NHL Archives - Kind of Lost

How to Play Fantasy Sports Strategically: My Review

A review of Haugh and Singal’s DFS paper on modeling opponents, and the simulation-based NHL lineup generator I built from it.

Earlier this week I wrote about what an MIT DFS paper taught my NHL lineup optimizer. Read that paper and you quickly run into its follow-up: Martin Haugh (Imperial College) and Raghav Singal (Columbia), How to Play Fantasy Sports Strategically (and Win), later published in Management Science. It builds directly on the MIT work and asks the one question that paper skipped: what is everybody else doing? Their answer is that to play fantasy sports strategically you can’t just maximize your own points. You have to beat a field of lineups you can’t see yet.

I read it for a selfish reason. I have been paper-trading my NHL lineups for a week (I build them before lock, then score them against the real DraftKings fields once the games are over), and after five slates no setup has made money. None of them (that is not a typo). So this post is half review, half lab notebook: what the paper does, what I borrowed, and the different kind of lineup generator I am building along the same lines.

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Bar chart of return on entry fees over five NHL slates with each night’s best prize removed: plain settings -81%, simulation picking by expected payout -71%, simulation with top-1% coverage -67%, power-play stack with Vegas filter -64%. The average entry loses about 16%. — Five DraftKings NHL slates, Oct 2–6, 2026, every contest filled to its entry cap and scored against the real field. Blue is the new simulation-based generator.

My NHL Lineup Optimizer Now Skips the Solver (Mostly)

My NHL lineup optimizer used to build every lineup the same way: hand the whole problem to a solver and wait. It now skips the solver for most of the work. It lists the stacks that are allowed, scores them, and picks the best one, and it does that for a whole batch on a DraftKings or FanDuel slate in about a tenth of a second. The solver I have always reached for is still in the tool, but as the referee rather than the player.

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Horizontal bar chart on a log scale. Time to build a batch of lineups with the solver versus the enumeration fast path: DraftKings 3-3 stacks 2.3 versus 0.1 seconds, FanDuel 3-2 stacks with cooldown off 44.9 versus 0.15 seconds. — Time to build the whole batch. The 3-3 rows were run through the app code on tonight’s DraftKings and FanDuel slates; the 3-2 rows were run against the engine directly on a FanDuel slate. FanDuel leaves its own projections blank this early in the season, so I used stand-ins, which do not change the timing. In every row the two methods produced the same lineup totals.

Yahoo DFS NHL Optimizer: Two Goalies, New Rules

My free NHL lineup optimizer now builds lineups for Yahoo, the third site after DraftKings and FanDuel. I expected a Yahoo DFS NHL optimizer to be a matter of a new file parser and a new roster shape. It was mostly that, except for one line in Yahoo’s roster that broke three of my assumptions: two goalies. This post is about what had to change, which settings would have quietly made every lineup impossible, and the one new rule I added because of it: never repeat the same goalie pair.

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Bar chart of distinct goalie pairs. 6 lineups: 4 pairs with the limit off, 6 with it on. 20 lineups: 6 pairs off, 20 on. — Same Yahoo slate, same settings. Without a limit the solver keeps coming back to the same two or three goalie pairs.

What an MIT DFS Paper Taught My NHL Lineup Optimizer

An MIT NHL DFS paper found win probability was the only goalie predictor that mattered. So I rebuilt my NHL lineup optimizer around goalies.

Last week I came across a paper from three MIT operations research people — David Scott Hunter, Juan Pablo Vielma and Tauhid Zaman — called Picking Winners in Daily Fantasy Sports Using Integer Programming. It is about building a set of NHL DFS lineups with a solver, which is exactly what my free NHL lineup optimizer does, so I read it with a pencil in hand. They did not just run simulations: they entered real DraftKings contests and report that “we are able to rank in the top-ten multiple times in hockey and baseball contests with thousands of competing entries.” Then they donated the money — “around $15,000” — to the Greater Boston Food Bank, which I thought was a classy touch.

A good chunk of the paper is theorems and proofs about submodular functions. I skipped those. What I wanted was the strategy: what they stacked, what they found, and whether any of it should change my tool. One thing did, and it made the tool more than twice as fast.

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Two bar charts. Seconds per lineup: 2.1 when the solver picks the goalie, 0.9 with the goalie fixed. Lineups built from 150 asked in 240 seconds: 70 versus 115. — Same FanDuel slate, same settings, same machine. Fixing the goalie before the solve cut the time per lineup by more than half.

Vegas Lines and Injury Reports in My Lineup Optimizers

My free lineup optimizers for MLB, NFL and NHL now pull two things you used to have to look up in another tab: the league’s injury report and the Vegas lines. The part I care about most is how the Vegas lines get used, because the first version of that rule quietly did the opposite of what I built it for. Implied team totals are the most useful number on a DFS slate that isn’t in the salary file, so this is the post about how the tool gets them, what it does with them, and the one rule I had to throw away.

Strip chart: QB game totals under three rule settings; the first Vegas rule put 0 of 10 stacks in 50+ games, the shipped rule put 9 of 10 in 47+ games — Ten NFL lineups per row, built on a FanDuel slate with test Vegas lines. My first rule made the solver dodge high-total quarterbacks; the one I shipped does the opposite.