One item always of interest to me is sleep; a stimulant is no good if it damages my sleep (unless that’s what it is supposed to do, like modafinil) - anecdotes and research suggest that it does. Over the past few days, my Zeo sleep scores continued to look normal. But that was while not taking nicotine much later than 5 PM. In lieu of a different ml measurer to test my theory that my syringe is misleading me, I decide to more directly test nicotine’s effect on sleep by taking 2ml at 10:30 PM, and go to bed at 12:20; I get a decent ZQ of 94 and I fall asleep in 16 minutes, a bit below my weekly average of 19 minutes. The next day, I take 1ml directly before going to sleep at 12:20; the ZQ is 95 and time to sleep is 14 minutes.
Rogers RD, Blackshaw AJ, Middleton HC, Matthews K, Hawtin K, Crowley C, Robbins TW. Tryptophan depletion impairs stimulus-reward learning while methylphenidate disrupts attentional control in healthy young adults: Implications for the monoaminergic basis of impulsive behaviour. Psychopharmacology. 1999;146:482–491. doi: 10.1007/PL00005494. [PubMed] [CrossRef]
In 3, you’re considering adding a new supplement, not stopping a supplement you already use. The I don’t try Adderall case has value $0, the Adderall fails case is worth -$40 (assuming you only bought 10 pills, and this number should be increased by your analysis time and a weighted cost for potential permanent side effects), and the Adderall succeeds case is worth $X-40-4099, where $X is the discounted lifetime value of the increased productivity due to Adderall, minus any discounted long-term side effect costs. If you estimate Adderall will work with p=.5, then you should try out Adderall if you estimate that 0.5 \times (X-4179) > 0 ~> $X>4179$. (Adderall working or not isn’t binary, and so you might be more comfortable breaking down the various how effective Adderall is cases when eliciting X, by coming up with different levels it could work at, their values, and then using a weighted sum to get X. This can also give you a better target with your experiment- this needs to show a benefit of at least Y from Adderall for it to be worth the cost, and I’ve designed it so it has a reasonable chance of showing that.)
Adderall increases dopamine and noradrenaline availability within the prefrontal cortex, an area in which our memory and attention are controlled. As such, this smart pill improves our mood, makes us feel more awake and attentive. It is also known for its lasting effect – depending on the dose, it can last up to 12 hours. However, note that it is crucial to get confirmation from your doctor on the exact dose you should take.
A Romanian psychologist and chemist named Corneliu Giurgea started using the word nootropic in the 1970s to refer to substances that improve brain function, but humans have always gravitated toward foods and chemicals that make us feel sharper, quicker, happier, and more content. Our brains use about 20 percent of our energy when our bodies are at rest (compared with 8 percent for apes), according to National Geographic, so our thinking ability is directly affected by the calories we’re taking in as well as by the nutrients in the foods we eat. Here are the nootropics we don’t even realize we’re using, and an expert take on how they work.
Please browse our website to learn more about how to enhance your memory. Our blog contains informative articles about the science behind nootropic supplements, specific ingredients, and effective methods for improving memory. Browse through our blog articles and read and compare reviews of the top rated natural supplements and smart pills to find everything you need to make an informed decision.
Analyzing the results is a little tricky because I was simultaneously running the first magnesium citrate self-experiment, which turned out to cause a quite complex result which looks like a gradually-accumulating overdose negating an initial benefit for net harm, and also toying with LLLT, which turned out to have a strong correlation with benefits. So for the potential small Noopept effect to not be swamped, I need to include those in the analysis. I designed the experiment to try to find the best dose level, so I want to look at an average Noopept effect but also the estimated effect at each dose size in case some are negative (especially in the case of 5-pills/60mg); I included the pilot experiment data as 10mg doses since they were also blind & randomized. Finally, missingness affects analysis: because not every variable is recorded for each date (what was the value of the variable for the blind randomized magnesium citrate before and after I finished that experiment? what value do you assign the Magtein variable before I bought it and after I used it all up?), just running a linear regression may not work exactly as one expects as various days get omitted because part of the data was missing.
Our 2nd choice for a Brain and Memory supplement is Clari-T by Life Seasons. We were pleased to see that their formula included 3 of the 5 necessary ingredients Huperzine A, Phosphatidylserine and Bacopin. In addition, we liked that their product came in a vegetable capsule. The product contains silica and rice bran, though, which we are not sure is necessary.
