You are confusing the issue but continuing to lump in normal cargo ships with actual warships with your discussion. This is a Navy (i.e. warship) discussion.
Chinese Maritime Activities and Socioeconomic Development, C. 2100 B.C.-1900 A.D.
The sub-average for Song-Ming for imperial transport ships is 10,320 and for warships 12,960.
There is nothing confusing about it, if you think it is, then you didn't understand the book.
Having read Gang Dengs's work, "Chinese Maritime Activity and Socioeconomic Development, 2100 BC to 1900" , I found his analysis is flawed and his conclusions incorrect.
1. He invalidly asumes a more or less constant rate of ship production. If the number of ships produced was 660, the something like that amount was produced the following year. That might not be the case. The production might be uneven, with a large batch produced one year and only a few next year. That would explain the spotty reporting of the amount , the years not reported produced too few ships to note.
Deng used primary sources from the Ming and Yuan period, showing transport shipping numbers as high as 12,837 during the early 15th century, meaning that his estimate of a sub-average of 9,060 transport ships total for the Ming is in fact a conservative under-estimatation.
"In Yuan times, apart from the grain carriers, there were 5,921 courier ships in the nationwide Imerial postal system. It is also documented that in Quanzhou alone, there were 15,000 government-owned sea vessels. Second, in the first half of the fifteenth century AD, the count of government owned grain transport ships was 11,839. In addition, there was an Imperial transport fleet of 998 vessels, which made the total number of ships in the Ming transportation operation up to 12,837. In the early Qing Dynasty, the grain fleet had over 10,000 ships. Such a number declined in the mid-Qing period but was still maintained at the 7,000 level. Meanwhile, in the second half of the eighteenth century there were some 130,000 private transport ships on the tax records. "
Gang Deng, Chinese Maritime Activities and Socioeconomic Development, C. 2100 B.C.-1900 p.69
2. If his assumption of course stsnt production was incorrect, then his estimatez of ship totals are way off. Perhaps by a magnitude.
Once one group of ships were built in a large batch. The replacements would have to be too. Steadily replacing the would result I ships replaced too soon or too late for the 10 year cycld you cited.
I will direct you where to start:
In 1291 AD, the loss rate in the Yuan grain transportation was reportedly 16 percent. This situation was improved only after 1292 AD, when some special efforts were made by the Mongol government to establish new sea routes, allowing the loss rate to drop to 2-3 percent...
In spite of these increases, the estimates are still conservative, because other items, such as regular maintenance of ships, are not counted. Under Ming government regulations, all grain-transporting boats were to be maintained in the third year of service, overhauled in the sixth year, and replaced in the tenth year...Thus, in a ten year life-span a ship would be pulled out of the service twice for routine maintenance.
3. The Chinese did not have to keep the numbers constant in ship totals. An Emperor could decide not to replace ships as they reached their end of life, allowing the navy to shrink, then later decide to build it back up.
One may argue that new ships may have been supplements to the existing fleet, not replacements. Or, new ships may constituted a fleet that had neve rexisted before those new ships were launched. Thus, to use new ships to estimate a fleet will inevitably lead to overestimation. This is certainly, true, especially if some isolated figures for new ships are picked up and used as the basis for estimation. However, if a long-term aberage approach is taken, the danger of overestimation can be minimized, if not eliminated.
The Ming naval institution demands every 100 household naval guards have one warship. This is a constant institution down to the end of the dynasty. This mean a force of 410,000 coastal guards would require a constant supply of 4,100 ships alone. This is not including the imperial fleets outside of these regulations.
4. The numbers he gives for the Mongol fleet is far too large. On page 71, he says the Yuan fleet was 12,750 and the Ming was 5,500.
The Yuan total is early wrong, we know this because if the Yuan had that many ships, the Yuan would not have needed to hastily build up ships for the Japanese invasion, which we know they did. Archeology of the some of Mongol invasion fleer ships shows these ships have signs of being hastily built, and if the Chinese fleet was anywhere near the size claimed, there would have been no need to bud these ships.
We have the annual data from 1270-1292, with 5,000 ships produced in 1270, 2,000 produced in 1273, 9,900 produced from 1274-1292. This describes a period of 20 years, not even a sub-average that spans out for decades.
As for why the Yuan needed to built ships in a haste for Japan and other states:
These estimates, for the Yuan in particular, seem to be inconsistent with the figures for the invading Yuan armadas to Japan, Vietnam and Java. However, if we accept that the basic principle in military arts is the same as that in economics - to keep the balance between costs and returns-then it may well be the case that the Mongols used only a proportion of their naval forces for the initial invasions and kept the rest in reserve as a second echelon.
5. His assumption for the average ship size of the Yuan and Ming ships.is far to high at 100 tons. It took 3,500 ships to transport 100,000 men in the Japanese invasion , about 28.5 men per ship on the average. The Mayflower carried 102 passengers, and was 180 tons, so adjusting the mass for fewer passengers gives an average of 50 tons for the Chinese ships. Thd Yuan used 800 ships to transport 30,000 men to Java, again giving 66 tons, far less than 100 tons. Note, if the100,00 and 30,000 also included sailors , the numbers would be lower yet, only 37 tons for the Japanese invasion ships.
It is known that during the Tang-Song Period, the loading capacity of an average sea vessel was around 230 metric tons, in Qing times, the loading capacity of the shallow water ship was between 100-200 tons. It is also known that in the Tang Dynasty over 2 million shi of grain (83,200 tons) was transported through the canals each year and in the Northern Song Dynasty, the amount reached over 6 million shi (278,900 tons), an average of 764 tons per day. This makes it possible to use the weight transported by ships as a base to estimate the size of transportation fleets.
We see the same results for the Ming ships. Gang also says on page 71 that Ming loyalist had 170,000 men on 8000 ships, implying ships of 37 tons on the average.
6. We know the Chinese have had a long history of exaggeration . The 450 ft size of the Zheng He treasure ships have shown to be not feasible and was not in the earliest accounts . Yet this figure was reported as fact in multiple dynasties and multiple sources. In 300 years, no Chinese called into question this exaggerated number. For more on this, see Sally Church article "Zheng He: An Investigation into the Plausibility of 450 FT Treasure Ships".