The physical size doesn't matter as long as the specs check out (which they do). You technically bought a slightly better resistor.

They've gotten smaller over time. As long as the wattage of the new resistor meets or exceeds the old one, you're good

Yes - physical size *does* matter for power resistors. Surface area is very important - larger the surface area = faster heat dissipation.

For the most part, resistors have not changed in physical size over the years (except for carbon composition resistors - which is not shown above). But, there is a set of small form factor resistors out there which is what you bought. These can withstand 2 watts but not over the long term. If you were to install this new 'small form factor' resistor - it won't last as long as the original.
Original was 2 watt - replace with a 2 watt resistor. Or replace it with a small form factor 3 watt resistor (which is same physical size as 2 watt resistor).

If you use a small form factor resistor - always make sure the wattage is higher than the one you are replacing.

I disagree, because he purchased metal film resistors to replace carbon ones. They should be able to handle anything the carbon resistor did, and for a longer life span.

As I said before - Bigger is ALWAYS better for resistors.

For heat dissipation - it isn't the composition of the resistor, it is the surface area which reduces the surface to air thermal resistance. The resistor he purchased can handle heat better but will *absolutely* run much hotter than the one he replaced. It is extended temperatures that affect and reduce the life span of a resistor. The difference between carbon film and metal film (or metal oxide or wire wound) is the metal film type can handle higher temperatures better than a carbon film. If you end up running the new, smaller metal film resistor at a hotter temp than a larger (any type) resistor --- the smaller one will have the lesser life span. As far as coating - both old one replaced and new one were enamel coated, a better coating is silicone for lower 'core' to surface thermal resistance but they run into the same surface to ambient thermal resistance problem.

The ratio of surface area to volume is a huge factor in lifespan. With the larger one, you have more volume to heat up (or cool down) and you have larger surface area for heat dissipation. Take a look at heat sinks on these machines: Which does better job at dissipating heat? Larger ones with higher surface area or smaller ones with small surface area? Different material but same principle.

The resistor in first post continuously dissipates 0.9W on that Gottlieb display board.
The resistor he picked is a small form factor 2W resistor. This resistor is the same size as a full size 1W resistor and has the exact same thermal dissipation as a 1W resistor. Based on the data sheet for the resistor he used (Vishay PR02000201001J) -- he will experience a 140F temperature rise above ambient (based on Vishay data sheet). Ambient of 70F will result in a normal operating temperature of 210F. Almost hot enough to boil water or burn your finger tip.

A 2W carbon film resistor running at 0.9W: Based on a Tyco data sheet (CFR200J1K0 - carbon film, 2W, 1K full size) - there will be a 107F temp rise. Using same ambient temp, this one will operate at just under 180F. Not a heck of a lot of difference but it is about 10% cooler.

If I were replacing that resistor - I would have chosen a 3W, reduced form factor metal oxide resistor. These are the same physical size as a 2W resistor... and have the same thermal dissipation. Difference being the metal oxide can handle it better.

Now, if we were talking about old carbon composition resistors - that's a different story.

If you have four of those resistors you could gang four together in a series / parallel arrangement and spread the power over all four resistors.

Great question and answer time though thanks all.

+1
Mike