Hi
can I run a 250w MH on an 400w MV gear?

Short answer : no. You can try it but expect unsatisfactory results and/or overheating, among other effects. Also, lamp life will be significantly reduced.

Better don't even try it. The MH's are normally running at very high pressure and quartz thermal load, so such overdriving will make the violent arctube explosion very likely.

@Medved : I take it that running a lower wattage lamp on a higher wattage ballast will overdrive the lamp. Will the opposite be true, that running say a 400 watt lamp on a 250 watt ballast underdrive the lamp ? Will it overheat the ballast ? I don't intend to try it, just curious.

From the ballast perspective is important, what does the arc voltage, as that is the parameter dictated by the lamp.
And if something bad could happen to the ballast depend on how the incorrect arc voltage influence the ballast reliability.

At rated power, MV and probe-MH lamps run all watages the same arc voltage (around 100..130V). European HPS run all wattages at about 70..90V, US HPS vary a lot, so mismatched lamp-ballast combinations wont simply work at all (higher wattage lamp mean higher arc voltage, above what the ballast could supply)...
US pulse-start and all European MH are designed either around 100..140V MV, or 70..90V HPS specification, both variants even on the same wattage.

If taking an MV lamp, we have an unsaturated lamp, which maintain quite constant voltage over quite wide supply currents, including the ~63% drive, so ballast will not see any difference. Only the lamp will warm up longer and have lower efficacy.

The HPS are of saturated vapor design, so their actual arc voltage depend on the arctube temperature and that somehow on the arc current. So when operated at lower current, the arc voltage would become lower, what could increase the ballast current. And that mean the ballast losses will be higher than designed for, so the ballast may overheat.

The MH concept vary, some use saturated, some unsaturated vapor concept. But even the ones with unsaturated vapor (talking about only the components, what influence the lamp arc voltage; mainly older designs) become unsaturated only with small margin, do not tolerate so wide current range as the MV's do.
Moreover you may end up with problems even on the same nominal wattage, if you mix up the "70..90V" and "100..140V" specs ("70V" ballast will overdrive the "130V" lamp,...).

But when the ballast output current (and/or mainly it's losses) do not depend on the load voltage (mainly CWA ballasts), they tolerate such lower arc voltage pretty well, without any danger, as simply the same losses mean same temperature and it is only the temperature, what could kill the magnetic ballast.


@JackAmp1H:
From your profile I could not read, what territory apply for you:
It depend on two conditions:
1) Is the nominal arc voltage of those lamps the same? If no (if the MH is 80V, while MV's are 130V), the MH would be underdriven and the series choke ballast (this apply mainly for the Europe). For US probe start, this condition is met.
2) Does the ballast OCV suffice to ignite the lamp? If not, you have to add a 750V ignitor. European MH's nearly all some ignitor, as the 230V is too low. US CWA ballasts for MH have higher OCV, so are able to strike the probe-MH without an ignitor, so it is not used. MV ballasts have OCV of about 200..240V, what could be too low for the MH to start reliably (mainly at colder temperatures) and it will take them longer time for hot reignition. Otherwise you will need the 750V parallel ignitor. But such device is not used in the US, so you will have troubles finding one designed for 60Hz (ignitor designs are tightly tied to the mains frequency, so 50Hz ignitor operated at 60Hz would mean incorrect phase of the generated pulses)