The oil hype of last week has been replaced by gloominess. A deal negotiated in Doha to freeze production fell through. Yet there is no reason for real despair, because data suggest that production may not increase all that much even without a deal.

The original deal in Doha aimed to cap oil production levels of OPEC members and Russia but excluded Iran. Recent OPEC data show either declining or stabilizing production among OPEC members and Russia. Table 5.5 in OPEC's Monthly Oil Market Report for March shows that overall production declined for these nations in February from January. Although the same table in the monthly report for April shows increasing production in March vs. February, that increase fails to make up for February's decline. In fact, even with Iran, OPEC oil production levels are expected to drop modestly by the end of 2016.

This puts the Doha deal into perspective. Even with a failed agreement, there seems to be some stabilization of oil supplies from OPEC and Russia.

Meanwhile, the situation in the U.S., according to the U.S. Energy Information Administration, isn't much different. Despite the shale boom in the U.S., from January 2015 to January 2016, production levels in the U.S. have more or less stagnated.

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Courtesy of U.S. Energy Information Administration

Deal or no deal, with no rise in production, oil prices likely have found a floor. That raises the question of whether a rally is coming.

"To get any significant rally, there's a very large stockpile to work through," Alex Beard, head of oil at Glencore, told the Financial Times. In other words, for oil to have a sustainable rally, oil stockpiles must fall.

Assuming global oil output won't move much, the variable that will cause stockpiles to decline is demand. Here, however, the data present a mixed picture. According to OPEC's Monthly Oil Market Report for April, global demand rose only 0.1% in the fourth quarter of last year from the third quarter (see Table 4.1), and Graph 4.1 indicates that demand growth is expected to remain at lower levels in 2016 than during the first three quarters of 2015.

What could change the demand side of the equation is global economic growth.

The past two quarters have been rather mild in the global economy. China's economy grew at less than 7% year over year in the first quarter. In the eurozone, growth stabilized, but inflation moved back below zero and manufacturing has been sputtering. In the U.S., unemployment remains low at 5%, but during the fourth quarter the economy grew at only 1.4% on an annualized basis. In Japan, the economy shrank as exports weakened.

Some recent data releases have been somewhat more encouraging. China's official manufacturing Purchasing Managers' Index surged to 50.2 in March, signaling a recovery, and Chinese exports smashed forecasts with an 11.5% year-over-year surge in March. In the eurozone, retail sales have recovered, signaling that European consumers are opening their wallets once again.

Other recent releases have been strikingly disappointing, however. U.S. retail sales disappointed, falling by 0.3% in March while industrial production fell by 0.5%. In Japan, the fall in industrial production was even steeper: 6.2%.

Tallying the good and the bad, we are left with only a meager improvement, which is hardly enough "horsepower" to push oil demand.

With enough evidence for an oil bottom but not enough for a rally, oil prices are likely to remain relatively range-bound for the near term, even if they're volatile on a day-to-day basis.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.