Personal blog on early retirement, a little traveling, and analytics projects. I write about what I learn as I am learning it.
Two dollars of income cost a couple I was modeling last week $9,574. Not two thousand — two. That is the Roth conversion vs ACA subsidy problem in one line, and as of January it is live again for anyone retiring before 65.
The enhanced premium tax credits that ran from 2021 through 2025 expired on December 31 and were not extended. What came back with them is the old 400%-of-the-federal-poverty-line cliff: below it you get a subsidy, above it you get nothing at all. Not a taper. Nothing.
A few days ago I wrote that a basketball rules file would come out nearly empty, and that the interesting part of an NBA optimizer is not the optimization. Then I went looking for something else and found a workbook I had forgotten I wrote: FCP Optimizer — Master v6.7, an NBA daily fantasy optimizer in Excel, with a change log that starts at version 4. So rather than speculate about NBA DFS optimizer constraints, here is the actual model, read straight out of the file.
It is a mixed integer program with about 200 binary variables, solved by CBC through the OpenSolver add-in. Everything below is what the sheet and its macros really do, not a cleaned-up version of it.
The textbook move, when a mixed-integer program solves slowly, is to tighten the linear relaxation. Add the constraint that makes the LP bound closer to the integer optimum, give branch and bound less room to wander, watch it finish faster.
I did that to the stacking constraint in my hockey lineup optimizer last week. It got twice as slow. Same slate, same solver, same lineups out the other end — 2.20 seconds a lineup before, 4.38 after. I reverted it and left a comment telling future-me not to helpfully fix it again.
Continue reading “The Textbook Fix That Made My MILP Twice As Slow”
The NHL lineup optimizer is live. Free, no account, no email, no cap on lineups. You upload one file — the player pool exactly as it downloads from DraftKings — and it hands back a CSV formatted for re-upload.
It is the hockey version of the football optimizer and the baseball one, same solver underneath, a different rulebook on top. Hockey turned out to be the easiest of the four sports I have tried, which was a pleasant surprise after basketball, where the stacking rules turned out to barely exist at all.
Continue reading “A Free NHL Lineup Optimizer for DraftKings”
In the last post I argued that basketball gives an optimizer nothing to stack, because no rule of the sport links two players’ scores the way a batting order or a quarterback does. That was reasoning, not evidence. So I pulled three seasons of box scores and actually measured NBA DFS correlation — 62,681 player-games, 3,690 games, and 505,721 pairs of players who shared a floor.
The short version: the structural argument holds, the numbers are far smaller than most stacking advice implies, and the most interesting thing in the data is something I had predicted backwards.