The benefits that they offer are gradually becoming more clearly understood, and those who use them now have the potential to get ahead of the curve when it comes to learning, information recall, mental clarity, and focus. Everyone is different, however, so take some time to learn what works for you and what doesn’t and build a stack that helps you perform at your best.
Kratom (Erowid, Reddit) is a tree leaf from Southeast Asia; it’s addictive to some degree (like caffeine and nicotine), and so it is regulated/banned in Thailand, Malaysia, Myanmar, and Bhutan among others - but not the USA. (One might think that kratom’s common use there indicates how very addictive it must be, except it literally grows on trees so it can’t be too hard to get.) Kratom is not particularly well-studied (and what has been studied is not necessarily relevant - I’m not addicted to any opiates!), and it suffers the usual herbal problem of being an endlessly variable food product and not a specific chemical with the fun risks of perhaps being poisonous, but in my reading it doesn’t seem to be particularly dangerous or have serious side-effects.
L-Alpha glycerylphosphorylcholine or choline alfoscerate, also known as Alpha GPC is a natural nootropic which works both on its own and also in combination with other nootropics. It can be found in the human body naturally in small amounts. It’s also present in some dairy products, wheat germ, and in organic meats. However, these dietary sources contain small quantities of GPC, which is why people prefer taking it through supplements.
Taken together, these considerations suggest that the cognitive effects of stimulants for any individual in any task will vary based on dosage and will not easily be predicted on the basis of data from other individuals or other tasks. Optimizing the cognitive effects of a stimulant would therefore require, in effect, a search through a high-dimensional space whose dimensions are dose; individual characteristics such as genetic, personality, and ability levels; and task characteristics. The mixed results in the current literature may be due to the lack of systematic optimization.
The concept of neuroenhancement and the use of substances to improve cognitive functioning in healthy individuals, is certainly not a new one. In fact, one of the first cognitive enhancement drugs, Piracetam, was developed over fifty years ago by psychologist and chemist C.C. Giurgea. Although he did not know the exact mechanism, Giurgia believed the drug boosted brain power and so began his exploration into "smart pills", or nootropics, a term he coined from the Greek nous, meaning "mind," and trepein, meaning "to bend.
If you could take a drug to boost your brainpower, would you? This question, faced by Bradley Cooper’s character in the big-budget movie Limitless, is now facing students who are frantically revising for exams. Although they are nowhere near the strength of the drug shown in the film, mind-enhancing drugs are already on the pharmacy shelves, and many people are finding the promise of sharper thinking through chemistry highly seductive.
Regardless of your goal, there is a supplement that can help you along the way. Below, we’ve put together the definitive smart drugs list for peak mental performance. There are three major groups of smart pills and cognitive enhancers. We will cover each one in detail in our list of smart drugs. They are natural and herbal nootropics, prescription ADHD medications, and racetams and synthetic nootropics.
Nondrug cognitive-enhancement methods include the high tech and the low. An example of the former is transcranial magnetic stimulation (TMS), whereby weak currents are induced in specific brain areas by magnetic fields generated outside the head. TMS is currently being explored as a therapeutic modality for neuropsychiatric conditions as diverse as depression and ADHD and is capable of enhancing the cognition of normal healthy people (e.g., Kirschen, Davis-Ratner, Jerde, Schraedley-Desmond, & Desmond, 2006). An older technique, transcranial direct current stimulation (tDCS), has become the subject of renewed research interest and has proven capable of enhancing the cognitive performance of normal healthy individuals in a variety of tasks. For example, Flöel, Rösser, Michka, Knecht, and Breitenstein (2008) reported enhancement of learning and Dockery, Hueckel-Weng, Birbaumer, and Plewnia (2009) reported enhancement of planning with tDCS.
“We stumbled upon fasting as a way to optimize cognition and make yourself into a more efficient human being,” says Manuel Lam, an internal medicine physician who advises Nootrobox on clinical issues. He and members of the company’s executive team have implanted glucose monitors in their arms — not because they fear diabetes but because they wish to track the real-time effect of the foods they eat.
