To add to
@Ram Sabaratnam's excellent answer, I think you should conceive of 'competitors' and 'the market' in two distinct ways. Firstly, you have the broad sense of the terms,
where we look at firms as a whole and compare them. Looking at a firm holistically will entail considering revenue and profitability, headcount, international offices and strategy, practice area/sector expertise, client base, history, growth model, patterns in type of deals/cases/matters the firm works on, various market recognition and so. Fortunately enough, over time an informal classification system of firms based on shared attributes has emerged - the legal press places firms in categories such as: the Magic Circle, the Silver Circle, more recently the 'Global Elite', the US firms, the large international firms, the regional firms, the high street firms etc. Then, to differentiate a given firm from other members in the category and to pinpoint its market position further, you can use the resources Ram mentioned for more in depth research.
To give an example, you can further break down the category of US firms between those that have large, medium or small-sized London offices. You can then break down between those that focus on providing a full service offering and those that target a specific selection of practice areas/sectors. If you then still need to break it down further, you should look at client base and volume and type of mandates advised on. You should be able to find statistics on deal/case values and volumes on publications like The Lawyer and Bloomberg Law, whereas for 'deal types' you should just take a look at the firm's listed expertise and see if you notice any patterns. Legal 500 is also quite useful here as it breaks down practice areas/sector expertise rankings with a more targeted/narrow scope and also lists related mandates/clients.
The second interpretation of the terms is a narrowed one, focusing on competitors and each firms' position
within the marketplace of a specific practice area/sector. When identifying a firm's competitors in a given practice area/sector, you can once again make a further distinction between (i)
competitors as in the selection of best firms in the area - the ones that are toughest to pitch against (which can be reliably identified by looking at the Chambers band 1 firms) and the one; and (ii)
competitors as the firms your firm actually competes most for work with - the ones it is actually coming across most often when pitching for the same work. To identify a firm's position in the given practice area marketplace you once again want to look at (ii). What you want to see is if there are any common characteristics of most of the work done by your firm in the given practice area and the work done by the firms it is most often pitching against and see if you can in any way classify it as a type. To this end, you should also research any available statistics relating to the practice area's revenue, profitability, headcount, and mandate-specific statistics.
To give an example, say we are analyzing
Davis Polk's corporate team. You can start with the Band 4 Chambers M&A ranking which in the context of its high profitability and small headcount can be seen as an indicator of great expertise. Going beyond this and looking at
Davis Polk's London corporate M&A work you can identify a couple of features, such as a higher deal value/lower deal volume strategy, a focus on Transatlantic mandates, and a prevalence of matters form institutional clients. This already distinguishes the practice from that of most rivals. Analyzing the other Chambers-ranked firms, the only ones that arguably still fit the same description are
Sullivan & Cromwell and Cleary Gottlieb. To further differentiate
Davis Polk's M&A team from theirs you should look into their respective list of past mandates and market recognition and once again find new characteristics. In
Davis Polk's case I would say those include the breath of types of deals they advise on (as they have comparable expertise in public M&A, private M&A, and PE) and particular expertise in TMT and financial services.
