The Hall of Fame register at Baseball-Reference.com now lists 44 former Cubs and 32 former White Sox inducted as players, including new members Lee Smith and Harold Baines.

Some of the connections are loose at best. Tony Lazzeri is in the Hall for his 1,659 games with the Yankees, not his 54 with the Cubs. Steve Carlton’s 10 games with the Sox didn’t put him in the Hall.

But among those with stronger Chicago connections — let’s say at least five seasons — which players could be considered inner-circle Hall of Famers, elite among the elite?

JAWS can help there. Devised by Jay Jaffe and applied to Hall of Fame credentials in his ‘‘The Cooperstown Casebook,’’ the Jaffe WAR Score System balances career value against peak value.

Career value is represented by a player’s full WAR, as listed at Baseball-Reference.com. Peak value is the WAR in his seven best seasons. The average of the two values is his JAWS.

Here’s how it works: Ernie Banks’ career WAR was 67.5, and the WAR of his seven best seasons totaled 51.9. The average of 67.5 and 51.9 is 59.7, and that’s his JAWS.

In the ‘‘Casebook,’’ published in 2017, Jaffe uses those numbers to divide the Hall into elite, rank-and-file and basement categories. To qualify as elite, a player must exceed Hall averages in all three components: career WAR, peak WAR and JAWS.

That’s a tough standard. Hall of Fame Cubs Ryne Sandberg and Cap Anson fall short in different ways, with Sandberg’s 68.0 career WAR below the Hall average of 69.4 at second base and Anson’s 41.8 peak WAR below the Hall average of 42.7 at first. Both top Hall averages in the other categories.

These players with at least five Chicago seasons meet that tough standard and qualify as Hall elite. Hall averages have changed since the book was published, so figures are from Baseball-Reference.com.

Catcher: Sox’ Carlton Fisk, 68.5 WAR, 37.6 seven-year peak, 53.0 JAWS vs. Hall catcher averages of 54.3/35.1/44.7.

First base: Sox’ Frank Thomas, 73.8/45.4/59.6 vs. Hall first-base averages of 66.8/42.7/54.8.

Second base: Sox’ Eddie Collins, 124.0/64.2/94.1 vs. Hall second-base averages of 69.4/44.4/56.9.

Third base: Cubs’ Ron Santo, 70.5/53.8/62.2 vs. Hall third-base averages of 68.4/43.0/55.7.

Shortstop: Cubs’ Banks, 67.5/51.9/59.7 and Sox’ Luke Appling 74.5/43.9/59.2 vs. Hall shortstop averages of 67.0/43.0/55.0.

Starting pitcher: Cubs’ Grover Cleveland Alexander, 118.9/69.4/94.2; Cubs’ Greg Maddux, 106.6/56.3/81.4 and Cubs’ Fergie Jenkins, 84.1/51.4/67.8 vs. Hall starting-pitcher averages of 73.2/49.9/61.5.

Relief pitcher: Sox’ Rich Gossage, 41.2/31.6/36.4 vs. Hall reliever averages of 39.1/26.0/32.5.

Players are listed at the position they would rank highest. Banks played more games at first than at shortstop, but most of his career value — including all seven of his peak WAR seasons — was at short. Similarly, Thomas played more games at designated hitter, but the larger share of his value was at first.

Missing from the list are outfielders. Chicago never has had an outfielder exceed Hall averages in all JAWS categories. The closest is the Cubs’ Billy Williams, whose 63.5/41.3/52.4 barely misses the Hall averages of 65.2/41.5/53.3.