the question posed here - does ath have diminishing returns - does have a short answer - 'sometimes it does, sometimes it doesn't'. however, this doesn't really provide insight or an opportunity for understanding. this is a complicated topic, and i do think i have a pretty good answer at the end - but as is standard with complicated topics - the biggest battle is trying to understand what the right question is. we have a long road to hoe on that front before we can circle around to an answer, so bear with me - or not - either way :) i had a lot shorter answer about 2/3rds typed, but im sort of convinced it wouldn't have made a lot of sense, so i decided to go with a really long answer that makes half as much sense.
before i jump in, i will say - if there is any magic in this game, metaphorically, other than the context in which it exists (a sports context which provides a lot of the intangible appeal this game has) - it is directly tied in to this answer. this diminishing returns question is significantly related to the question 'why does this relatively simple simulation hold such durable intrigue for the folks who it ensnares?' - why haven't a few folks come along with their statistical analysis, broken this game wide open, and ruined the mystery? this monologue will likely answer that question in a more satisfactory way than the original question, without even really trying to - i'll just point out the magic bit as we pass it by.
i want to make a key distinction right up front. i talk about diminishing returns all the time, but for the most part, i'm talking about team building. while similar in many conceptual ways, from a mechanical standpoint, there is a great difference in how you evaluate what makes teams good, and what makes players good. while teams are more complex on one hand, as a complex aggregate of players, for whatever reason, the diminishing returns concepts are just way more straight forward and understandable from a team standpoint - at least with the way i frame things. i actually think the framing has a lot to do with it, because in truth, you can't evaluate a player without knowing how to evaluate a team, and you can't evaluate a team without knowing how to evaluate a player.
let's talk about evaluating teams for a second, because that is, at least in the way i can frame it, more straight forward with respect to diminishing returns. one of the keys to understanding the quality of a team, is understanding the quality of the offense. the way i simplify the team planning question is to ignore the question, 'what makes a player good', and to replace that with a cardboard cut out of a player of specific goodness, if you will. this is half of why i talk about abilities, not ratings. so let's ask, if you are looking at building an offense in the form of a lineup of 5 players, what makes that offense good? a key part of this is each player's offensive ability - but at this point, we'll ignore what makes a player good at offense, and instead just talk about how good they are. to keep things simple-ish, let's also ignore the distinction between 2 and 3 point scoring.
so, if i'm looking at building an offense, there's a lot of options. i could have 5 terrible players (offensively). i could have 5 elite players. obviously, the former is going to give me a crap offense, and the latter is going to give me an awesome one. however, with finite resources, we face a massively complex optimization problem (this is where the magic is, but more on that later), where most likely, i am shooting for something in the middle of those two extremes. if we get 5 elite offensive players, sure, our offense will be great - but what about everything else? we are probably going to be pretty crappy at the rest of the things we need, like defense and rebounding. somehow, we have to find a balance!
this leads us to questions like, should i get 5 good offensive players? are 5 good offensive players more effective than 2 elite offensive players and 2 terrible ones? concretely, the real question here is - given an amount of talent i can hope to fill my team with - what is the optimal amount of that talent i would dedicate to offense, and how would i dole that offensive talent out among the 5 players? reality is going to be messier of course, you can't just draw up arbitrary players - recruit gen happens, you have competition, sometimes you have more talent and sometimes less, all of those things. but even without all that mess, just the clean optimization problem is hard enough. how hard? (ill shut about the magic for a while after this) - its a problem that today's humans cannot solve, except for trivial cases. the most powerful computer in the world is barely better at solving these kinds of optimization problems than the original iphone, and even all the computers in the world put together can only solve extremely simple cases. most computer scientists believe that optimization problems of this nature cannot be solved by classical computers - but its unknown - and answering that question is by far the single greatest unanswered question in the entire field of computer science. everybody in computer science knows it, its also a millenial problem, the p=np problem (some folks are familiar with np complete or np hard - this is roughly the same thing). i know i'm off in left field here, but i also think its really a cool feature of this game (i don't really think it was intentional but really a necessary by product), so i'm going to talk about something simpler so folks perhaps understand what i find so cool about this aspect of HD.
