It makes intuitive sense that the states with the most people, which means the largest congressional delegations, tend to have the most influence over national lawmaking and the federal purse strings.

The formula for the Roll Call Clout Index was designed to reflect that notion, with its emphasis on the number of lawmakers each state has at the Capitol, their seniority and assignments to leadership positions and the most powerful committees.

It would be tough for California, by far the most populous state since the first clout study back in 1990, to finish in a spot other than No. 1 — and it never has. It’s big enough that seven of its House members sit on the Appropriations Committee and their share of the panel’s seats (14 percent) is only slightly ahead of the their share of the national population they represent (12 percent).

Size and stability also mean that in the index for the 113th Congress, out this week, the delegations from Texas, New York, Florida and Michigan also continued to hold spots — that they’ve never yielded — in the top 10, and Pennsylvania re-entered that tier after a time away.

But the delegations from four of the 10 most populous states underperformed in the new study — most significantly, the team from Illinois, which at 12.9 million residents is the fifth biggest state, but which dropped seven notches since its 2011 and 2009 rankings. Illinois is now No. 17 in overall clout.

Not only did the state lose a House seat in reapportionment, but the resulting redistricting was orchestrated by the Democratic legislature to make that party dominant in the congressional delegation again. It worked, but at a significant cost in influence: Only one out of every three House seats is held by a majority Republican, and one out of every three is also held by a newcomer, so the delegation’s cumulative House service is now comparable to a handful of states half its size. Federal spending in the state has also plummeted to less than $6,000 per capita — a figure that was lower in just two other states in fiscal 2011, the most recent Census Bureau data available.

The main factors preventing the state’s clout from shriveling further are the delegation’s assignments to 10 seats on prestige committees — only Texas and California have more — and the fact that Richard J. Durbin is the Senate Democratic whip.

Georgia finished one notch below Illinois, at No. 18, even though its delegation represents the eighth most populous state. Below average per capita spending, both senators in the minority caucus and modest collective House seniority were the main contributors. And Georgia’s ranking is sure to slip in two years if, as expected, four of the 14 House members give up their safe GOP seats for bids to succeed fellow Republican Saxby Chambliss in the Senate.

Ohio is seventh in population but its lawmaker’s potential clout now ranks 14th, continuing a decline that began after the state peaked at No. 6 a decade ago. That’s when its members held the gavels at three House committees, two Appropriations panels and a dozen other subcommittees. The bottom line for Ohio now is that having native son John A. Boehner as speaker only delivers so much clout by itself. Although the state’s 18 members claim nine exclusive committee seats, not one of them is chairman or ranking member of a clout-worthy panel, a clear reflection of the group’s declining seniority. Seven of the 16 House members have been in office less than three years.

North Carolina is 10th in inhabitants but 13th in clout — a relatively small differential explained in part by consequences of redistricting that countermanded what happened in Illinois: Four of the 13 House members are Republican freshmen, but what they lack in seniority they make up for by being in the majority.

For every state with sway that stops short of its size, however, there are states with delegations in position to bring back victories disproportionate to their size. Earlier posts detailed the outsized sway expected of the eight members from Louisiana (No. 4), the 10 from Maryland (No. 9) and the trio from Delaware (No. 27).

But two others should be viewed as the little states that should.

The Hawaii delegation may feature two brand new senators, two House members with 28 months’ congressional experience between them and a Democratic feud in the making. But the amount of federal money spent on the islands — $18,200 per person, more than all but two states, even without much earmarking two years ago — gives each of those junior lawmakers the power to deliver considerable benefits to their constituents. This has kept the delegation’s clout at No. 19. (To be sure, that’s down eight notches from two years ago, when the late Daniel K. Inouye was chairing Appropriations, Daniel K. Akaka chaired Indian Affairs and the pair had 73 years of Senate seniority between them.)

Alaska, with half as many people as Hawaii, came in at No. 21. That’s a reflection of its top 10 level of per capita spending, the top GOP spot Lisa Murkowski holds on Senate Energy and Natural Resources, Mark Begich’s claiming of a seat with Murkowski on Senate Appropriations this year and, not to be forgotten, the extraordinary longevity of Republican Rep. Don Young.

The state’s sole GOP House member is chairman of no committee this time (he’s timed-out at both of his), but his own 21 terms are more than the cumulative House seniority of 19 other delegations this year.