This app was mentioned in 12 comments, with an average of 5.33 upvotes
Football coach is a super fun little simulation game.
https://play.google.com/store/apps/details?id=achijones.footballcoach
Edit: very actively developed as well. Make some suggestions on /r/footballcoach
I'm so frickin addicted to the College one (which is free, btw). I've purchased the pro version just because I love the free one so much. I've yet to play it because I have so much time into the college one. Right now I'm working on all the records using the Samoan team.
Shoutout to /r/footballcoach where you can report bugs and request new features for both apps.
Obviously much of this doesn't exist this long before the season, but some ideas:
Depth charts instead of just rosters would be good.
Games should have more info. Things like betting odds and some offensive and defensive rankings plus a link to the opponent's main page.
Honestly, check out the football manager app that one of the users here made for some ideas. https://play.google.com/store/apps/details?id=achijones.footballcoach
My wheelhouse!
First, go to zengm.com, they have web-based leagues for most sports. I've played the NHL one (30+ seasons across two franchises), the MLB quick seasons one, and the USFL one. They are a bit simplified, but for the hockey one, I think they strip out some of the needless complexity. Downside is you need a connection to the internet, but it is by far the best game for popping in for 2 minutes and simulating a couple games. No load times.
MMA Manager - I am not an MMA fan really, but I like boxing manager games. Lacking a good one on Android, I tried this. And it's GREAT. Again, not too complex, but it has enough depth that you get your money's worth. Its really fun scheduling fights and moving your guys through the rankings and the various MMA championships as they get better.
Football Coach - College football sim. Skews towards the simple side, but it is very engrossing. Good stat tracking, and records keeping. There is a pro version with downloadable rosters, but I find the college game adds the complexity the game needs. https://play.google.com/store/apps/details?id=achijones.footballcoach
College Hoops Coach - From the same guy above. This game layers in a LOT more in-game and coaching complexity. For that I like it a little less. (That, and I could never win the championship.) But I liked it a ton despite not being a college hoops fan. https://play.google.com/store/apps/details?id=io.coachapps.collegebasketballcoach
Football Mobile 2017 - The most complicated game I've played. But you get a ton of depth. A TON. For soccer fans, nothing is better, and no pay to win. Rosters accurate. Lots of fun scouting and signing young players.
NBA 2k18 - I bought this to play the game manually, primarily. But the "Association" mode is a fully fledged GM mode. You could sim the games to rule out the human element. I haven't checked to see if you can "watch" the game, b/c the game looks SO good, it would be exciting to watch.
MLB Manager 2017 - I've actually played an earlier version of this game, and I recommend this one b/c its cheaper than the 2018 version. I don't think they change much year to year, so that's a knock on the franchise. But the games are pretty good. Scratches the itch for a baseball sim. lots of players and stats and good farm team depth.
NASCAR Manager - Its a FTP game with in-app purchases, but I never had to buy anything to get to the top. I found it a surprisingly large amount of fun. There is a little glitch where you get "nitro" or something like that over time. So you can use a bunch in the 1st part of the race, pause it. Finish the race later and you have fully loaded again. Probably shouldn't be allowed, but I like to think I'm getting rewarded for my patience. :) Sneaky good game. (Supp, Zo?)
Apex Race Manager 2018 - I've played an earlier version and it was fun. You don't need to do the quicktime minigames in-race, but the pitstop one is pretty fun. Game focuses more on in-race aggression sliders, which I find fun. Also, the penalty for not doing well is less severe than in MM1 and MM2. https://play.google.com/store/apps/details?id=com.beermogul.games.formulalegend
Dynasty Manager 2014 - NBA basketball. Free game because the dev has a 2016 version for $2. If baskettball is your think, this is excellent. Played 10+ seasons in this too, so I must have liked it!!
Grand Prix Story by Kairosoft - Arguably their best game. From before they went P2W. The 2nd version has better in-game management elements, but that is just a timer hog.
Women's Soccer Manager - Yeah, just kidding. But I sure do play too many games...
Football coach - https://play.google.com/store/apps/details?id=achijones.footballcoach
Pro football coach - https://play.google.com/store/apps/details?id=com.achijones.profootballcoach
College basketball - https://play.google.com/store/apps/details?id=io.coachapps.collegebasketballcoach
For anyone into college sports simulation games, there is Football Coach and College Hoops Coach. The creator also made Pro Football Coach as well. All are currently free and very addicting if your into sports simulation.