My counterfactual fantasy

So long Mo Salah, and thanks for all the lives you saved.

According to the lamestream media, Mo Salah was merely an Egyptian king. Over here in Fantasyland, where everyman can pick his own poison and make his own name, Mo is our MVP, the Most Valuable Prophet.

Blessed as I was to manage Mo for five years and win three titles together, nobody knows better how he floated above the fray, immune to the vagaries of form and fate that afflict the rest of us grappling in vain with the least random parts of the number generator. The ascendance of Steph Curry established beyond doubt in the mid-2010s that three is greater than two. Until 2017, most of us had six being greater than two threes filed away under Huge if True. Mo revealed it to be true, and huge.

While many tokens are being spilled at the moment on the two Premier League titles Liverpool won in Mo’s nine years, grossly overlooked have been the four titles our MVP won in the seven seasons which overlapped with Theo Walcott Fan Club, the fantasy league which shut up shop in 2024 on account of its membership finding the demands of elite competition unsustainable as we aged out of our prime. As Mo moves on to the next realm,¹ inshallah, it’s time to share how he guided my path, with faith that you too will apply his teaching to the part of the simulation rubes call “real life”.

The GOAT and a goat. I retained the Theo Walcott Fan Club trophy, like Brazil and the Jules Rimet (according to me), or because I forgot to give it back (according to league sources).

Every corner of Fantasyland is built on prediction, but different jurisdictions incentivize different strategies. In auction- and draft-based formats typical of American sports, each player is in the game only once. No convergence on the same set of players whose cost-effectiveness becomes obvious as the season unfolds, a variance-sapping scourge all too familiar to managers who grew up playing traditional Fantasy soccerball. In the highest form, you either pony up for Mo on auction night, or you spend the season looking up at him scoring shedloads for your rival. The most important question facing bidders for the last decade has been not ‘can you predict the MVP?’, but ‘what’s the most you’re willing to pay to have Mo grace your team?’

First time out, I paid a pittance. Most had memory-holed the 21-year-old who did nothing in one season at Chelsea. Only the nerds who watched his loan spell in Italy on their spreadsheets - including the nerds who were running the show at Liverpool - had noticed him become a star-in-waiting, and the nerds with blogs were kind enough to notify their readers about the promise of his second coming. Nobody, though, expected quite what happened next: 32 goals and 10 assists produced an outlandish total of 277 Fantasy points, only topped once since (by the MVP himself), turning the TWFC title race into a procession.²

It wasn’t much of a fluke: the underlying stats showed him a bit over his head with his finishing, but even with some regression to his expected rate of converting shots into goals into points he still projected as one-of-one.³ And that’s what came to pass. In his first three seasons, the MVP averaged 6.4 points per gameweek. Second, Raheem Sterling, was more than a full point back at 5.3. Over the course of seven seasons, seven different players topped the non-Mo division, and even if you’d been able to predict each of them (you couldn’t), you’d still have been better off with Mo, 5.9 to 5.7.⁴ How, you might wonder, did my rivals allow me to get my hands on this points machine for five of seven? Why did others think I was lucking my way out of making the same expensive mistake and somehow getting the same winning results?

The answer, as far as I gleaned from Mo’s teaching, starts with what happens without him, the counterfactual. My willingness to pay more than anybody else for the MVP flowed, counter-intuitively, from me and my elaborate spreadsheet paying closer attention to the critical importance of the 90th most valuable player.

In a league with six 15-player squads, whoever ranks 90th is the replacement player, the worst player you might end up with, and 45th is the median. Let’s have Victor Moses and Gabriel Jesus play those parts, and predict they’ll score two and three points per respectively, against Mo’s six. And then let’s ignore Moses for a second, and consider that anybody who doesn’t automatically clock that Mo is twice as valuable as Jesus is a trolley with a wheel loose.⁵

A chart made by my editor, who with some prompting did a much better job more quickly than I would have alone.

Not so fast. What happens if you get neither Mo nor Jesus? The counterfactual isn’t you get nothing. You get Moses, and you get his two points per. If every spot in the squad is spotted two free points, the difference of three between Mo and Jesus isn’t what it seems. Rather than the difference between six and three, it’s the difference between plus-four and plus-one points above the replacement player (Points Above Moses, PAM). That’s what you’re paying for, Value Over Moses (VOM). And so Mo isn’t worth two Jesuses after all. He’s worth four Jesuses.⁶

Mohamed’s Value Over Moses is four times as high as Jesus’s Value Over Moses.

