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Comment by dmurray | Hacker News Reader

I'm not sure if the article is tongue in cheek, but almost all of the skill and almost all of the noise in these games usually comes from your choice of value function, i.e. your ability to predict how many points a player will get in a given week.

Picking the best team subject to the constraints is trivial in comparison and you can solve the knapsack problem by eye, or with some kind of greedy/beam search approach.

This is different from the financial markets where almost all of the alpha (outperformance of one stock over another) has been taken away by other market participants, so a lot of professional time is spent on risk management, portfolio optimization, etc.

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Generally incorrect. The critical thing here is that many player scores are correlated. Various configurations will have a lot more swing to their outcomes, and when you only care about being the number one spot, highest expected value probably won’t win it.

Player value correlation is indeed a thing. So too match ups in the next game, player playing out of position, etc. I haven't experimented but you are probably right that a model that could use factors like these effectively would outperform what I described.

But they aren't critical to building a model that will beat your mates and land you on the single-digits top%.

This is something I’ve been trying to find a way to account for in my fantasy drafting the last few years, after trying to maximize expected value has not gotten me the desired results (probably also due in part to the delta between expected and actual value). It’s occurred to me that a “boom or bust” lineup that scores +2 st dev one week and -2 the next is way better than one that performs +1 every week (hand waving exact values).

Build a correlation matrix between player positions and teams. Add a constraint the forbids the solution from having negative correlations below X.

The way you would want to test it is take the top 500 solutions from each approach and see how many of them are winners under whatever framework you care about.

The value function is crucial, sure. But back testing over a couple seasons I can usually land on something much better than what I as a (usually pretty casual) fan has in my head.

From an automation perspective the harder problem is getting match day squad selections (some sports regularly announce last minute teams, like at the time of the toss) and accounting for whatever special cases the game rules have tossed in (e.g. select a captain and vc, special reduced fees on trades this round, etc).

And to really win these games, rather say just beating your friends and landing top 5% globally, you also need risk management and portfolio optimisation strategies: e.g. when to play your "captain scores double this round" card? everyone has Mbappe, do you also pick him to hedge your riskier picks? I have no doubt that some players have built all this automation but I sure haven't.

If you want to maximize your chances of winning a very large game like this, you need to play quite a lot riskier than is intuitive, you definitely do not want to pick a popular player if your model predicts someone else will outperform him.

If you want to finish top 5%, having the best model should do it, with some attention to risk management in the last few games of the season (play riskier if you are in the 90th percentile than in the 99th).

If you want to maximise your chance of beating your friends, have the best model and think a little game theory at the end of the season based on whether you are leading or chasing.

yeah matches my experience

I don't have the numbers to back this opinion, but I believe that consistently ranking in the top 5% in all the games will greatly increase your chances of winning the league. It's not necessary to win every stage, but just having high scores consistently will likely make you win the league.

I also don't have numbers, but I'd opine that you need that (top 5% every round) AND you need to be to have a few big rounds where you greatly outperform almost everyone. Getting those big rounds means taking some calculated risks.

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