Starting from the studies in my meta-analysis, we can try to estimate an upper bound on how big any effect would be, if it actually existed. One of the most promising null results, Southon et al 1994, turns out to be not very informative: if we punch in the number of kids, we find that they needed a large effect size (d=0.81) before they could see anything:
My answer is that this is not a lot of research or very good research (not nearly as good as the research on nicotine, eg.), and assuming it’s true, I don’t value long-term memory that much because LTM is something that is easily assisted or replaced (personal archives, and spaced repetition). For me, my problems tend to be more about akrasia and energy and not getting things done, so even if a stimulant comes with a little cost to long-term memory, it’s still useful for me. I’m going continue to use the caffeine. It’s not so bad in conjunction with tea, is very cheap, and I’m already addicted, so why not? Caffeine is extremely cheap, addictive, has minimal effects on health (and may be beneficial, from the various epidemiological associations with tea/coffee/chocolate & longevity), and costs extra to remove from drinks popular regardless of their caffeine content (coffee and tea again). What would be the point of carefully investigating it? Suppose there was conclusive evidence on the topic, the value of this evidence to me would be roughly $0 or since ignorance is bliss, negative money - because unless the negative effects were drastic (which current studies rule out, although tea has other issues like fluoride or metal contents), I would not change anything about my life. Why? I enjoy my tea too much. My usual tea seller doesn’t even have decaffeinated oolong in general, much less various varieties I might want to drink, apparently because de-caffeinating is so expensive it’s not worthwhile. What am I supposed to do, give up my tea and caffeine just to save on the cost of caffeine? Buy de-caffeinating machines (which I couldn’t even find any prices for, googling)? This also holds true for people who drink coffee or caffeinated soda. (As opposed to a drug like modafinil which is expensive, and so the value of a definitive answer is substantial and would justify some more extensive calculating of cost-benefit.)
He used to get his edge from Adderall, but after moving from New Jersey to San Francisco, he says, he couldn’t find a doctor who would write him a prescription. Driven to the Internet, he discovered a world of cognition-enhancing drugs known as nootropics — some prescription, some over-the-counter, others available on a worldwide gray market of private sellers — said to improve memory, attention, creativity and motivation.
In most cases, cognitive enhancers have been used to treat people with neurological or mental disorders, but there is a growing number of healthy, "normal" people who use these substances in hopes of getting smarter. Although there are many companies that make "smart" drinks, smart power bars and diet supplements containing certain "smart" chemicals, there is little evidence to suggest that these products really work. Results from different laboratories show mixed results; some labs show positive effects on memory and learning; other labs show no effects. There are very few well-designed studies using normal healthy people.
Given the size of the literature just reviewed, it is surprising that so many basic questions remain open. Although d-AMP and MPH appear to enhance retention of recently learned information and, in at least some individuals, also enhance working memory and cognitive control, there remains great uncertainty regarding the size and robustness of these effects and their dependence on dosage, individual differences, and specifics of the task.
Vitamin B12 is also known as Cobalamin and is a water-soluble essential vitamin. A (large) deficiency of Vitamin B12 will ultimately lead to cognitive impairment . Older people and people who don’t eat meat are at a higher risk than young people who eat more meat. And people with depression have less Vitamin B12 than the average population .
For obvious reasons, it’s difficult for researchers to know just how common the “smart drug” or “neuro-enhancing” lifestyle is. However, a few recent studies suggest cognition hacking is appealing to a growing number of people. A survey conducted in 2016 found that 15% of University of Oxford students were popping pills to stay competitive, a rate that mirrored findings from other national surveys of UK university students. In the US, a 2014 study found that 18% of sophomores, juniors, and seniors at Ivy League colleges had knowingly used a stimulant at least once during their academic career, and among those who had ever used uppers, 24% said they had popped a little helper on eight or more occasions. Anecdotal evidence suggests that pharmacological enhancement is also on the rise within the workplace, where modafinil, which treats sleep disorders, has become particularly popular.
Neuroplasticity, or the brain's ability to change and reorganize itself in response to intrinsic and extrinsic factors, indicates great potential for us to enhance brain function by medical or other interventions. Psychotherapy has been shown to induce structural changes in the brain. Other interventions that positively influence neuroplasticity include meditation, mindfulness , and compassion.
“As a neuro-optometrist who cares for many brain-injured patients experiencing visual challenges that negatively impact the progress of many of their other therapies, Cavin’s book is a god-send! The very basic concept of good nutrition among all the conflicting advertisements and various “new” food plans and diets can be enough to put anyone into a brain fog much less a brain injured survivor! Cavin’s book is straightforward and written from not only personal experience but the validation of so many well-respected contemporary health care researchers and practitioners! I will certainly be recommending this book as a “Survival/Recovery 101” resource for all my patients including those without brain injuries because we all need optimum health and well-being and it starts with proper nourishment! Kudos to Cavin Balaster!”
