Battlegrounds in general gets a lot of heat. It is arguably the best game mode added to the game ever. It is strategic. You get to use more of your champs than anywhere else. Rewards are great. I definitely has deep trouble though. Bug and Modders are unacceptable. Participation seems to be plummeting and metas don't always feel interesting. However, I want to focus on Matchmaking and why it is not easy.
Before discussing what an ideal matchmaking system looks like, we need to consider what goals a good system needs to reach in order to be successful.
A good competitive game mode should -
1) Maximize participation
2) Feel Fair
3) Be free of manipulation
Why bother have matchmaking?It is a common argument that within any tier, it should be a free for all. All Silver 2 should be fair game to other Silver 2. The reason this is not great is because to skews very heavily in favor of the biggest accounts. Why is that bad? Because players hate feeling like losers. If a player loses 4 out of 5 matches in a mode, they are likely to give it up. If the bottom 20% of players drop out of the mode, then the new bottom 20% have their win rates drop. If they drop too low, they will quit too. This will continue in a cascade until it becomes clear that you shouldn't start playing until you are Paragon with a large account.
There has to be a way to protect the weakest players from the strongest ones or else it is only fun for the top 10%. Uncollected, Cavalier and Thronebraker players should all be able to get started and not worry about being crushed by decks beyond their comprehension.This can go to far though. Should smaller players get into Gladiators Circuit much more easily because they were the best in their league? There are a lot of valuable 5 star relic fragment to acquire there that are normally reserved for bigger accounts.
A basic problem is that the "best" matchmaking system is one that benefits yourself the most. There are many parties present that need to be considered.
Current Victory Track MatchmakingThe exact method is not revealed to us players (probably in fear that we will try beat the system somehow). I've recorded my opponents for the last 3 seasons and have noticed a pattern emerge. The system seems to be Prestige based with a dynamic range. In early tiers like Bronze and Silver, the matches are closer to you, then as you progress the range gets wider. The distribution appear as a Bell Curve within +/- 20% of your prestige with the vast majority between +/-10%. The April-May season seems to have a new quirk where around Platinum, the Bell gets wider and both higher and lower opponent appear. I had an opponent 4762 prestige points higher (33.5%) and an opponent 3946 point lower (27.7%).
A weird byproduct, Platinum and Diamond were much easier to advance through than normal because there were so many Thronebreakers to fight instead of the swarm of Paragons I got in lower tiers.
So with a Prestige based system
Pros-
1) Simple. The number is on your profile, its used in other game modes and it broadly reflects progression.
2) Virtually impossible to manipulate. You can't lower your prestige so you can't force easy fights.
Cons-
1) Prestige does equate to strength. Some high prestige champs are not very useful. Sig level has a disproportionately large impact too
2) Prestige is only your top 5 champs. This means that player with top heavy accounts will be treated the same as accounts with wide and highly leveled.
3) Traffic Jam - Matching similar opponents suppresses your win rate artificially. So early in Victory Track you face off against many similar opponents. If you win rate is around 50%, each tier of the 3 Medal tiers should take on average 9 matches to progress. In some cases you may find yourself effectively "stuck" in a low tier. I personally faught 30 matches in Silver 3 and another 30 in Gold 30. It was just a huge mass of Paragon players (like me) everywhere. The frustration of being stuck in the low tiers is not a good feeling.
Neutral-
1) Smaller accounts may find themselves getting into Gladiator's Circuit at first but then use the rewards to progress their accounts and be left wondering how they are doing worse the next season.
What about matching based off of Deck Strength? In the early versions, this was the system.
Pros-
1) Simple enough
2) Much better than Prestige at evaluating strength.
3) Doesn't "punish" player for having high prestige champs and not using them (Like Silver Surfer)
Cons-
1) Manipulation - Sandbagging. It can backfire, but generally it doesn't If you make 20% of your deck trash, it would have been possible to avoid matching with opponents like yourself. Creates greif for smaller players.
2) Pseudo-Sandbagging. Hypothetically a top tier Paragon player could make a deck full of only Rank 5 5 Stars. And get matched with mostly Cavalier and Thronbreaker Players with similar decks. On the surface, it might sound fair, the smaller accounts might even have some Rank 3s and look stronger. However a Paragon player has much better access to more champs and can rank them up faster. They could create a deck of the strongest meta-relevent champs and decimate the newer players.
What about a moving rating similar to War Rating or AQ Prestige?
Pros-
1) Separates opponents with similar decks but different skill levels
Cons-
1) Match Manipulation - Tanking. You could hypothetically lose 5 matches in a row to guarantee progression. Also allows statigic use of Elders marks to boost points. Sure the players you forfeit against get easy rides but it is in poor spirit.
2) Somewhat punished talent
Neutral -
1) Would effectively normalize win rates to about 50% for most players
So pretty much every option is full of cons. There are hybrid ideas too but they all run into similar problems. Currently, I feel like the biggest non-bug problem is the Silver-Gold Traffic Jam. It turns Victory Track into an absolute nightmare for so many.The new changes coming to the Medal system are actually MASSIVE! It may well fix the whole mess.
Before explaining the fix I need to explain the mathematical model for Season 7 and prior.

The above model is for 3 Medal tiers (most of Victory Track). In this simplified example 50% win rate was used. So there is a 1/8 (12.5%) chance of winning the first three matches and progressing. The idea is tracking all possible outcomes and calculating the probability of each. To progress in exactly 5 matches there are only 3 paths (00111, 10111, 11011). The probability of those combined are 3/32 (9.375%). The probability of taking 3, 4 and 5 matches to progress add up to 28.1% and thus suggest that 28.1% of players with 50% win rates will progress in no more than 5 matches.
The 50% would be the average. This method is how I came to the conclusion that the average would be 9 in the earlier part.

The Above graph shows the model applied to 2,3,4, and 5 Medal tiers (Gold, Blue, Orange, and Grey respectively) with 50% win rates.It highlights how much more difficult it is to progress needing 5 than 3 (On average 22 Matches with 50% win rate).
Applying the 50% to the current Victory Track, the "average" player with a 50% win rate, should expect to take about 144 matches to reach Gladiators Circuit. Win Rates are not static of course so it is purely theoretical.

This graph shows the 3 Medal tiers with different win rates. It shows that you can progress with a. sub-50% win rate as it gets lower in becomes significantly more painful.
Now with the New system that allows 2 Medals on vicotry and only -1 for a loss, the model looks like this for 5 Medal tiers (Gold and Platinum) -

Then comparing lower ones-

50% Win Rate gets through silver tiers on average in 3 matches each. Hypothetically, a person with a win rate of 50% can now get to Diamond 3 in 47 matches on average. From my spreadsheet, a person with a 30% win rate will get to Diamond 3 in 97 Matches. That's actually amazing. It means that persistence will get you far even if matches aren't great. My win rate at the end of Season 6 was 37% and it took 194 matches to get there. Season 7 was a 54% rate and it took 122. This is a major acceleration incoming.
The only thing to remember is that the end of Victory Track is unchanged. I suspect Diamond will become the new traffic Jam area. That is much better than the ones in Silver and Gold though.
All in all, this is an incredible change that I'm really excited to try out.