in HD, if you have an optimal team setup given the players, then you'd be in good shape, right? i mean this is sort of the ultimate goal. now, make any player slightly better (or worse). what is the new optimal team setup? even knowing the old one, this is impossibly hard. maybe the guy who is a bit better needs a bit more distro and a different guy who takes similar shots needs to take fewer. maybe the guy who is a bit better now should start instead of play backup. this is very similar to a very simple problem anyone can understand (the elegance of mathematics is that simplest among us can pose and understand questions that the most advanced cannot solve).
think about a UPS truck getting packed with boxes. there are a crap ton of boxes, and you want to fill the truck up as much as possible before sending the truck out and bringing up the next one. once you get to a few hundred boxes and let's say, space for about half that many, all the classical computers in the world combined (every computer you've ever used is a classical computers - but quantum computers, which i don't think really exist yet, but i don't understand all that, would not count) would have no hope of solving the problem before the end of the universe brings about the destruction of all matter as we know it, some countless quintillion years from now. that is, unless a computer scientist solves that greatest unanswered question in all of computer science, and the answer is what nobody expects - in that case, your iphone could solve the problem in about a second. just on a side note - a truck is 3 dimensional. HD has a ton of aspects, you are optimizing on all kinds of dimensions. if you had a 1 dimensional truck, basically a fixed width and you filled it with little sticks in a straight line, its a trivial problem - a good freshman in college can code up a program to solve any arbitrary instance of that problem in about 15 minutes. but once you go to 2 dimensions? humans lack the power to solve all but the most trivial of cases. you don't even need a 3 dimensional truck. i've never tried to formally prove to myself that the HD team optimization problem is at least as complicated as the 2 dimensional box filling problem - but it sure as hell feels like it. i mean like seriously... is the optimization problem of HD, with depth charts, distro, practice plans, and everything else - is that really simpler than filling a square of paper with smaller squares of papers, trying to fit as many small squares on the big one as possible? (a sheet of paper is basically the 2 dimensional truck - the small squares the 2 dimensional packages). there's no way.
so long story short, even with the source code to HD itself, humanity lacks the math to explain how to best build a team - we can come up with heuristics, maybe we can get answers that are close - but the fully correct answer is beyond the grasp of our time. even with the source code!
alright, so moving back to the land of the living... the best anyone can do is come up with a heuristic to try to come close to the solution, and this usually involves some simplification. obviously, i am bound by this same limitation. here's how i tackled it. i came up with an amount of talent i felt was achievable, not necessarily the most talent possible but roughly about the best you could do on a consistent basis if you were a top recruiter in this game - and then tried to think how i'd arrange that talent in a way that is close to optimal. here's my take.
its not really important what these categories mean precisely, but let's suppose you are only concerned with winning championships, so high caliber talent is available to you, and you can classify players talent's into buckets - elite, very good, good, and decent (for simplicity, i generally assume high end title teams are not running around with players who are straight garbage at really important stuff). i also categorized all of the things players do into 4 abilities, offense (really i mean scoring), defense, rebounding, and 'guard skills' (the things guards do that are important outside of scoring, defense, rebounding - so mostly dribbling and passing). that's basically the entire model i used to figure stuff out, and which i still use today by and large, although 3pt vs 2pt scoring is very important.
from observing recruit generation and players on teams, in my model, i felt like you could fairly reliably get two kinds of players - well rounded guys, good to very good at all 3-4 abilities (guards/bigs have 3 core abilities - excluding reb for guards and guard skills for bigs - but including all 4 for sfs). you could also get guys with 2 clear strengths, high end very good to elite level, with the 3rd core abilities being roughly decent, not like massive liabilities and stuff.
i get im moving really slow so skipping ahead a bit - i basically concluded really early on, the well rounded guys were worse than the specialized ones - because it feels like high end teams get enough talent that they can sort of have all the folks who are doing important stuff, being really good at that important stuff, so at that point what good does it do to have well rounded guys? if you needed 5 scorers, 5 rebounders, 5 defenders, 5 guard skills strengths - well rounded would be the way to go. but you don't. so if you have 5 guys with 2 clear strengths readily available, that is 10 for a lineup, and really good teams will usually have a truly elite player or two who manages 3 clear strengths - so roughly 10 to 12 clear strengths. 10 is plenty to be about the #1 team in the country, 12 is plenty to be favored over the entire NT field.