Following our intuitions about Jesus doesn’t make anybody a bad person, but it will mean leaving expected points all over the floor. Without considering the counterfactual, without drawing a line at replacement level, everyman will systematically overpay for journeymen, and neglect the superstars breathing rarefied air up where the curve gets steep. Your squad having eight of the top 30 might feel like a safer bet, but all else being equal my squad having three of the top eight will eat it alive.

The same dynamic plays out in “real life” leagues, especially those with salary caps (although it’s often obscured by combining squad-wide caps with maximum individual salaries).⁷ And it plays out in other markets for talent. The next time you’re buying or selling some labour, you’ll be doing yourself a disservice if you aren’t thinking about what Moses brings to the team. You can bet your bottom dollar the AI researchers perpetually auctioning themselves off, not to mention the labs doing the bidding, have all been advised by their editors to think this way.

This content, though, unlike so much else that comes out of clubhouses in Fantasyland, is not coming to you as a get rich quick scheme.

Expecting better

The same counterfactual-replacement dynamic underpins higher-minded endeavours like clinical trials, where the control group are Moses. And it underpins all the decisions we make in “real life”, where something will happen regardless of what we do, or don’t do.

Take saving the lives of others. Something we all do, in expectation, continuously, whether routinely, like driving slowly near schools, or exceptionally, like running the London marathon to raise money for the fight against cancer. Often, we face a choice: which life to save? Assuredly when we’re choosing which charity to run for, or donate to, and hopefully not whether to run over a grandmother on the school run or her granddaughter.

It would be better if we lived in a “real world” where we didn’t have to make these kinds of tradeoffs. For now, though, once you’ve put your time or money on one thing, you can’t spend that time or money again. If all lives are equal, and we can’t save them all, aren’t 75 years of one more valuable than five?

Which life to save, God forbid, depends on the counterfactual.

Following our intuitions about saving grandmothers doesn’t make anybody a bad person, but it will mean leaving expected life-years all over the floor. Without considering the counterfactual, everyman will systematically neglect the far too many granddaughters who die before they’re five.

My mum just became a Grandma for the first time, and promptly endorsed a pro-granddaughter allocation of resources. My Granny just became a Great Granny and her idiosyncratic beliefs (Mrs Thatcher mixed with Matt Yglesias) have had her advocating for defunding herself for as long as I can remember. My daughter declined to comment.

Relatively little money can go a very long way

In a rich country, if you couldn’t save everyone, you’d need to be saving grandmas for something like 1/15th (5/75) what it costs to save granddaughters to save a comparable number of life-years. If we go global, that order of magnitude jumps up. Some life-years can be saved for more like 1/100th the cost of others.

There is not, as far as anyone knows, any rich country Grandma who can be saved for less than $8000. The lowest figure I could find for buying a cancer patient one year of life with chemotherapy is $17,131.⁸ I think we’d all want that paid for another year with Grandma. $100k of the most cost-effective chemo buys 5.8 precious life-years.

At the same time, though, there’s the counterfactual: countless poverty-stricken granddaughters who can be saved for much less. Not if there were a cure, or if we could only break down the structural barriers to systemic change, worthy as those aspirations are. Just if you send the cash-strapped charity with a tried-and-tested intervention a small fraction of your disposable income.

GiveWell somehow heard the word before the MVP was preaching it. They started studying the cost-effectiveness of charitable dollars for a living in 2007, when Mido was the only Egyptian who’d ever played in the Premier League.⁹ Their exhaustive research and elaborate spreadsheets show that distributing inexpensive insecticide-treated bed nets to people in the poorest parts of Africa is highly effective at preventing malaria, saving an expected life for every $3000-$8000 spent.¹⁰ Three-quarters of those lives belong to children under five. If we make some overly-conservative assumptions (see footnote), then $100k of bed nets buys 500 precious life-years.¹¹

500’s an awful lot of life-years for the price of one of Pete Hegseth’s populist grand pianos.

In Fantasyland, when I first saw how much my model thought the MVP was worth, it blew my mind. I did a triple take, and then spent countless hours discerning the meaning of the message. With that divine inspiration, when I first found out how little it can cost to save someone’s granddaughter in “real life”, I could take it in stride, and take appropriate action.

A donation of $200 (£150) buys a child a year of life.

If I could inspire one more person to save one more child one more year of life by putting the MVP’s preaching into practice, that would be a fitting tribute.

Training data

• 📖Moneyball (2003) and 📺 He Gets On Base (2011). Michael Lewis x Brad Pitt. The rest is history.

• 🎵American Sports (2018). “Can I please have my money back? / My virtual reality mask is stuck on “Parliament Brawl” / Emergency battery pack just in time / For my weekly chat with God on video call.”¹²

• 📝How Data (and Some Breathtaking Soccer) Brought Liverpool to the Cusp of Glory (2019). Amazing how nerds get cooler when they win at the jocks’ own game.