Up to 20% of Ivy League college students have already tried “smart drugs,” so we can expect these pills to feature prominently in organizations (if they don’t already). After all, the pressure to perform is unlikely to disappear the moment students graduate. And senior employees with demanding jobs might find these drugs even more useful than a 19-year-old college kid does. Indeed, a 2012 Royal Society report emphasized that these “enhancements,” along with other technologies for self-enhancement, are likely to have far-reaching implications for the business world.
These are the most highly studied ingredients and must be combined together to achieve effective results. If any one ingredient is missing in the formula, you may not get the full cognitive benefits of the pill. It is important to go with a company that has these critical ingredients as well as a complete array of supporting ingredients to improve their absorption and effectiveness. Anything less than the correct mix will not work effectively.
Blinding stymied me for a few months since the nasty taste was unmistakable and I couldn’t think of any gums with a similar flavor to serve as placebo. (The nasty taste does not seem to be due to the nicotine despite what one might expect; Vaniver plausibly suggested the bad taste might be intended to prevent over-consumption, but nothing in the Habitrol ingredient list seemed to be noted for its bad taste, and a number of ingredients were sweetening sugars of various sorts. So I couldn’t simply flavor some gum.)
I had tried 8 randomized days like the Adderall experiment to see whether I was one of the people whom modafinil energizes during the day. (The other way to use it is to skip sleep, which is my preferred use.) I rarely use it during the day since my initial uses did not impress me subjectively. The experiment was not my best - while it was double-blind randomized, the measurements were subjective, and not a good measure of mental functioning like dual n-back (DNB) scores which I could statistically compare from day to day or against my many previous days of dual n-back scores. Between my high expectation of finding the null result, the poor experiment quality, and the minimal effect it had (eliminating an already rare use), the value of this information was very small.
“In the hospital and ICU struggles, this book and Cavin’s experience are golden, and if we’d have had this book’s special attention to feeding tube nutrition, my son would be alive today sitting right here along with me saying it was the cod liver oil, the fish oil, and other nutrients able to be fed to him instead of the junk in the pharmacy tubes, that got him past the liver-test results, past the internal bleeding, past the brain difficulties controlling so many response-obstacles back then. Back then, the ‘experts’ in rural hospitals were unwilling to listen, ignored my son’s unexpected turnaround when we used codliver oil transdermally on his sore skin, threatened instead to throw me out, but Cavin has his own proof and his accumulated experience in others’ journeys. Cavin’s boxed areas of notes throughout the book on applying the brain nutrient concepts in feeding tubes are powerful stuff, details to grab onto and run with… hammer them!
First half at 6 AM; second half at noon. Wrote a short essay I’d been putting off and napped for 1:40 from 9 AM to 10:40. This approach seems to work a little better as far as the aboulia goes. (I also bother to smell my urine this time around - there’s a definite off smell to it.) Nights: 10:02; 8:50; 10:40; 7:38 (2 bad nights of nasal infections); 8:28; 8:20; 8:43 (▆▃█▁▂▂▃).
Each nootropic comes with a recommended amount to take. This is almost always based on a healthy adult male with an average weight and ‘normal’ metabolism. Nootropics (and many other drugs) are almost exclusively tested on healthy men. If you are a woman, older, smaller or in any other way not the ‘average’ man, always take into account that the quantity could be different for you.
Endoscopy surgeries, being minimally invasive, have become more popular in recent times. Latest studies show that there is an increasing demand for single incision or small incision type of surgery as an alternative to traditional surgeries. As aging patients are susceptible to complications, the usage of minimally invasive procedures is of utmost importance and the need of the hour. There are unexplained situations of bleeding, iron deficiency, abdominal pain, search for polyps, ulcers, and tumors of the small intestine, and inflammatory bowel disease, such as Crohn's disease, where capsule endoscopy diagnoses fare better than traditional endoscopy. Also, as capsule endoscopy is less invasive or non-invasive, as compared to traditional endoscopy, patients are increasingly preferring the usage of capsule endoscopy as it does not require any recovery time, which is driving the smart pill market.
