The error in the usual calculation
The common shortcut multiplies 160 gold by the number of Transmutes and calls the result Midas income. That is gross value. The alternative is killing the same creep normally and collecting its bounty. The item's economic value is only the difference between those two outcomes.
With a 40 gold baseline bounty, each use creates 120 incremental gold. Divide the 2,200 gold item cost by that value and the model needs 19 uses. With a 90-second charge restore and an immediate first use after a minute-12 purchase, break-even arrives around minute 39.
Why expected match length decides the case
If the game ends at minute 42, the model gets 21 Transmutes. Gross incremental value is 2,520 gold, net economic value after item cost is 320 gold and realized ROI is roughly 14.5%.
If the game ends at minute 35, only 16 uses remain. They create 1,920 incremental gold - 280 below item cost. The same Midas becomes a positive or negative investment purely because the available payback window changed.
What the formula deliberately does not solve
Midas provides attack speed and interacts with the current Madstone mechanic. For one hero those effects may outweigh a monetary loss; for another they may not compensate for surrendered tempo. Assigning one universal value would be invented precision.
Use Other value when you are willing to price the hero-specific effect yourself. The model does not choose the item for you. It separates the provable economic part of the decision from game judgement.
Replace the baseline with your inputs and get an answer for your scenario.
Data note. Every numeric example is a transparent baseline scenario. It is not presented as official publisher data and can be recalculated in the linked tool.