• 📖Noise (2021). You no doubt know the OG, Thinking, Fast and Slow. The sequel contains all sorts more insights relevant to building better prediction models in Fantasyland and in “real life”, including developing the leg-break provision: only override your model if information it’s missing is as obvious and consequential as a player being seriously injured.

• 📝Against Malaria Foundation (via GiveWell). Why not?

1. Seems like he’s soured on becoming a Saudi prince, maybe because he doubts the palaces will still be standing by summer.

2. There have only been two 30-and-10 seasons in Premier League history. When the MVP broke his own record for the highest Fantasy score in 2024/25, he had 29-and-18. The season was four games longer when Alan Shearer had 34-and-13 in 1994/95.

3. There’s so much more to say about the “underlying stats” like expected goals (xG) and all the ways there are to find edges (in Fantasy and “real life”) with probabilistic prediction models, but that’s for another day.

4. Mo was the top-scorer in four of the seven seasons, and again in his eighth (post-TWFC). His non-first place finishes were second, third and seventh (when he missed a month for the African Cup of Nations).

5. There is some finessing of the details going on here for legibility reasons, but if you can't do that in a blog about the relationship between models and "reality" where can you? In the three seasons Mo averaged 6.4, median “Jesus” averaged 3.1 and replacement “Moses” averaged 2.6. Everyone having different models (mental or otherwise) means it's very unlikely you'll end up with the player you think is 90th. You can be more aggressive and set replacement level at whatever number of your top 90 you expect will end up being bought, because other people will prefer the guy you have 99th (or in some cases, 999th). My line moved around a bit over time, but it was generally in the 70-75 range.

6. There’s nothing magic about Jesus being the median here. The same logic applies at the top end where the curve gets steep, and that’s often where it matters most: the difference between Mo’s six and Raheem’s five is actually +4 VOM vs +3 VOM, and so whatever you’re willing to pay for Raheem you should be willing to pay 33% more for Mo (4/3), not 20% more (6/5). However, it’s not an iron law that using VOM increases the relative value of the MVP: if the Moses waterline is negative, then the relative gap between top options narrows. In our model, if Moses is at -2, then Mo and Raheem are +8 and +7, and so you should be willing to pay 14% more for Mo (8/7), not 20% (6/5) or 33% (4/3).

7. In TWFC with its salary cap of 250m, Mo’s price ticked up from 89m (36% of the cap) in 2018 to 111m (44%) in 2023. In the NBA (which also has 15-player squads), individual salaries are capped at 35% for 10-year vets, and 30% or 25% for the prime-age players delivering most of the VOM. For all that being able to reliably get under-valued journeymen on below-market contracts is an edge, by far the best way to achieve surplus value is to hook or crook your way into a Mo-level superstar who the rules prohibit you paying fair value. (Not that non-cap leagues are bastions of fairness, or that the supercategory value can be collapsed into its sub-category market value, but that’s for another day.)

8. I know it's mostly not chemo that cancer charities are providing, but it's surprisingly hard to get cost-effectiveness estimates for hospice care. In any case, chemo or bed nets is a tradeoff governments make when it’s the same Treasury that pays for national health and international aid. Since we can’t count on some such Treasuries to pay for either, it’s increasingly a choice we have to make ourselves.

9. This is one where the joke is even people who’ve gone way too deep into Fantasyland won’t remember the name. The sickest sickos who do remember know who they are.

10. Other highly cost-effective charities and causes are available. GiveWell has four top-rated global health charities. If your priority is to reduce animal suffering (reasonable, there’s an awful lot of it), check out Animal Charity Evaluators and Animal Welfare Fund. Lots of people's top priority at the moment is making AI go safely (autonomous nukes, anyone?), but I don't currently know where the marginal dollar is best spent in pursuit of that goal, and it's beyond the scope of my parental leave to find out. If you want to take a squad-building approach, this cool new donation weighting tool from Rethink Priorities can help.

11. High-end estimate of cost of saving one expected life, $8000. Expected lives saved for $100k, 100 / 8 = 12.5. Low-end estimate of life expectancy for a 5-year-old whose life is saved, 50. Low-end estimate of life expectancy for a 35-year-old whose life is saved, 60. High-end estimate for average age of someone whose life is saved between 6- and 49-years-old, 35. Proportion of lives saved under 5, 75%. Expected life-years per life saved, 0.75 * (50 - 5) + 0.25 * (60 - 35) = 40. Expected life-years saved by $100k, 12.5 * 40 = 500.

12. “...A montage of the latest ancient ruins / Soundtracked by a chorus of you don't know what you're doing.”