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+---- Thread: *Expansion: Modeling growth rate (/showthread.php?tid=19588)
*Expansion: Modeling growth rate - Troen - 02-29-2020
After reading AdamS' recent article suggesting that the NSFL will have to expand by 4 teams next year due to the size of the S22 class increasing the number of active players, I wanted to think about what number of teams the league should have at steady state of user acquisition.
Consider a player career loop where you spend 7 years in the NSFL, retire for the 8th year because eww losing TPE sucks who would want that, and play the 8th year with a new player in the DSFL while your retired player finishes the last year still in the NSFL. Combining that 8 year long career pattern with the OL-bots approach of a minimum of 18 players per team (QB, 5 RB/WR/TE, 11 defenders, kicker), then each team needs to get 2.25 active players per year to maintain a full starter roster. (Note: This is obviously a vast simplification vs. the actual league since you have positional needs and declines plus might want to plan for future retires in a position and draft someone to play in the DSFL for a year or two but I'm ignoring all that for now). Looking more broadly, with 10 NSFL teams then the steady state expectation would be 22.5 active players per draft year (I'll round up to 27 for convenience in later analysis) and 180 total active players.
Now I strongly presume the real pattern of players doesn't quite match this seeing as people go inactive and maybe eventually come back, you have new players joining, etc., but it's interesting to consider in the steady state. Also, I looked at way too many forum accounts recently and don't want to try to come up with a deeper model of user lifecycles at this point in time. Maybe later though.
So, with the S22 class of over 270 players, what should the expectation be for league size? I'll go through a couple cases.
1. An anamoly - low retention
Scenario: This class was large but it's basically a 1 time thing. The normal 23 players who are recreating with 250 new people of which 10 percent (25 players) remain. League total player size grows to 205 (180 plus the 25 new people) but future class sizes remain at 12.5% of active players, ie there are no more net recruits to the league.
Outcome: Well first of all this will make every 8th year really awkward unless retirements get spaced out a bit, but I'm ignoring that for now. With simple math, 25 new players means about 1.4 more teams should be around to absorb them. It's hard to have 0.4 of a team, but adding 1 is rough for scheduling. Going to 12 teams would result in an average of just over 17 players per team while not expanding would leave the leage at 20.5 players per team. Having 2-3 extra slots which aren't starters could be fine, giving teams a bit more flexibility to play situational offensive or defensive alignments or to take on more developmental players. Player satisfaction might drop a little bith with fewer starting positions.
2. An anamoly - medium retention
Scenario: like scenario 1 above, but 25 percent (63 players) of the new players remain. League total player size grows to 243 (180 + 63) with no more net recruits to the league.
Outcome: 63 new players means about 3.5 more teams should be around to absorb them. Adding 4 new teams would average 17.36 humans per team while 12 teams would average 20.25. With similar math as amove, I think 12 teams would probably make the most sense.
3. An anamoly - high retention
Scenario: like scenario 1 above, but 60 percent (150 players) of the new players remain. League total player size grows to 330 (180 + 150) with no more net recruits to the league.
Outcome: With my simple math 150 new players means about 8 1/3rd more teams should be around to absorb them. Expanding by 8 would leave 18 1/3rd players per team which would be a similar result as the starting point situation I'm basing my assumptions on. In this case, however, one class being almost half the league would cause some real big shakeups for draft if every 8th year is a draft class about 7x the size of others. I think the league would want to encourage more staggered retirement somehow to get that giant spike to smooth out eventually. The risk might be overstated since people probably wouldn't retire in lockstep and instead consider their teams' situation when it comes to players/positions, but it would still cause shocks to the system down the line.
4. Not just an anamoly - low retention, fixed low future recruitment
Scenario: This class was large and it's not just a 1 time thing. The normal 23 players who are recreating with 250 new people of which 10 percent (25 players) remain. League total player size grows to 205 (180 plus the 25 new people). However, future years each attract 25 more new accounts which provide an average of 3 new accounts per year.
Outcome: Initially the same as scenario 1 but 3 new accounts per year means that roughly every 6th year there's cause to add a team. Since you want to add teams in pairs, will probably have cycles of creating 2 teams at a 16.5-17 player/team average, building up until it's at 20-21, and then expanding again.
5. Not just an anamoly - medium retention, fixed medium future recruitment
Scenario: Basically scenario 4 but with 25% retention of the current and future new players leading to ~6 new accounts/year.
Outcome: Basically the same as scenario 4 but on double the pace.
6. Not just an anamoly - high retention, fixed high future recruitment
Scenario: Basically scenario 4 but with 60% retention of the current and future new players leading to 15 new accounts/year.
Outcome: Adding almost a team worth of new players each year would result in rapid expansion, naturally. Probably wuoldn't actually continue at this pace indefinitely but if it did I can only imagine that the league structure would need to change once there were 30+ teams.
7. Friend of a friend - low retention, low percentage future recruitment
Scenario: This class was large and it's enough to cause a complete change in new players joining. 10% of the 250 new players stay around but now each year sees everyone in the league telling their friends how fun it is which causes additional new players. For the low/low case, the new player creation count is equal to 10% of the playerbase with 10% of those new players becoming regular active players. So for S23 the league's 205 players bring 20-21 new players of which 2-3 become regulars, and then S24 the league 207-208 players bring in more, etc. This strictly speaking is exponential growth though it takes until about S34 to get over 230 players.
