It's very unpopular here, but I can easily understand the argument that the Lakers franchise has been better than the Celtics franchise over the course of history. We've had far too many down years while the Lakers have been far more consistent - no major stretches of futility like we had in pretty much the entire 90s. So I can't dismiss the argument. As a Celtics fan, I still put my franchise first, but I would even if the count was 18 to 17.
We have the biggest bullet, obviously, in the 17 to 15 or 10 advantage in titles. However, the Lakers have been to about a dozen more Finals than the Celtics and had far fewer years of non-contender status. And in the past 30 years of the modern NBA, the count is 9 titles, 15 Finals (half of all seasons) and 7 years of non-contender status for the Lakers to 4 titles, 6 Finals and 15 years of non-contender status (again, half of all seasons) for the Celtics. And unlike some, modern history does weigh a little more heavily for me because it has more relation to where the franchises are right now. And what "is" the best franchise is a present-time evaluation, albeit based on history.
That said, the OP's +12 or whatever advantage to the Lakers way overstates things even if the Lakers are a better franchise. You don't get points when a non-contender Lakers team loses in the first round and a non-contender Celtics team misses the playoffs. Neither gets an advantage in that situation. Like others have pointed out, where the teams lose to the same team in the playoffs (i.e., Celtics lose in ECF, Lakers lose in Finals or vice versa), neither gets an advantage - both teams were contenders, neither won it. Similarly where one team wins a championship and the other doesn't make the playoffs, that's a far bigger advantage than one team winning the Finals over the other. Like I said, due to consistency, I can understand the Lakers franchise coming out on top, I just don't think your method of calculation is very good.
As for the breakdown of types of teams by furball into three categories (champions, playoff teams and non-playoff teams), I respectfully disagree. As you may have guessed, I think that if there are three categories, those categories are champions, contenders and non-contenders.
For example, this year, the Pistons weren't better than the Suns, or even the Bobcats or Warriors or Pacers, just because they got to lose 4 straight games by double digits in the playoffs. None of those teams were contenders at all, so it really doesn't matter that the below .500 Pistons got into the playoffs. They're not of the same quality as the Celtics, Magic, Nuggets, Rockets or Cavs just because they were among the top 8 teams in a 3 deep conference. For that matter, the Hornets, Jazz, Sixers and Heat really weren't contenders either. Truthfully, the only teams that could have won it this year were the Lakers, Nuggets, Rockets, Cavs, Celtics and Magic. So if I were to break it into three categories, I'd say the Lakers are category 1, those 5 other teams are category 2, then everybody else.
In the modern NBA, I'd have to have five categories - champions, legit contenders, longshot contenders, non-contenders and dregs. This year it would go 1- Lakers; 2- Magic, Cavs, Nuggets, Lakers, Rockets; 3- Spurs, Mavericks, Blazers, Jazz, Hawks (differentiation for me isn't based on record but on how a team looks heading into the playoffs - the other playoff teams clearly weren't going anywhere though the Bulls were closest); 4- Bulls, Hornets, Heat, Sixers, Suns, Pistons, Bobcats, Pacers, Nets, Raptors, Bucks, Knicks, Warriors; 5- Timberwolves, ex-Sonics, Grizzlies, Clippers, Wizards, Kings. Of course, back when there were 8-12 teams in the league, you could only have the three, which usually came out 1- Celtics; 2- Lakers, 1 or 2 of Sixers, Hawks, Royals, Warriors; 3- everybody else. If I were to try to numerically evaluate it, I'd give 10 points for a championship, 5 points for being a contender, 3 points for being a longshot contender, 1 point for being a noncontender, 0 for the dregs. Maybe the Lakers come out on top, but at least it more appropriately rewards greatness and punishes absolute futility.
Those are my thoughts. 17 championships are all well and good, but being a non-contender for about 15 straight years in the 90s and 00s is just much much more futility than the Lakers ever had and weighs very heavily for me. (As fun as the 02 Celtics team was, they never had a chance against any of the 8 Western playoff teams that year - I would almost contend there was no real "contender" in the East from 00 through 03). So I can definitely see the argument, and if I wasn't a Celtics fan I might even give it to the Lakers.