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Convergence bidding has been adopted in recent years by most Independent System Operators (ISOs) in the United States as a relatively new market mechanism to enhance market efficiency. Convergence bidding affects many aspects of the operation of the electricity markets and there is currently a gap in the literature on understanding how the market participants strategically select their convergence bids in practice. To address this open problem, in this paper, we study three years of real-world market data from the California ISO energy market. First, we provide a data-driven overview of all submitted convergence bids (CBs) and analyze the performance of each individual convergence bidder based on the number of their submitted CBs, the number of locations that they placed the CBs, the percentage of submitted supply or demand CBs, the amount of cleared CBs, and their gained profit or loss. Next, we scrutinize the bidding strategies of the 13 largest market players that account for 75\% of all CBs in the California ISO market. We identify quantitative features to characterize and distinguish their different convergence bidding strategies. This analysis results in revealing three different classes of CB strategies that are used in practice. We identify the differences between these strategic bidding classes and compare their advantages and disadvantages. We also explain how some of the most active market participants are using bidding strategies that do not match any of the strategic bidding methods that currently exist in the literature.