There is no official data on their usage, but nootropics as well as other smart drugs appear popular in the Silicon Valley. “I would say that most tech companies will have at least one person on something,” says Noehr. It is a hotbed of interest because it is a mentally competitive environment, says Jesse Lawler, a LA based software developer and nootropics enthusiast who produces the podcast Smart Drug Smarts. “They really see this as translating into dollars.” But Silicon Valley types also do care about safely enhancing their most prized asset – their brains – which can give nootropics an added appeal, he says.
Began double-blind trial. Today I took one pill blindly at 1:53 PM. at the end of the day when I have written down my impressions and guess whether it was one of the Adderall pills, then I can look in the baggy and count and see whether it was. there are many other procedures one can take to blind oneself (have an accomplice mix up a sequence of pills and record what the sequence was; don’t count & see but blindly take a photograph of the pill each day, etc.) Around 3, I begin to wonder whether it was Adderall because I am arguing more than usual on IRC and my heart rate seems a bit high just sitting down. 6 PM: I’ve started to think it was a placebo. My heart rate is back to normal, I am having difficulty concentrating on long text, and my appetite has shown up for dinner (although I didn’t have lunch, I don’t think I had lunch yesterday and yesterday the hunger didn’t show up until past 7). Productivity wise, it has been a normal day. All in all, I’m not too sure, but I think I’d guess it was Adderall with 40% confidence (another way of saying placebo with 60% confidence). When I go to examine the baggie at 8:20 PM, I find out… it was an Adderall pill after all. Oh dear. One little strike against Adderall that I guessed wrong. It may be that the problem is that I am intrinsically a little worse today (normal variation? come down from Adderall?).
Frustrated by the lack of results, pharmaceutical companies have been shutting down their psychiatric drug research programmes. Traditional methods, such as synthesising new molecules and seeing what effect they have on symptoms, seem to have run their course. A shift of strategy is looming, towards research that focuses on genes and brain circuitry rather than chemicals. The shift will prolong the wait for new blockbuster drugs further, as the new systems are developed, and offers no guarantees of results.
The evidence? In small studies, healthy people taking modafinil showed improved planning and working memory, and better reaction time, spatial planning, and visual pattern recognition. A 2015 meta-analysis claimed that “when more complex assessments are used, modafinil appears to consistently engender enhancement of attention, executive functions, and learning” without affecting a user’s mood. In a study from earlier this year involving 39 male chess players, subjects taking modafinil were found to perform better in chess games played against a computer.
Racetams, specifically Piracetam, an ingredient popular in over-the-counter nootropics, are synthetic stimulants designed to improve brain function. Patel notes Piracetam is the granddaddy of all racetams, and the term “nootropic” was originally coined to describe its effects. However, despite its popularity and how long it’s been around and in use, researchers don’t know what its mechanism of action is. Patel explained that the the most prominent hypothesis suggests Piracetam enhances neuronal function by increasing membrane fluidity in the brain, but that hasn’t been confirmed yet. And Patel elaborated that most studies on Piracetam aren’t done with the target market for nootropics in mind, the young professional:
The difference in standard deviations is not, from a theoretical perspective, all that strange a phenomenon: at the very beginning of this page, I covered some basic principles of nootropics and mentioned how many stimulants or supplements follow a inverted U-curve where too much or too little lead to poorer performance (ironically, one of the examples in Kruschke 2012 was a smart drug which did not affect means but increased standard deviations).
"They're not regulated by the FDA like other drugs, so safety testing isn't required," Kerl says. What's more, you can't always be sure that what's on the ingredient label is actually in the product. Keep in mind, too, that those that contain water-soluble vitamins like B and C, she adds, aren't going to help you if you're already getting enough of those vitamins through diet. "If your body is getting more than you need, you're just going to pee out the excess," she says. "You're paying a lot of money for these supplements; maybe just have orange juice."
Many of these supplements include exotic-sounding ingredients. Ginseng root and an herb called bacopa are two that have shown some promising memory and attention benefits, says Dr. Guillaume Fond, a psychiatrist with France’s Aix-Marseille University Medical School who has studied smart drugs and cognitive enhancement. “However, data are still lacking to definitely confirm their efficacy,” he adds.
