Tom Tango uses wOBA to measure the spread in runs per game between the best and worst lineups a team can put on the field. He gets a value between 0.2 and 0.25 runs per game:

Now, let’s swap the first batter and the last batter. What happens? Well, instead of 5 PA going to the .400 wOBA batter, 5 PA will go to the .290 wOBA batter. That’s a drop of .110 wOBA, or .110/1.2 = .092 runs, per PA. For 5 PA, that’s a drop of .458 runs. However, our .400 wOBA batter will now increase the 9th place by .092 runs per PA, albeit for only 4.111 PA. So, that’s .377 more runs for that slot. The swap of the 1st and 9th batters will give us a total net runs value of .081 runs.

TangoTiger.com

He then repeats this process for every swap. This is where I have a quibble. Tango keeps the plate appearances by lineup slot constant across switches. The poor hitters at the top of the worst possible lineup should make more outs per PA, and they take away chances from the better hitters at the bottom of the order. In fact, they take chances away from everyone. If the worst lineup loses 100 PA over a season compared to the worst lineup, that would be about four games worth of outs, or about 17-18 runs. That would add on another 0.1 runs per game loss.

The you can measure this spread for a particular lineup with the Lineup Analysis Tool (LAT). Going into the 2023 season, the average distance between the best and worst lineups came in at 0.29 runs per game. Again, this is a quibble, but using poor hitters at the top of the lineup takes away opportunities from everyone, reducing the overall offensive context.