alright, so if you get 10 clear strengths - how would you arrange it? ill include this rambling sentence to give anyone who cares to a chance to answer the question. i would roughly go with something like 2 scorers, 2 rebounders, 2 guard skills, and 4 defenders. why? well, diminishing returns of course. consider rebounding, if i've got a mediocre team, and i add 1 elite rebounder - it is a massive advantage for me. i put him at center (only consider 5 man teams, this game runs on 5 man teams - you can build understanding of full teams from the 5 man cases, but the sim engine thinking should all be about 5 players because that's what the sim engine uses), and he really helps my team a lot. give me a 2nd guy. i put him at pf, and now i'm pretty happy - i've got two elite rebounders at the 4-5. i can run three 1 reb guards from the 1-3 and still compete with the best teams in the country, at least in d2/d3, and in d1 ill be behind, sure - but not massively so. by now, i've gotten most of the value i can get from rebounding - adding an elite reb sf would be nice, but by then, its really not helping me much to add subsequent elite rebounders. its not nothing, but the 5th rebounder is giving me way less value than the 1st and 2nd - at least several times less.
offense is similar - give me 2 elite scorers to carry about 70-75% of the scoring for that lineup, considering another 10% or so comes from stuff like put-backs and tip-ins which you do not get distro control over, and which run on ratings in a much different way than regular shots - in a way where ratings are not very important to the outcome. those first 2 elite scorers give me so much value, and really, once i have 3, its done. i already have the maximum amount of elite scoring. 3 elite scorers are vastly better than 5 very good ones, because i'm roughly upgrading 100% of my non-putback shots from very good to elite talent. that 3rd elite scorer is nice, but with finite talent (10 elite slots), 2 should suffice to build a very good team. same with guard skills - if you've got a smoking pg and a really strong player at sg or sf, you are set. perhaps 1.5 or 1.75 guard skills strengths with 2.25 or 2.5 offensive strengths is in order, but like, im trying to keep it simple here.
then you have defense. defense is unlike the other 3, and this is the rational basis behind applying the 'defense wins championships' mantra to HD. defense, the first elite player, he helps - but hes roughly doing 20% of the defensive work. through m2m game planning, or even zone game planning with a SF (switching 2-3 and 3-2), perhaps you find a way to get that defender doing low-mid 20% of the work - but its still pretty close to 20. fast forward to 4 elite defenders - you still have a mediocre guy out there, defending about 20% of the shots. you can try to hide him, depending on your scheme, or perhaps its press and you got your defense in your guards which matter more because of the pressing / turnover part. so maybe this last guy isn't really 20%, but if you focus on normal cases, not edge cases, its still close to 20%. the last guy is nearly as valuable as the first guy - dead opposite of offense, where even if you see value in 4 scorers, the 5th elite one is so close to useless we can safely call it such. so defense is the area in which diminishing returns most weakly apply. there are there a bit - through good coaching - but its very minor. offense is the opposite - if you went from 0 elite abilities on your team to 1, there's no question - you take a scorer. its not even close. he can do a third of your total scoring, that is a massive contribution.
anyway, thats about it. you sort of have the constraint of 2 strengths per player, so its worthwhile to consider actual scenarios - i consider the base scenario to be roughly this:
pg - def/gs
sg - off/gs
sf - off/def
pf - reb/def
c - reb/def
now, this isn't really exactly what a great team looks like, but its not really that far off either. its always good to kind of sanity check what the model proposes. also, consider adding those next 2 elite strengths. i'd take a 5th defender and a 3rd scorer. in reality, i'm pretty darn happy (favored over the field) with 2 elite scorers and a very good. by 12 elite strengths, if you arrange it well and coach well, you roughly have a team on par with the greatest ever assembled. easy enough right?
