positions, but it’s also the only option that has ever resulted in the much-coveted player’s choice selection, which means the guys at Red Letter Media, if their intention is to choose from the best of the worst (hey, that’s the name of the show!), they’re right on the money to be dropping the ball from directly above the middle spot of the board.

My guess is that it’s not their intention to create a truly random VHS selection process—they could use the wheel of the worst for that (a wheel with movies is spun to randomly select a tape, which is inherently much more random than the Plinketto board). The point of the Plinketto board is to provide some modicum of control over an otherwise random process by allowing the player to select where the ball is dropped, in which case, the Plinketto board is a huge success. Look at the columns for the most frequently selected starting positions (3, 6, 5, and 7). With the exception of column 7, which has a strange tendency to select tape 2, the distributions for these columns looks, again, Normal. It’s more common to select tapes directly underneath the starting position, and the further away the tape is, the less likely it will be selected.

Let’s not get ahead of ourselves. Before we congratulate the RLM guys for perfecting a game they (allegedly) stole from The Price is Right, let’s look at the correlation between starting positions and movement on the board.

A bubble chart of the starting positions and the movement. Positive movement means the ball moved to the right, and negative movement, to the left. Darker bubbles means a higher frequency of the starting/movement combination.

Whoa. A clear negative trend. The Plinketto board might be bowed or something because lower starting positions tend to move the ball towards the higher end, and higher starting positions tend to move the ball towards the lower end. In other words, the ball seems to be directed towards the middle regardless of where the player drops it. This would explain why the end positions (1 and 11) have never been selected. It might be tempting to say that this is only happening because the truncated nature of the ending positions means that there’s a barrier keeping the outer ending spots from being chosen. Another explanation could be that when the ball is dropped in left-side columns, it has more room to move to the right, and vice versa. But even if we remove the directionality from the equation and compare starting positions with the ball’s absolute movement, we see that certain columns tend to make the ball a little more intrepid than others.

A bubble chart of the starting positions and the absolute movement. Darker bubbles means a higher frequency of the starting/absolute movement combination.

We would expect the distribution for each column not to be Normal here, indicating that the ball typically falls within a couple of spots from where it was dropped and occasionally travels further. What we see instead is that column 7 is particularly notorious for sending the ball further away from its starting location, as is column 4.

We can give the guys the benefit of the doubt and assume that many of the strange distributions that we see here are a result of low populations—if the ball was dropped down each column 10 or 20 times, then perhaps a more expected pattern of guided randomness would emerge. But the frequency with which the middle of the board is both selected as a starting point and an ending point (even when outer starting columns are selected), seems to point to my theory of a bowed Plinketto board.

The board itself appears to be a large sheet of plywood. Plywood tends to bow in the middle as a result of its wide but thin shape, and although this can be corrected in construction by screwing the middle of the plywood to a flat surface, the Plinketto board almost certainly does not have a flat support behind it that spans the entirety of its height. The installation of the pins in the middle of the board may have increased any bowing that existed when the board was purchased, and if the board is propped up from behind by supports on the outer edges, this would again increase a natural bend in the wood, again caused by a lack of support in the middle.

If such a bow in the board exists, it would explain why starting positions on the edge of such a valley (columns 4 and 7) can pick up momentum by falling into said trough and then use the randomness of the pins to wind up on the opposite side of the board. It seems a little too convenient to me that both starting positions 4 and 7 (just outside of where a middle bow would be) create the most lateral movement, and although they have low sample sizes, they frequently send the ball between 3 and 5 positions away.

Now, lest this be mistaken for a pure complaint about the Plinketto board, and I really hope it isn’t taken that way because I love Best of the Worst and especially Plinketto, I’d like to offer a couple of solutions, in the off chance that someone from RLM actually wastes their time reading this.

If they wanted the process to be a little more random, I think the key is to slow down the ball’s momentum as it falls. This could be accomplished by tilting the board back just a bit more, which would cause the ball to slow down and would give the pins a larger impact on the ball’s trajectory. If the goal is to give the player more influence over which tape is selected, either tilt the board so it is more upright (of course, then you have to be concerned about the ball falling out), or go back to using the puck from the first episode (or a heavier ball). The puck, although dropped only three times in the inaugural episode of the gimmick, was dropped in columns 2, 4, and 8, and ended in columns 1 (the only time column 1 was chosen), 5, and 8 respectively. Much less lateral movement as opposed to the lighter rubber ball. You can see why they moved away from it, because it didn’t sufficiently randomize the selection process. An additional backwards tilt of 5 degrees could largely increase the randomness of the game and would hardly be noticeable on camera.

Mike Stoklasa of Red Letter Media in Best of the Worst: Plinketto Episode 10