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I am trying to figure out which planet has mathematical equations when having more bad teams as potential matchups, increases active teams chances of drawing other good active teams?

That is silly talk.

If you got rid of all the inactive teams, all you would be left with are active teams, and the further you go along, all you would have left are good teams, thus increasing your chances to draw a good team.

The way it is now, you have a greater chance of drawing a bad, incactive, or bot team. Not saying that is good or bad, but that is just the way it is.

If you draw a very good team now, that is just the random luck factor. If you remove all bots and inactive teams from the equation, you are removing luck, and pretty much ensuring tougher matchups.

The point is more a fairness issue than a mathematical probability one. While you are correct in that more bots give you a greater chance to draw a bot, try explaining that to someone unfortunate enough to draw nothing but quality opponents while his conference mate draws nothing but bots. Now add to that a presumption that the guy drawing tough opponents has a quality team and the guy drawing bots has a mediocre one. Who has the greater chance of advancing?
What I am advocating is a more competitive tournament that rewards the active manager who's put time and effort into improving his team and setting his lineups. The current tournament set up favors pure dumb luck over rewarding good managers. We just had the fourth round in the USA. There's no reason why bot teams should have even been in the tournament by that stage. If you want to make the tournament a lottery, well that's your design choice. It's your game, not mine. I'm just saying, I don't find the current tournament to be a rewarding experience given the complete randomness of pairings and the astronomical number of computer controlled entries.

What I am advocating is a more competitive tournament that rewards the active manager who's put time and effort into improving his team and setting his lineups. The current tournament set up favors pure dumb luck over rewarding good managers. We just had the fourth round in the USA. There's no reason why bot teams should have even been in the tournament by that stage. If you want to make the tournament a lottery, well that's your design choice. It's your game, not mine. I'm just saying, I don't find the current tournament to be a rewarding experience given the complete randomness of pairings and the astronomical number of computer controlled entries.

What you are suggesting would end up pitting #1, vs the lowest team, #2 vs 2nd lowest, etc. In doing that, teams like yours (Level IV, V) would never make it out of the second round of the tournament. If that is the case, it would make just as much sense to limit the National Tournament to the top 3 divisions, because in that type of format, that is pretty much what you are going to end up with anyway.

The Random factor creates an opportunity for lower level teams to also have a chance to make a cup run. This run is a boost to their income, season ticket holders, fan survey, enthusiasm etc. The Cup Tournament can be a boost for lower level teams to use in their effort to advance and promote.

Everyone in the tournament has the exact same odds of drawing a bot, as they do a quality team, or drawing an away game, or home game. This is why last season we had a DV team make a run all the way to the final 64.

Regardless of how you do it, the teams that should be in the tournament at the end, are in the tournament at the end...which in my mind makes for a competitive tournament. I like this system as I am only a D3 team and have had the chance to move on in the tournament even if I may not deserve to...

To say that a fair and balanced approach to pairing is on par with limiting the tournament to the top 3 divisions is disingenuous. You know as well as I do that there are weak DIII teams that belong in DIV and strong DIV teams that could handle their own in DIII. To illustrate my point about the negative effect of randomness in pairings, take the top team in my conference. An 11 point loss to the second place team, on the first week of the season when everyone's GS and enthusiasm was low, is his only blemish. He has beaten everyone since then pretty handily. Yet he drew the #88 team in the second round and was ousted. By contrast, the second to last team in the conference, who he beat by 28, is 3-6 in conference play, and due to the fact he faced 3 straight unranked teams, then a lower ranked team in the fourth round, he's advanced to the fifth round. Does that seem competitive? Are the better teams advancing, making advancing to the next round more of an accomplishment? And I haven't even brought up the ridiculousness of using randomness for who has home court advantage. Using my team as an example, I've been the higher ranked team three times and the lower ranked twice including the upcoming round. I've been on the road the entire time.

If you include the top 4 divisions, then the D4 teams would get eliminated in the first round by the D1 and D2 teams. So do you want to go out in the first round? You might as well just limit it to the top 3 divisions and save everyone the time of the extra round. The fact is that nobody outside of the top 2 divisions have a shot at winning the tournament and it always plays out this way. Every once in a while a team like the Popcorn Fairies in D3 will make the semis, but even that was like three seasons ago.

Sounds like to me you want D4 teams to play the D5 teams and bots, then once you advance far enough you will take your loss to the D3-D1 teams...correct?

Great points!

Also, strategy plays a big part as well. Some teams choose to focus on their cup run, while others focus on league play leaving them more suceptible to losing in the cup. There are plenty of upper division teams with 3-5 records that are 3-5 because they are saving their best players for their cup games.

Like you said, there are many ways to go about things in this game, and the randomness feeds that so we do not have a cookie cutter style appraoch to success making the game boring and uneventful.

If you include the top 4 divisions, then the D4 teams would get eliminated in the first round by the D1 and D2 teams. So do you want to go out in the first round? You might as well just limit it to the top 3 divisions and save everyone the time of the extra round. The fact is that nobody outside of the top 2 divisions have a shot at winning the tournament and it always plays out this way. Every once in a while a team like the Popcorn Fairies in D3 will make the semis, but even that was like three seasons ago.

Sounds like to me you want D4 teams to play the D5 teams and bots, then once you advance far enough you will take your loss to the D3-D1 teams...correct?

Tbh, the $50k per week for advancing doesn't make or break me financially, but then again I've been pretty frugal with my money since day 1. That being said, no, I wouldn't mind getting ousted in the first or second round to a better team, provided it wasn't simply just a bad luck of the draw. In fact, I'd welcome having to actually put some thought into the lineup and tactics than just throw some scrubs in there on TIE because I know I'm still going to steamroll the bot, even if I lost.

If we start complaining about the randomness of the draw, why not also complain about the randomness of the home-away draw in the interconference schedule? And why not also complain about the randomness of injuries? What about divisions that have more bots over divisions that have fewer bots? Or about the fact that events within games are themselves random?

The point is: if everyone were dealt the same hand, the game would be boring and stupid. Randomness is a feature, not a bug.

The design principle then becomes: design a game in which there is enough random events that no single one of them determines the destiny of any one team.

Teams luck out and get easy cup draws, but then maybe catch a 4-week injury on their best player. Or get a hard interconference schedule, but by some stroke of luck manage to sell a player for more than they are worth.

What you're suggesting is an all or nothing approach. I have not asked for such. Home/Away draw for inter-conference play is part of the scheduling. It's a 22 game schedule. Surely you can make up for a bad draw in your other games. The tournament is single elimination. There's no make up games for a bad draw. Injuries are also part of the game. You have other players to make up for the loss of one. And if not, there's always the transfer list. Your examples draw on extremes to try and discredit what I'm talking about, but they're invalid comparisons. I'm talking about a bit of balance in how the National Tournament is drawn. It's a one-shot deal. It shouldn't be so grossly lopsided. Someone had a suggestion in my thread on the Suggestions forum about coding it so it was impossible for Bot vs. Bot match-ups. That sounds like a reasonable compromise.