so in summary - on a *team level*, things are pretty straight forward, diminishing returns wise. defense doesn't have much in the way of diminishing returns. consider what the 'curve' for defense looks like - the value of defense as you add more and more talent. its roughly a straight horizontal line - or perhaps a straight line gently sloping downward.
offense, rebounding, and guard skills all have diminishing value for subsequent talent, not necessarily right from the first guy - but it drops off after 2 and way off for the last 2 guys. think about what those curves look like. you can think of a line sloping down and to the right, like a roof, or the side of a triangle. this is a simplification - better yet, you can think of a curve, perhaps its almost flat for the first two guys, then drops a good bit for the 3rd, then a good bit for the 4th to a very low level, and then pretty flat to the 5th. you can sort of practice drawing this with your finger in the air, or a pen and paper, to kind of see the curve in your mind better.
clearly, the two curves just mentioned are not the same. a steady down sloping line - a straight line - is pretty different from the curve where the 2nd guy is pretty flat to the 1st, and the 5th to the 4th. specifically, the way the 2nd and 4th guys are valued is meaningfully different. IMO, the curve, not the line, is a far better representation. it is important this makes sense before moving on - for player evaluation, straight lines are far more inappropriate, and curves (luckily, of similar complexity to what i just described) are in order.
alright, so that is roughly diminishing returns in the team planning sense. i hope you guys see that even in this more straight forward case - diminishing returns isn't really that precise. does diminishing returns mean a straight line, down and to the right? is it a curve as described above? is it something else entirely? also, where on the graph does the curve fall - is that 5th guy worth 0% of the whole - is it 5%? 10%? in offense, its damn near 0. in rebounding, its not - its in the mid to high single digits, adding guard rebounding to a great reb line from the 1-3 is a lot more valuable than adding a 4th and 5th elite scorer to a squad that already has 3. this also corresponds to the first great rebounder contributing less, as a % of great rebounding, than the first great scorer does, as discussed earlier (the most valuable guy is that first scorer).
now, last point i need to make about team planning before stepping into the less straight forward player evaluation (which will however be shorter). a lot of this is about perspective, about the specific situation someone is in. someone who is trying to make it in low d1 is going to have some similar conclusions, but also some different ones. that first elite scorer is still the most valuable guy - but you are going to have way less talent, and as a result, low d1 teams should take a 1 strength elite offense player if that is what it takes to get the offense. also, instead of good to very good talent being nearly useless, because you can just have elite guys do all the work - those levels of talent are quite useful. perhaps you can only really aspire to having 'very good' players in most areas (this is definitely not a universal truth, even with d prestige, some elite abilities can be had), and so you sort of take a similar approach with 'very good' in place of elite. or perhaps you recognize that you'll be taking some 1 strength players, and something has to give - so you emphasize defense significantly less - because you are really trying to get the high value stuff first, which is your first couple scoring, rebounding, and guard skills players.
you'll also have major deviations based on the off/def and system being played by each coach. some folks value stamina tremendously and need to tolerate a significantly lower talent level outside stamina - others go for walkons and a slowdown zone or man and are really trying to concentrate talent as much as possible, so they plan around a higher level of talent but in a scheme with a lower ceiling. the conclusions are obviously going to vary significantly from case to case, but with the understanding that the type of thinking i outlined above, using the ability model and considering tradeoffs in the manner we went through, would i rather have this talent here or that talent there (from a given starting point) - it can be used to come up with a reasonable, balanced approach for any team planning situation. so, the method is similar - but the answers can differ significantly.
alright, i think its finally time to get back to the actual question! so, what is that question? it isn't, 'does ath have diminishing returns'. or do ratings in general have diminishing returns. a better question is 'does, and if so, when does ath experience increasing and diminishing returns'? or similarly, 'what is the shape of the curve of the value of ath as ath increases (as you have more ath, how valuable is each marginal point of ath)'. a better question is 'what is the nature of increasing and diminishing returns for ratings in HD, given the diversity of scenarios - also, is there a unifying theme or model we can use to explore and attempt to understand this nature for a variety of ratings and scenarios, and if so, what is it?'
