In the book, Hindu Dharma: The Universal Way of Life §, Swami Chandrasekarendra Saraswati cautions these japas and homas don't work always:
It may be that sometimes the Varuna japa does not succeed in bringing rains. But this is no reason why all mantras should be rejected outright as of no value. Sick people die even after the regular administration of medicine. For this reason do we condemn medical science as worthless? We have an explanation for the patient's failure to recover: his illness and reached such an advanced stage that no medicine could be of any avail. Similarly, no mantra is of any help when it has to contend against the working of powerful karma. There is also another reason. If you are not strict about your diet, the medicine taken may not work. Similarly, if we are lax in the observance of certain rules, the mantras will not produce the desired result.
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I tend to believe that there is 50-50 chance of any japa or homa bringing rain. When the homa does yield rain, people tend to attribute it to the homa. But correlation does not imply causation. The homas that don't bring rain are not reported by people in the same way when it "really worked."
Ironically, in 2015, when Telangana Chief Minister K. Chandrasekhar Rao was conducting a mahāyāga for universal peace, a fire broke out:
HYDERABAD: A fire broke out at the 'yagna' organized by Telangana chief minister K Chandrasekhar Rao on Sunday afternoon.
The incident occurred at around 1.30pm at Erravelli village in neighbouring Medak district when fire, that erupted from the 'homagundam' (pedestal for sacred fire), spread to the 'Yagashala' shed (made of grass), they said.
"No one was injured in the incident and all the people present there were immediately evacuated. The flames have been brought under control," the DSP said.
According to reports, about 2,000 priests from Telangana, Andhra Pradesh, Maharashtra, Karnataka and Tamil Nadu are taking part in the mega 'yagam' being performed for universal peace.
Rao has spent about Rs 7 crore on performing 'Ayutha Maha Chandi Yagna' in the state for universal peace.
The reason I quoted the above news article is to simply show that despite the best intentions a yajña can go wrong. All the more reason to believe it's a hit-and-miss. Also, there is no way to tell if a yajña done for "universal peace" really worked or not.
Here's an example of a yajña that seems to have worked:
For about four years i.e., from 1985 to 1988 there was a continuous and constant failure of rains in Andhra Pradesh. The state in general and Hyderabad in particular were reeling under the conditions of drought.
Sri Swamiji (Chinna Jeeyar) was merciful enough to perform a Varuna Yagna in Hyderabad for a period of 9 days. From the last day of the yagnam (i.e. Poornahuti day) miraculously there were heavy rains.
The bio however doesn't tell if Chinna Jeeyar Swami performed other such Varuna yajñas and if there were "heavy rains" immediately following the other yajñas.
§ An older and copyright-free version of this book is available for free here.