WPA.LI follows two key constraints. The first is that, for a given game state (i.e. the inning, the score, the number of outs, and the placement of any runners on base), the relative value of a play is determined by how much that play affects the team's chances of winning. If the bases are empty, a walk is credited the same as a single. If the bases are loaded with the winning run on third, a walk is credited the same as a home run. This constraint works exactly like WPA (as one might expect from a WPA-based metric).
The second constraint differentiates WPA.LI from WPA. One of the properties of WPA is that some situations are inherently weighted more strongly than others. A key at bat late in a close game can swing a team's chances of winning by several times as much as the same result in a blowout, and it is credited accordingly. WPA.LI, on the other hand, ensures that the average play in every situation gets the same weight.
So, on the one hand, you have WPA, which weights PAs according to their immediate impact on the game. One clutch PA might be worth as much as 4 or 5 normal PAs, and one mop-up PA might be worth practically nothing. On the other hand, you have WPA.LI, which weights every PA equally, just like most other stats do. Basically, it is linear weights, but with the ability to tailor the value of each event to the specific situation rather than sticking to a blanket value for each event across all situations. While WPA tells the story of clutch hitting (who got the big hit when the team most needed production), WPA.LI tells the story of situational hitting (who got on base when the team needed baserunners, put the ball in play when the strikeout was most costly, or hit for power when advancing runners quickly was more important than getting another guy on first).
There is a third important constraint which WPA.LI does not adhere to, however. Ideally, the average value of each event would match its linear weights value. If a home run is worth 1.4 runs above average across all situations, then you would like the average WPA.LI value of a HR to be 1.4 runs (or rather, the equivalent value on the wins scale). That is not the case, however.
The following linear weights values represent the average change in run and win expectancy for that event across all situations, along with the average WPA.LI value of each event. All three versions have been placed on the runs scale by setting the value of the out at -.27 in order to make them easier to compare directly:
As you can see, WPA.LI does fine at assigning the correct value to most events, but the value of the HR is way off. This may seem counterintuitive; if WPA.LI just creates custom linear weights for each situation based on the WPA values, why would the average WPA.LI value be different from the average WPA value? We can look at the mathematical relationship between WPA and WPA.LI to see why this is.