quick digression - the ticket - the question there is probably best summed as 'when ratings are plugged into the formulas used by the game for things like rebounding and turnovers, is there any direct transformation applied to those ratings that causes the raw input into the formulas to adhere to diminishing returns'? and seble's answer, appropriately, was no (the answer is definitely no). however, this digs about 1 inch deep into a 100 ft mud pit.
alright, so lets go through a similar process as the team building part - its very analogous. we want to consider - as ratings increase - what kind of impact does that rating increase have on the value of that player's ability? the ultimate question, if you will, is what impact does that rating increase have on the quality of the team? truly, that is what matters - but that is so much more complex, we at least have to use the player ability impact as a stepping stone along the way - and for the most part, it is safe to split that question into two parts. hopefully its evident by now how essential finding ways to massively simplify these problems is, while still considering simplified problems that fairly closely align with reality. this is why i will often talk about ratings that 'don't matter' and the like - there is truly very little that doesn't matter - and there are some core concepts we could use, like the overall offensive caliber of a player, that actually take into account just about every single rating of that player (including defense) and at least 50 attributes from the team as a whole. because of this, i like to focus on the top couple/few/whatever things, that tell most of the story. there's just no other way for our mortal brains to approach such complexity.
anyway, for starters, let's just try to walk through a *really* simplified example of how the player rating increase might work, in a manner consistent with the general functioning of the sim engine. let's consider a guard shooting and another guard defending him. in the real game, there are tons of factors, like fatigue, the other offensive and defensive players - but none of that is important right now. let's assume guard scoring uses a very simple linear formula, 1*per + 0.5 * bh, and the defensive side does as well, 1 * ath + 1 * def.
now, let's think through how this might play out in a ridiculously simple sim engine. let's suppose we've got a 70 per/bh shooter, and a 60 ath/def defender. the offensive score is 70 + 35 = 105, and the defensive score is 60 + 60 = 120. now what? the engine needs to compare these scores somehow, and get to a % odds of the shot going in, and then the shot happens via RNG (let's assume this is all that happens in an offensive possession - no TOs, fouls, all that jazz - no fatigue or iq either).
if you are thinking - well **** - even the simplest ability formulas ever, a simple linear formula that strips away 90% of what actually happens - it gets complex real fast. how do you compare 105 to 120? lets say this is a jump shot, and an expertly guarded jump shot goes in 20% of the time, while a wide open one, like almost a shooting contest situation, is 70%. this leaves a 50% spread. what does the sim engine do? it *has* to have a curve for this - i don't mean the game creator is drawing one - but there has to be one implied by the formulas and the logic.
this could look several different ways. let's think of a few examples to kind of get our heads around the challenge. suppose we have a 1 per/bh player, and a 100 ath/def player. their scores are 1.5 and 200. let's just call it 0 and 200 to keep numbers simpler. this is going to be the most extreme case, right? the 20% shot case. conversely, if you have a 100 per/bh player, and a 1 ath/def player, its 150 points to 2, or let's call it 150 to 0, and the 70% shot case.
so those two simplest of cases are simple. but then what? how do you figure the rest of this? you could do the simplest thing and say well, theres a 50% spread - and on one extreme, the off guy was +150 points, and on the other, the def guy was +200 points. give each guy half the range - 25% - and then give points for each - so thats like, 6 points of offense for every 1% of shooting, and 8 points of defense. so then for a guy with 50 spd/bh against a guy with 50 ath/def is a 75 score vs 100. this is the dead middle case - 45% chance of scoring (the math would look like, pick either of the extreme cases and just modify from there - so like, if we pick the 20% case with the worst shooter and best defender ever, this offensive guy is 75 points higher, so thats an extra 12.5% on the base case, and the defensive guy is 100 points lower which is also 12.5% on the base case - so 20 + 12.5 + 12.5 = 45%).
alright, so now we have a system! we can compute, for any 2 arbitrary players, the odds of each shot. and also, under this extremely rudimentary scheme - with a purely linear ability formula - and a purely linear comparison curve - we actually have no increasing or diminishing returns anyway.
