Only the hoop is over the line.
We have a similar situation. They could have positioned the hoop so the boys spent much more time in their own yard (not mine) and they did not do so. As a result, after many years of abuse, I spent a few thousand dollars replacing beds and plantings with sod due at least partially to their trespassing and destruction of property. Now I just have dead grass and divots in the yard instead of ruined mulch and plantings.
Not really happy about this. This will probably be an ugly scene. The parents have refused to have their children respect our property rights. Instead they made us the enemy in this situation. I will speak with the husband not the wife .....
PSU_Chicago: A couple of thoughts from a lawyer, albeit a California lawyer::
1.. My reaction to your OP was like Midnighter's. Talk to the neighbor and see if you can resolve this amicably. It would save on legal bills, and perhaps allow you to maintain good neighborly relations. But your followup post, above, suggests that this is not a viable option, and that there is already a lot of bad water under the bridge with you and this neighbor. Even if you have poor neighbor relations, it may be worth making the attempt. That attempt tends to put you in a better light in the event you later end up litigating.
2. You said "only the hoop is over the line." Wut?! Does the backboard face onto YOUR property, necessitating that the people playing at this hoop spend 99% of their time in YOUR yard?! If so, that is seriously messed up.
3. You need to consult a Pennsylvania lawyer, but I can tell you a bit about how this would turn out if you were California residents. It may well be that the result would be very much the same in Pennsylvania.
If you have had a survey done and there are survey stakes in the ground which make it clear that the neighbor is using YOUR property, and doing so without asking for your consent, that use will, with the passage of time, likely ripen into what is known as a "prescriptive easement." That simply means the legal right (i.e., easement) to use someone else's property. In California (and most states), a prescriptive easement cannot be created if the prescriptive use is founded on mistake as to the boundary line (and, thus, ownership of the real property in question). The use must be "open, notorious, and non-consensual." as would be the case if the neighbor used your property without asking for your consent. The use must also be more than occasional, and occur for a period of at least five years (the "prescriptive period").
I don't recall your saying how long ago you had the survey done and stakes planted, but it was clear that open, notorious and non-consensual use of your property began AT LEAST as long ago as the survey was done. I'm guessing that such use began much more than five years ago, since your post refers to "many years of abuse." Your post suggests that the neighbor apparently put up the hoop so as to use a rather large swath of your property (the free throw line would be fifteen-plus feet onto your property). I doubt that such a significant encroachment onto your property would be deemed a "mistake."
4. You have perhaps heard of the term "adverse possession." That is a legal doctrine which is closely related to prescriptive easements. Both require a period of open, notorious and non-consensual use by the party claiming rights of use, and the prescriptive period is usually the same for both prescriptive easements and adverse possession, but adverse possession (if established in a "quiet title" lawsuit) gives the user full ownership of the property in question, whereas a prescriptive easement does not, giving only the right to use. In California, the user would also have to prove that he or she paid the real property taxes on the real estate in question in order to establish adverse possession. This rarely happens, particularly with respect to something less than a full legal (taxable) parcel.
5. Did the neighbor EVER say anything to you that would suggest he or she was asking for your consent to install the hoop or continue using your property for basketball games? If so, reduce it to writing and mention it to your lawyer. If you can put forward evidence that the use was consensual, you may be able to prevail. Even if your case is relatively weak, it may be worth sending the neighbor a demand letter asking him to relocated the hoop, or at least turn it around 180 degrees. He may not be willing to spend the attorneys' fees necessary to educate himself on his legal rights.