Minimum Values are for the Global Rankings, not an individual game's Score Value
Minimum value is an interesting idea, what size of minimum do you have in mind? In score, minimum might have to be fairly large to make any impact on games with 400,000+ top scores ...
Let's remember the context of a minimum value... we are talking about the Global Rankings table. The actual score values have already been scaled against a percentage scale when they hit the Global Rankings table (I've seen values in the Global Rankings table of 0.1% through 100%, or a blank value indicating no applicable value), so a minimum value would be implemented against the Global Ranking's scaled values (3% for retirements, 5% for losses, or what-have-you, instead of seeing a value like 1.3%, for the most recent set of games in the Global Rankings table).
These "minimum values" would get scaled down over time as scores "stagnate" from previous games, just like all other values stagnate, but I think that picking a value like 3% or 5% for the most recent set of games in the Global Rankings table will not "interfere" with the top rankings in any way (so you won't get complaints from the top players) but will encourage more regular participation from those who don't often win our XOTM games. It will also encourage more submissions from those who do win regularly but "have a bad game" that they otherwise would not have submitted.
We learn not only from top players but also by sharing our knowledge with and teaching less-experienced players (teachers often learn just as much as their students do, by the very act of teaching). One goal here is to give some sort of recognition to the less-experienced players who seem to fit the model that the Global Rankings table is set up to encourage, which is that of rewarding regular participation. The other goal is to have our "regular players" submit every game that they play.
As for the individual games, the "see the full results here" tables would not need to see a change at all.
Losses vs Retirements
As I said earlier in this thread, the goals for rewarding losses and retirements are slightly different:
For losses, we want to encourage people to play out their games and submit, regardless of how well they do.
For retirements, we want to encourage people to have less of an incentive to retire "just because they will keep losing Score if they continue on with the game."
By rewarding the players that stick it out for a loss slightly higher than those who retire are rewarded, we encourage people to try and turn-around a dangerous-looking situation, which is often actually possible to do.
We also give players more incentive to "keep playing for longer to see if they have a hope of turning-around a dangerous-looking situation" before retiring if we have a maximum value (in addition to a minimum value) for retirements. One would be less inclined to retire as soon as a war breaks out and could play on to see how they can salvage the situation if they will not score any better by retiring earlier than by retiring later. The players will be encouraged to learn more and may realise that a lot of situations that otherwise looked hopeless are not always as hopeless as they initially appear to be.
Minimum vs Maximum
The other idea previously raised was to actually give a MAXIMUM value for retirements--both a Minimum and a Maximum value.
Here's where the model can get slightly more complicated in how we'd want to implement it, but if we truly want to discourage people retiring just to get a higher Score value when they are losing a war, instead of playing out their games for a bit longer to try and learn from the experience, then a historical evaluation of Global Ranking Scores against Retirement Score values could give us an idea of what kinds of numbers we see. Using the existing values, we can get a feel for what numbers might make for good "minimums" and "maximums."
It would be a lot easier for someone with access to the database to perform a query against Retirment games to give us a few values than to manually calculate them, such as the highest Score, lowest Score, and median Score seen for Retirements. It probably would help to have a few other values for comparision's sake, such as the same values for Losses and the lowest Score value seen for a win.
If it is not possible to get this data, then I would arbitrarily suggest the values of:
Losses = Minimum of 5%, where the loss meets a certain set of criteria
Retirments = Minimum of 3%, Maximum of 5%, where the retirement meets a certain set of criteria
The "certain set of criteria" would be aimed at preventing people from abusing these minimum values for "free" Global Ranking points by not seriously participating, such as by retiring before even playing very far into the game or intentionally allowing Barbs to walk into your undefended City or Cities just to lose. The "certain set of criteria" can be as simple as using a single criterion, such as finishing date.
Erkon suggested using the criterion where the finish date must occur after the earliest submitted victory date, which sounds like a pretty reasonable suggestion. However, depending upon how much information about finishing dates is carried over to the Global Rankings tables behind the scenes, this information may be incredibly easy or incredibly difficult to extract and apply. We'd need someone who knows about the database's structure of the Global Rankings to chime in on what's possible in this regard.
In fact, if the Global Rankings tables do have some way of easily referencing finishing dates, then this concept could even be retroactively applied to the current Civ 4 XOTM Global Rankings tables (I don't know how the Civ 3 Global Rankings tables work but perhaps even there, too, if the model is the same). It wouldn't necessarily be a trivial matter to implement, as you'd probably want to store static values instead of constantly recalculating minimum and maximum values every time that the tables are displayed, to avoid causing a performance hit to the existing Global Rankings tables. So, that might mean creating a new "Adjusted Score" column in in the Global Ranking Score table behind the scenes that gets displayed in place of the current Score values. It might even be a lot of manual work to set up if the Global Rankings can't easily reference the historical finishing date values. Thus, I won't hold my breath to see it happen for the Civ 4 Global Ranking tables. But, now's the time to plan for any such required changes to the Global Rankings' database structure for Civ 5.
Global Rankings: Score vs Speed
Losses are always worthless in the speed side, are you suggesting a minimum there as well?
Losses and retirements do not even get a value in the Global Rankings table for the Speed value, so I do not see a change happening there.
However, both the Score and, by extension, the Combined table, would give a bit of a boosted reward to Losses than is currently seen.