but we have to consider - is this simple curve at all doing what we want? lets think about that 100 ath/def guy for a sec. when hes facing the 1 per/bh guy, some pf who a confused coach is running at the 2 for some strange reason... and hes taking 3s, lol. ok, so this guy gets wrecked right? hes worst case so hes 20% shooting - we are all good with that (now maybe 20% isnt a good floor but conceptually, it feels sort of reasonable, a guy who actually plays college ball cant be *that* bad - but he'll still get crushed by the best d1 defender in the country). facing an ultra elite 100 per/bh guy, step curry from the nba comes down, we are calling that the median 45%. now lets think of a 50 per/bh guy, half way between. what do we all want to happen there? i mean, the guy needs to get smoked, right? he shouldn't be half way between (like he is, with our simple curve). this is like comparing the best d1 player in HD to some freshman d3 guy. he's got to get smoked, he can't be up there at 32.5% already - if so, then when you compare say, a 60 per/bh guy to a 75 ath/def guy, its not much of a difference - and none of us are ok with that, either (neither are the game creators or real life).
in this last case, we know a 60/60 scorer vs 60/60 defender is 45%. what does the boost to 75/75 defender cost? this is a very significant difference in HD terms, so hopefully, a lot - right? the defensive score goes from 120 to 150 - 8 points per % - so this is an additional, uh, 3.67% or so of defense. so 41.33% scoring, if my math is right. this really isn't that big of a shift, i mean it sounds low if you think HD numbers where 50% is average FG or so (i should have done my example from 25% to 75% to feel more natural, my bad). but if you consider like, a guy dropping from 50% against a 60/60 defender to 46.33% on a 75/75 defender, none of us really feel this is appropriate.
so what do we do? we draw the same freaking curve as the team planning stuff, except upside down. instead of starting high on the left, slowly dropping, then speeding up, then slowing down again - we start low on the left, slowly raising, then speeding up, then slowing down again. basically, we want to say ok, so you went up from 1/1 to 50/50 against that 100/100 defender - you don't get 50% of the fg boost - maybe you get 20%. this way a 20% advantage in score might represent 40% of the fg boost, so that differences between guys like 60/60 vs 75/75 is meaningful.
ok, so apparently i lied about the player part being shorter - my bad. this is really the essence of the game we play though, i'm struggling to cut corners. anyway, the second you do this - the second the curve is *anything* but a straight line - as soon as you add *any* texture to put faster rate of change in one area of the curve and slower in another - you have both increasing and diminishing returns. but also, whether they are increasing or diminishing isn't really important as the question, in my range of reasonable players, where do i get the most value for my points? if you are increasing say to 80 ath/def and decreasing to 100, then the biggest bang for your buck is around that 80 mark - perhaps 75-85, or 70-90, depending on how you look at it. the curve could also be inverted - medium differences in player talent could result in very small advantages - but we'd all despise the game if this were so. luckily, its not. the curve i made up a paragraph ago, to amplify differences in the middle, and minimize ones in the ridiculous extremes - that is basically how the curves for most ratings in most situations in this game work.
just like the different in the off and reb curve for team planning - where they have similar shape but the off curve is more severe, with more value on the 1st guy and less on the last - the curves for player evaluation differ. but the vast majority have the same shape, at least. using this shape to guide your thinking generally, in my experience, leads to some pretty solid conclusions.
now, to get specifically back to the question - when is it increasing, when is it decreasing... where's the bang for my buck? hopefully you can see that immediately, most stuff, it relies on your opponents and their caliber. you cant answer the question for a scorer without knowing what defense hes facing. if hes facing 50/50 caliber defense, then returns from 1 on up start slow and increase, up to the 50 mark, then decrease back down to nothing by the time it gets to 100. more importantly, the highest value returns per point are in the 40 to 60 range.
i hope folks are able to follow that at this point, we started with the simplest ever step 1 - the ability formulas - and soon as we did anything but the simplest ever (and clearly totally illegitimate) in step 2 - the comparison between ability scores - the whole answer about the value of the ratings got complicated. however, we are not done. the real goal is step 3 - what is the value to my *team*. let's continue with the previous example.