Outcome: Initially the same as scenario 1 and it will take a very long time to look different at the recruitment/retention rates. But stay tuned to the scenarios 8 and 9!
8. Friend of a friend - medium retention, medium percentage future recruitment
Scenario: Like scenario 7 but with 25% of the 250 new players stay around and year year there's new accounts equal to 25% of current accounts with 25% of the new ones staying around.
Outcome: This case grows way faster, hitting over 300 active users with the S27 class and 500 in S36. S22 remains an outlier with 45 new active users but S23 has 14 new added accounts and the numbers get bigger.
9. Friend of a friend - high retention, high percentage future recruitment
Scenario: Like scenario 7 but with 60% of the 250 new players stay around and year year there's new accounts equal to 60% of current accounts with 25% of the new ones staying around.
Outcome: This goes off the rails really fast, breaking 1k users in S27 and 10k in S34. In the unlikely event the NSFL explodes in popularity like this, I can only think that it would need to fundamentally change way more than just expansion.
These scenarios are obviously not exhaustive - eg what about a low retention rate but high recruitment rate - but I think it does give a couple interesting ways to think about the math of the rate of growth in number of active players and how that can play into expansion needs. There's also ways to have more players without having more teams such as by making bots worse or giving fewer of them to get more people to play OL. Conceptually I think requiring more depth on teams could be interesting too, but it sounds like the sim software has a number of limitations preventing that from being a great alternative. And 'more depth' can mean 'fewer plays per player' which could lead to less interest from non-starters. And that gets to the next point - not expanding can potentially lead to more players doing less which can potentially lead to less retention of users as their players don't get to do cool stuff. Is that better than expansion? I don't know - I've been around here for a whopping 2 weeks so I don't really know what's up with cycles of user activity, especially as different seasonal things like vacations, holidays, or the actual NFL season happen. But I do think measuring the past and predicting the future pattern of user creation and retention should be important aspects of the conversation around expansion.
*Expansion: Modeling growth rate - Raven - 02-29-2020
Quote:retire for the 8th year because eww losing TPE sucks who would want that, and play the 8th year with a new player in the DSFL while your retired player finishes the last year still in the NSFL.
My mans doesnt know about the retire after trade deadline trick for that max TPE gain.
Interesting scenario's. I`d say we are kinda in a mix of 2 and 4.
Where we have these big draft classes every 6 months (3-4 season) when we do our big r/nfl recruiting, but these big classes are only every few season and not every like in scenario 4.
So then we kinda fall back into scenario 2 in which the draft classes between the big recruitments are a bit on the bleak side. We do some recruitment stuff in the meanwhile, targeting team reddits for instance.
With that said I`d say we closest fall on scenario 8. Althought with a bit of a slower grow rate I imagine.
*Expansion: Modeling growth rate - Troen - 02-29-2020
(02-29-2020, 02:12 PM)Raven Wrote:My mans doesnt know about the retire after trade deadline trick for that max TPE gain.I had the impression that if you do that then your retiring player completes the season but then during your DSFL year you won't have your retired player in the NSFL while if you retired during the offseason then you'd be able to have your retired player remain on the NSFL team (with no TPE gains). I didn't re-verify that in rule book, though, because it made my math easier.
So anyway, yeah that part of the model could be way off.
(02-29-2020, 02:12 PM)Raven Wrote:Interesting scenario's. I`d say we are kinda in a mix of 2 and 4.Yeah, I didn't really try to analyze the past. Could be an interesting followup though - measure past retention and net recruiting then try to fit it with these various scenarios to come up with a more predictive model.
Where we have these big draft classes every 6 months (3-4 season) when we do our big r/nfl recruiting, but these big classes are only every few season and not every like in scenario 4.
So then we kinda fall back into scenario 2 in which the draft classes between the big recruitments are a bit on the bleak side. We do some recruitment stuff in the meanwhile, targeting team reddits for instance.
With that said I`d say we closest fall on scenario 8. Althought with a bit of a slower grow rate I imagine.
*Expansion: Modeling growth rate - AdamS - 02-29-2020
Excellent work here. Puts a really definitive number on certain things and I accept you as my son.
*Expansion: Modeling growth rate - Raven - 02-29-2020
(03-01-2020, 12:24 AM)Troen Wrote:I had the impression that if you do that then your retiring player completes the season but then during your DSFL year you won't have your retired player in the NSFL while if you retired during the offseason then you'd be able to have your retired player remain on the NSFL team (with no TPE gains). I didn't re-verify that in rule book, though, because it made my math easier.
So anyway, yeah that part of the model could be way off.
You are absolutely right. Retiring at the trade deadline and not after ultimus does indeed leave you without a player in the NSFL. So in an ideal situation everyone is nice and only retires after the ulitmus leaving their player to play for another season.
*Expansion: Modeling growth rate - Troen - 02-29-2020
(02-29-2020, 02:28 PM)AdamS Wrote:Excellent work here. Puts a really definitive number on certain thingsThanks!
(02-29-2020, 02:28 PM)AdamS Wrote:and I accept you as my son.Oh so in that case, I have this submerged collection of wood in the shape of a goat that used to be a sea-going vessel. Any thoughts on how I could get it seaworthy again? I tried ping pong balls but it's still sunk.
(AKA can you help me float my goat boat?)