I think there is still a chance for the Ottomans to win the Balkan wars. The Ottomans were in the process of re-organizing their armies when the armies of the Balkan nations attacked. Bulgaria in particular had done lots of recon and had a good amount of intelligence on the state of the Ottoman army. If the Ottomans were attacked at a different time, or if they have more of their army available in Europe, as OTL most of it was in Asia at the time, unable to be brought over quickly enough due to the abysmal infrastructural system.
This being said, it is still relatively hard, especially when compared to the Ottomans sitting out World War One. They had joined the Germans originally due to a fear of partition by the victors afterward, as well as due to the requisitioning of their ships without compensation (one of Churchill's patented "smart ideas") which enabled pro-German members of the Ottoman cabinet such as Enver Pasha to fully declare in favour of Germany. OTL he had signed a secret alliance with Germany a few days previously, but it is unknown as to whether the rest of the Ottoman cabinet would have gone along with it. Make the British a bit more competent with their diplomacy, or the Germans a bit less competent with theirs, and the Ottomans might sit out the war. Assuming they don't join the allies later on of course.
This being said, it is still relatively hard, especially when compared to the Ottomans sitting out World War One. They had joined the Germans originally due to a fear of partition by the victors afterward, as well as due to the requisitioning of their ships without compensation (one of Churchill's patented "smart ideas") which enabled pro-German members of the Ottoman cabinet such as Enver Pasha to fully declare in favour of Germany. OTL he had signed a secret alliance with Germany a few days previously, but it is unknown as to whether the rest of the Ottoman cabinet would have gone along with it. Make the British a bit more competent with their diplomacy, or the Germans a bit less competent with theirs, and the Ottomans might sit out the war. Assuming they don't join the allies later on of course.