suppose you are facing 100/100 defenders. now, that growth from 1/1 per/bh to 50/50 per/bh doesn't give you 75 points anymore, or 11% ish more (so 31% total) - now, let's suppose its half that, so you are like 25.5%. are you going to use this guy? does it matter that he went from 20% to 25.5% shooting? if you are literally the worst team to exist, like that dude who has 12 walkons somehow, then i guess it matters some. but for just about any real coach, the answer is a universal no. so now, we have another curve imposed on top of the old one - the math for this gets hopelessly complex, even in really simple cases, so i won't even try. but just think about it for a second. until you get up to a shooting % where you are able to replace another team mate's scoring with this other guy, its really, really close to useless. once you hit that mark, its like, take off! the value starts racking up, quick.
let's suppose you are facing a more reasonable 60/60 type defense, so solid d3 play or so. lets suppose you are a really good team, your offense is about 70/70. now, for this team, if you consider a guy with 1/1 and how he increases - even though by 60/60, hes up to average performance, 45% fg, which is a huge gain from 20% - hes still useless to the team. so literally, half of the entire range right here - we just threw it out - half of the range of ability performance, its just 100% **** worthless. now, as the guy gets up to 60/60 he presumably starts replacing some of your worst guys, who do a bit of scoring. lets ignore flexibility and only look at replacement advantage to keep it simple. anyway, it really starts to matter as he gets to 70/70 and starts going up, as he starts replacing a bunch of offense, with significantly better offense. in replacement, the value you get is basically your amount of scoring times the amount of % increase for that scoring. so from 70/70 to let's say 85/85, hes racking up advantage in massive terms - hes increasing his share of scoring, and hes increasing his %, both at rapid paces. but eventually, around 80/80 or so, he maxes his scoring - and because we are in diminishing returns in step 2 (the ability score comparison curve) after the 70/70 point (because that is what the defender is), once we are no longer taking more shots, and we start getting less increase in fg% - our value is going to start dropping fairly quickly. from 80/80 to perhaps 85/85, things start to drop - but they were so high, the returns are still pretty darn good. then from say 85/85 to 100/100, he is racking up much less advantage, in raw fg% terms, because we are deep in the diminishing returns - and more importantly, the severely low returns part of our curve in step 2.
so, let's consider what this curve looks like - its the ratings themselves across the X axis, as usual - but the y axis is the value we get for each point - which is really what we want to know. this curve would start on the bottom left corner, like the curve in the last step. however, it is exceedingly close to 0, and it stays there all the way over to 60/60 - you basically have most of your curve as this big flat line, right next to 0, all the way from 1 per/bh to 60/60. then it picks up pretty majorly, slowing down as it approaches 80/80. then it starts dropping pretty meaningfully down to 85/85, and then slowly the rest of the way to 100/100. the 85/85 to 100/100 is still meaningful, as we are talking about a 20ppg scorer or so, with small fg% increases - even though its small fg% increases, its applied to a lot of scoring - so the curve in those 90s is no where near as low as it was in the 0-50 range.
alright, so if you are kind of picturing this - the *vast* majority of the returns are coming in from roughly that 65/65 to 85/85 range. perhaps, as much as 75% or so of all returns. its very possible the value of 1 point of per/bh at 75/75 is worth 50x 1 point of per/bh at 40/40 and 500x at 1/1. maybe its 3-4x compared to 99/99.
so by the time we get here, diminishing returns are not really the name of the game - its really about the value proposition. and what we can see is basically, around whatever level the opponent is playing us at - along with the level we are playing at, for replacement cost comparisons - we get the bulk of the value from rating increases. whether they are on offense, defense, rebounding, whatever - we get some really sick returns on our investment, even though something like offense is *way* more concentrated around this point than something like rebounding. example: if the opponent is around 70/70/70 ath/spd/def, and our team is of similar caliber, we get most of our spd/per/bh value going from 65/65/65 to 85/85/85 or so. but far away from that point - and especially on the lower end, the return on our extra points are really low. ridiculously low, on the low end of the rating (0-50 or whatever it may be), because we simply will not allow the player to fill that role, when he is that bad. also, ratings cannot be considered alone - you have to consider the core ratings that make up each ability together, both from your standpoint and the opponent standpoint.