Dopaminergics are smart drug substances that affect levels of dopamine within the brain. Dopamine is a major neurotransmitter, responsible for the good feelings and biochemical positive feedback from behaviors for which our biology naturally rewards us: tasty food, sex, positive social relationships, etc. Use of dopaminergic smart drugs promotes attention and alertness by either increasing the efficacy of dopamine within the brain, or inhibiting the enzymes that break dopamine down. Examples of popular dopaminergic smart drug drugs include Yohimbe, selegiline and L-Tyrosine.
When you drink tea, you’re getting some caffeine (less than the amount in coffee), plus an amino acid called L-theanine that has been shown in studies to increase activity in the brain’s alpha frequency band, which can lead to relaxation without drowsiness. These calming-but-stimulating effects might contribute to tea’s status as the most popular beverage aside from water. People have been drinking it for more than 4,000 years, after all, but modern brain hackers try to distill and enhance the benefits by taking just L-theanine as a nootropic supplement. Unfortunately, that means they’re missing out on the other health effects that tea offers. It’s packed with flavonoids, which are associated with longevity, reduced inflammation, weight loss, cardiovascular health, and cancer prevention.
As expected since most of the data overlaps with the previous LLLT analysis, the LLLT variable correlates strongly; the individual magnesium variables may look a little more questionable but were justified in the magnesium citrate analysis. The Noopept result looks a little surprising - almost zero effect? Let’s split by dose (which was the point of the whole rigmarole of changing dose levels):
The intradimensional– extradimensional shift task from the CANTAB battery was used in two studies of MPH and measures the ability to shift the response criterion from one dimension to another, as in the WCST, as well as to measure other abilities, including reversal learning, measured by performance in the trials following an intradimensional shift. With an intradimensional shift, the learned association between values of a given stimulus dimension and reward versus no reward is reversed, and participants must learn to reverse their responses accordingly. Elliott et al. (1997) reported finding no effects of the drug on ability to shift among dimensions in the extradimensional shift condition and did not describe performance on the intradimensional shift. Rogers et al. (1999) found that accuracy improved but responses slowed with MPH on trials requiring a shift from one dimension to another, which leaves open the question of whether the drug produced net enhancement, interference, or neither on these trials once the tradeoff between speed and accuracy is taken into account. For intradimensional shifts, which require reversal learning, these authors found drug-induced impairment: significantly slower responding accompanied by a borderline-significant impairment of accuracy.
Modafinil is a eugeroic, or ‘wakefulness promoting agent’, intended to help people with narcolepsy. It was invented in the 1970s, but was first approved by the American FDA in 1998 for medical use. Recent years have seen its off-label use as a ‘smart drug’ grow. It’s not known exactly how Modafinil works, but scientists believe it may increase levels of histamines in the brain, which can keep you awake. It might also inhibit the dissipation of dopamine, again helping wakefulness, and it may help alertness by boosting norepinephrine levels, contributing to its reputation as a drug to help focus and concentration.
A week later: Golden Sumatran, 3 spoonfuls, a more yellowish powder. (I combined it with some tea dregs to hopefully cut the flavor a bit.) Had a paper to review that night. No (subjectively noticeable) effect on energy or productivity. I tried 4 spoonfuls at noon the next day; nothing except a little mental tension, for lack of a better word. I think that was just the harbinger of what my runny nose that day and the day before was, a head cold that laid me low during the evening.
Certain pharmaceuticals could also qualify as nootropics. For at least the past 20 years, a lot of people—students, especially—have turned to attention deficit hyperactivity disorder (ADHD) drugs like Ritalin and Adderall for their supposed concentration-strengthening effects. While there’s some evidence that these stimulants can improve focus in people without ADHD, they have also been linked, in both people with and without an ADHD diagnosis, to insomnia, hallucinations, seizures, heart trouble and sudden death, according to a 2012 review of the research in the journal Brain and Behavior. They’re also addictive.
…Four subjects correctly stated when they received nicotine, five subjects were unsure, and the remaining two stated incorrectly which treatment they received on each occasion of testing. These numbers are sufficiently close to chance expectation that even the four subjects whose statements corresponded to the treatments received may have been guessing.
With just 16 predictions, I can’t simply bin the predictions and say yep, that looks good. Instead, we can treat each prediction as equivalent to a bet and see what my winnings (or losses) were; the standard such proper scoring rule is the logarithmic rule which pretty simple: you earn the logarithm of the probability if you were right, and the logarithm of the negation if you were wrong; he who racks up the fewest negative points wins. We feed in a list and get back a number: