🎙️ Podcast Link 🎙️
I’ve been wanting to do this video for a while now, and thanks to Maceon Knopke’s lovely 3D printed dice, here it is!
This is also my 50th 🎂 Hacking Academia video 🎉🎉🎉 !!!
A lot of academic research career coaching I do revolves around basic concepts of probability and variance in an academic career: for awareness, and for how your strategy can be shaped to mitigate these challenges.
One of the key examples of this is funding pipelines: an integral part of most researchers’ lives whereby they regularly apply for funding to do the research they want to do.
Rolling dice* is such a lovely way to visually capture some of the key concepts and considerations, as shown in this video: rolling a “1” is considered a successful grant outcome, and any other number is considered a rejection.
The key concepts illustrated in this video include:
🎲 the variation in outcome possible when you’re putting in a single application at a time, perhaps on a yearly basis
🎲 the effect of improving repeated applications (seen in switching from a 6-sided die to a 4-sided die, representing increased odds of 25% up from 16.7%) – but still the lack of any guarantee that even a vastly improved application will be successful in any specific time frame
🎲 that for low acceptance rate schemes – those tough single digit acceptance rate, or even notorious alleged zero percent acceptance rate schemes (😡), it’s basically a lottery where many highly qualified applicants will strike out. It took 31 attempts to roll a successful grant in a simulated scheme with 8.3% acceptance rate (this was an unusual but not impossible outcome, and has actual odds of happening 6.7% of the time – so 1 in 15 people would apply 30 times and not be successful 🤯
🎲 that, of course, having multiple applications in consideration at any time drastically increases your chances, and that having some diversity in those applications: diversity in whether fundamental or applied, whether large or small, and whether low chance or high chance of success, can help
This information can be presented in graphical, or textual form, but sometimes visual (with satisfying dice clinking sounds as well) can be the best way to illustrate concepts like this!
*I will never not need to mentally check, is it “dice” or “die” for plural / singular
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Full Video Notes
This is a six-sided die, and it represents your grant funding pipeline. In the early days of your academic or research career, you might apply for one grant or fellowship per year. A fairly competitive scheme might have an acceptance rate of around 16 or 17 percent. So, each roll of this die represents the chance of success for one of those grants—each face has roughly that chance of coming up.
Let’s say a roll of “one” means you’re successful. Anything else means you’re unsuccessful. Let’s give it a try. First roll: five—unsuccessful. Second roll: one—success! So, in this case, you were successful on your second attempt, perhaps in your second year of applying.
Let’s reset and try again. First roll: five—unsuccessful. Second roll: six—still unsuccessful. Third roll: one—success! Now let’s try one more time. First roll: six. Second: six. Third: three. Fourth: six. Fifth: six. Sixth: three. I’ve lost count, but eventually, we land on a one—success! This demonstrates the randomness and persistence often required.
Of course, in practice, the idea with grant proposals—or any submission—is that if you’re unsuccessful the first time, you try to improve it. To simulate that, we’ll start with the six-sided die (representing a one-in-six chance), and if unsuccessful on the first roll, we’ll then switch to a four-sided die, representing a one-in-four chance—reflecting the improvement of your proposal.
First roll: unsuccessful. Now we switch to the four-sided die. Second roll: four—unsuccessful. Third roll: two—unsuccessful. Fourth roll: one—success!
Let’s reset. First roll: two—unsuccessful. We switch to the higher-probability die. Second roll: one—success! Another round: first roll, three—unsuccessful. Then we go on: three, unsuccessful; three, again; then four; then four again; then four once more; finally, a one—success on the ninth attempt. If you’re still applying and in the game on your ninth try, hats off to you for your persistence and resilience.
Now, let’s consider the very prestigious, extremely competitive schemes. Some of these have single-digit percentage success rates. To simulate this, we’ll use a 12-sided die, representing a one-in-12 chance of success. Let’s roll and see how long it might take.
First try: no success. Second: no. Third: still nothing. This continues—fourth, fifth, and beyond. Finally, on the 31st attempt, we roll a one—success. That illustrates the reality: these highly competitive schemes can be effectively a lottery. Even extremely talented individuals with excellent track records can apply many times and never get funded.
The final concept I want to illustrate with dice is diversity. As your career progresses, ideally you’re applying for multiple schemes at once. Diversity might mean different disciplines, or a mix of applied and fundamental research. It also applies to the types of schemes you target: a highly prestigious, high-risk scheme; a “bread and butter” mid-tier scheme; and a lower-prestige but higher-probability scheme.
Let’s simulate this using three dice: a 12-sided die (low chance, high prestige), a six-sided die (moderate chance), and a four-sided die (higher chance). Let’s roll all three.
First round: none of them hit. Second round: still no luck. Third round: success with the four-sided and six-sided dice—two grants landed! We still missed out on the very prestigious one, but the others give us enough to keep going. That’s the value of diversification.
This is, of course, a simplified illustration of the grant pipeline, but it highlights a few key concepts.
First, there’s huge volatility. Sometimes a grant hits on the first try. Sometimes it takes 31. When you track a group of equally talented and hardworking individuals, some will appear very successful, and others will repeatedly miss out—largely due to randomness. That’s the reality of this system.
Second, there’s the value of having multiple irons in the fire. Submitting several applications increases your chances of landing something. This is basic probability, but once you get to the postdoctoral or more senior stage, it becomes a practical necessity.
Finally, there’s the importance of having a mix of opportunities in play. A well-rounded strategy includes both high-risk, transformative projects and more achievable ones. That mix helps ensure that you secure enough funding to support your research goals, even if the big wins remain elusive.