It's not a stupid question, but the answer will probably disappoint you: it's not very likely that you are the direct descendant of a Spartan warrior. On the one hand, with the way human gene pools work, most modern Greeks (and perhaps most modern people all around the Mediterranean) may well have a Spartan somewhere in their ancestry. On the other hand, just being from the Greek city of Sparti, the modern-day settlement a few miles away from the site of ancient Sparta, doesn't necessarily make this more likely.

I'm assuming that by "Spartan warriors" you mean the Spartiates or homoioi, adult men of Spartan birth with full citizen rights. If so, demographics are not in your favour. There were, at most, about 8000-9000 Spartiates alive at any one time (namely in the second half of the 6th century BC). If we include women and children, that number can be expanded to about 40,000 full Spartan citizens (though only the boys who made it to adulthood would be warriors). They were only a small minority of the population of Lakedaimon, which consisted of several other major groups:

• Helots (slaves)

• Perioikoi (freeborn non-citizens)

• Neodamodeis (freed helots)

• Hypomeiones ("inferiors", those who had lost citizen status)

• Mothakes/nothoi ("bastards", those of mixed descent)

No source gives us total numbers for any of these groups, but we can take it for granted that most of them were significantly larger than the Spartiate class. In the case of the helots, on the basis of Herodotos' claim that there were 7 helots fighting alongside every 1 Spartiate at the battle of Plataia, scholars have concluded that helots must have outnumbered Spartiates at least 7 to 1.

To make matters worse, the number of Spartiates declined spectacularly throughout the Classical period, driven by peculiar inheritance practices as well as natural and military disasters. As many Spartiates fell below the property threshold for citizenship, they fed the ranks of the hypomeiones while citizen numbers shrank. There may have been 8000 Spartiates in 480 BC, but by 370 BC there were fewer than 1000 left. Plutarch tells us that by about 240 BC there were no more than 100 Spartan citizens who still owned land. Others may have claimed Spartan ancestry, but they were no longer Spartiates.

Now, if we're willing to be more generous and define "Spartan warrior" as "anyone who was born in Lakedaimon and fought for Sparta", we could include a much larger group under that definition. Those who lost their full citizen rights were still liable to military service, as were the perioikoi, the mothakes (who were sometimes sponsored to undergo the Spartiate upbringing), the neodamodeis and even the helots. In fact, when the kings Agis IV and Kleomenes III tried to rebuild the foundation of Spartan power in 240-222 BC by reconstituting the citizen body, they did so by raising thousands of perioikoi to citizen status; these people might not be able to claim Spartiate ancestry, but they eventually became Spartiates all the same. So, if we grant to all these groups the status of Spartan warriors, the odds of a local family having Spartan warriors in its bloodline becomes much higher.

However, if we focus entirely on the "original" Spartiate class, that group was very small and constantly shrinking. A family from modern Sparti that has no family record of having ever moved in from somewhere else is still vastly more likely to be descended from helots or perioikoi than from Spartiates. The modern town of Tsakonia, which claims to preserve intact some form of the Dorian dialect of Greek spoken by the Spartans, will almost certainly also derive this from local groups of perioikoi and helots rather than from the Spartiates themselves. That is, if such claims can even be given credence, since the region has hardly been immune to migration movements over the last 2500 years, and the local population is very likely to have seen its gene pool constantly refreshed by new arrivals from all over the Mediterranean and beyond.