this is why it is *so* hard to put together a simple formula (1 pt for ath, 0.8 for speed, so forth) to evaluate a player. hell, its basically impossible just to evaluate 1 aspect of 1 player. if you know the opponent's level, which you can approximate by your level, you can put something together - but the formula is not simple. it needs to know those first 50 points of per are worth jack **** and then it gets insanely valuable (at whatever point) and then drops off at the end (usually - for really high d1, it doesn't drop off that much at the end because you'll face elite 95/95 caliber guys reasonably frequently).
i kind of hope this all makes sense and illuminates some of the mystery behind the value of ratings in evaluating players, and of player abilities in evaluating teams. its all so relative - this is why so many threads you'll see a question like, which pg is better, and i'm like well.. what is your scheme and how much do you need offense from this guy? the answer can vary wildly based on the underlying conditions. as i hope you guys can see, even if you have the simplest of ability formulas in step 1 - which HD most certainly does not - by the time you get to step 2, the ability score comparisons between sides, and then step 3, the true value returned to the team (which is that optimization problem, that even when its ridiculously simple, man kind cannot solve)... it just gets insanely complex. our reality is step 1 is complex. this is why simple, direct questions like 'do ratings have diminishing returns' just totally miss the mark!
again, i don't mean that to be critical! i certainly don't consider this all to be obvious :) however, i do think understanding why the question misses the mark is the most important thing for folks to take from this. most ratings follow the rough outline i laid out - but you'll need to observe to identify differences, just like we had to observe how HD works to say confidently, it does *not* treat a 1/1 guy going to 50/50, against a 100/100 defender, as a 50% improvement. i'm sure everyone agrees with that, but until you look? how the hell should we know. we can guess based on like, how we think basketball works or something, but once you start getting into stuff that is much harder to translate to real basketball - like what ath and spd in HD actually mean in real terms - observing in HD is the only answer.
because the scenarios vary *so* significantly, i strongly suggest folks going down the exploration path to try to stick to something for a while. if you like high d2, then play it a while and do your exploration there, running a consistent scheme (with incremental improvements you make as you learn). if you want to win titles, you can only seriously observe what is happening with your title caliber teams, facing title caliber opposition. this is why i so often have to put that disclaimer in my posts - this is in the context of high d1 teams playing top opponents answer. my methods often translate, but the specific conclusions often don't. i would basically recommend picking a level a tad above what you are shooting for, and try to schedule a lot of those opponents, and try to learn a lot from those games. ignore what happens against garbage opponents - its totally irrelevant.
in that vein - if one actually wants to master this game - you need good data. nobody can try to make sense of 3 games of good data swimming in a sea(son) of garbage. if you want to consistently win titles, go join one of the top 3 conferences in the game at whatever level it is, and schedule a ball buster ridiculous non conference - not because its smart scheduling - but because when the pursuit of knowledge is the game, its the only game in town. you can scheduling optimize later when you are beating those non conf and conf opponents and you are ready to convert from the learning phase to cashing in. you don't get a wide range either. if you are a top 3 team, playing a 10th best team is meaningful. playing a 25th best team is already *barely* meaningful. by 50 its trash. when i really wanted to get good, i was by a huge margin the #1 sos team every year, and that is running as many away games as possible (which do not factor into SOS). i'd have 10 games against the top 10 teams, that sort of thing. as long as you can win half your games or so, there is no such thing as too hard of a schedule.
alright, im going to cut it off there. if anyone made it this far, let me know what doesn't make sense and i can try to clarify. i'll definitely try to keep the follow ups shorter... i could have cut to the chase here a *lot* quicker, but i feel like for a lot of folks, the value is kind of in taking the journey if you will, there's a lot of concepts in there that build on top of each other. for experienced folks who already have thought about this stuff 10 times, im sure it was painfully slow. my apologies!
6/5/2020 7:06 AM (edited)