Posted by gillispie on 1/26/2023 6:22:00 PM (view original):
i used to be focused on whether the HD formulas behind the scenes were linear or non linear, i used to feel its definitely non-linear. back when i worked on formulas myself (11 years?) i addressed it by multiplying things like per and spd and bh as part of their weighting (with also a linear component). which is pretty similar to what you are doing.

at this point though, i kinda think its less about if the HD formulas themselves are linear or non-linear, as much as the curve for marginal value of the ratings which you'd plot for a single player. which is highly situational, highly dependent on the player's other ratings and the defense he is facing (the man defender or the overall zone defense, plus other key defensive factors). things like offense are also highly dependent on the offensive efficiency of the rest of the team. it usually doesn't or barely matters how good your 5th scorer on the floor is, for example, no matter where that player is in the spectrum from useless to pretty darn good.

anyway, i don't think there is a perfect or near-perfect way to capture this, even taking away all the situation stuff (rest of the team, opponent, etc), but the best i came up with for single players was similar to what you are doing (per * per as a factor or ath * ath as a factor).

i think what is really happening behind the scenes, if you considered something like 3pt scoring, that is being compared to the defense along with probably some other factors, and then the difference or ratio is used to pick the spot on the curve that says what 3pt% should result from the overall scenario. the performance of a 70 per, spd, bh player against a 70 ath, def, spd player is going to be fairly similar to what you see when all players are 90. what really matters to us though is the utility from the player's offense, and we operate in really tight margins. a 56% fg scorer might be great while a 50% fg scorer is passable at best. even if everything that happened behind this point was super simple and super linear - say, the player had a fg% rating that could range from 1 to 60 and that was their fg% no matter the defense etc - the actual utility we care about would still be incredibly non-linear. we'd effectively assign 0 value from 1 up to maybe 40, 45, depending on your team, maybe even a bit higher. the value would really pick up around 50 and would be crazy high all the way up to 60.

i guess all i'm getting at is, i used to be concerned about the behind the scenes way per scoring skill was calculated, that sort of thing. now i barely care because its basically irrelevant. what matters to us is utility and marginal utility (how much value does 1 point of extra per matter at a given point, similar to the +20 example in the last post). which is really situational in so many ways. not sure that helps address the question in any way... i guess i feel like its safe to say non-linear is probably in order though, because that is always going to be the reality, as a player transitions from very slightly useful on offense to highly useful. for example, there's going to be a massive spike in value around that 90 per/spd/bh mark for high d1 no matter what the base per skill formula is. and that is pretty darn hard to capture!

i think that's right gil - the main determinants of a player's value is their skill above the replacement player on your roster and relative to the skills of the opponent he's facing. skill growth up to the point of replacement level matter much less than improvements above replacement level (and a similar effect relative to the opposing player's/players' skills). my aim was to capture this not just in how player ratings are calculated, but also (and more so) in how team ratings are calculated, where your team's ability in any key area of the game (scoring, defending, rebounding, passing) is the sum of the stack-ranked skills of each player on your team (in that specific area) with steep diminishing weighting as you progress from your best players in that area to your worst.

this approach was actually guided largely by your many historical forum posts impressing upon the importance of balance in team-building, gil - thanks for sharing your thoughts here

Thanks for the tool, Trail!
I connected it to cub's sheet so I only have to update the link to the team ID one time and then I either use your sheet for "quick" game planning and then fill in the positions on cub's for analyzing the matchups in the big games. Great stuff!

Question(s) for you...
I play D3 exclusively. And when I analyze one of my M2M defense teams against a Press team, many times my team's "ability" (measured by your ratios or cub's or just looking at overall attributes) is higher or the same as those of a press team. However, the result is usually that the press team keeps the game close or is actually superior to my team--and I know this is because of stamina/depth and turnovers. And now that I'm playing press with some of my teams, I'm seeing that my teams clearly outplay more talented teams as well.

So my question is: Is there a way to capture this "impact" that the press has in a calculation like yours (using some type of ratio like the other abilities)? I feel like I can use cub's for general matchup settings and I can use your sheet for certain areas to pick apart a team (very useful stuff). But I've always wondered whether there could be an indicator that shows how much of an impact the press team might have with respect to 1) an increase in turnovers and 2) how much stamina/depth will factor into the game. Fastbreak offense is probably part of this same conversation, at least for the stamina/depth aspect, especially when combined with the press. And technically, these turnover impacts and stamina/depth impacts apply to M2M and Zone as well, but to a much lesser extent.

I have just struggled with understanding how much of an impact the press is "expected" to have on the game, and how to measure that. I know I can go through each team in detail and somewhat figure some things out, but a quick indicator would be really cool to have.

An example for you... compare teams 5160 (Eastbay) and 5157 (Texas, Tyler). The ratios indicate Eastbay is slightly better or maybe even with Texas, Tyler. But this isn't the case--Texas, Tyler is a better team and the results from our first matchup supports this too. To be fair, cub's sheet does show them as slight favorites but this isn't always the case from what I've seen (and I think Texas, Tyler was more than just "slight" favorites so I think it's understating their advantage). There are some game planning things I can change to try to alter the result next time, but I'm more interested in seeing some indicator that shows Texas, Tyler has a major advantage in "ratio X-turnovers" and "ratio Y-stamina/depth" and that's why they're better. That way I can see it right away during my game planning (without trying to sift through other details to figure it out).

Not an easy thing to put into an equation, just something that I've wondered for a while. I'm happy to take the conversation offline too, and share thoughts over Site Mail instead if you'd prefer.

i can't speak to any of the spread sheet stuff, but i'm guessing the defensive ability thing is basically going off of ratings to give you a defensive score - which is probably appropriate. it probably would make the most sense for the press-ness of press to NOT be factored in there - but there's no reason there can't be a separate press score that tries to capture turnover generation of press?

going back to the game side of things, press really is unique in two major ways. first is the turnovers, an elite press team is going to generate about +5 to +8 turnovers per game, over their average opponent when running an average #1 SOS season. this may be skewed in d2/d3 due to the incredible volume of sims, but assuming 90% humans or so on that #1 SOS... this translates to the #1 press team in the country usually being about +5 possessions per game against the #1 man team in the country, assuming quality depth on both sides. i'm guessing those 2 teams get an equal score in the sheet, but in reality, the press team would usually have a major edge on overall defensive contribution.

it defintely makes sense to look at the above turnover differential separately from the fg%/3pt% component. where press gets perhaps an unfair edge is, with full depth (12 deep and ~82 stamina on a normal tempo straight press, no fb, or ~85 stamina for fb/pr)... is that press team can generate almost as good 2pt% and 3pt% defense as any other scheme. its about 1% behind m2m on both fronts and perhaps 2-3% behind a 2-3 or 3-2 zone, respectively.

the other aspect of press is the depth, and this is harder to figure, but certainly a spread sheet could take a good crack at it. press generates much more fatigue for the team running it, and a bunch more (but not as much more) for the opposing team. this is driven by 2 factors, one is the increased # of possessions inherent in the press, which is really most of what hits the other team. the second is the higher per defensive possession fatigue of a press possession.

generally speaking, in d2/d3 there is sufficient depth on the top teams to stand up to the press, so the turnovers becomes the biggest differentiator. a m2m team only needs about 78 stamina and a balance 10 deep team to stand up well to a straight press, and only a tad more for fb/pr. depending on the respective depths of the two teams, this factor can easily help one side of the other. because press teams are always more at risk from fatigue/foul trouble, even at full depth, than full depth m2m and zone teams, this factor can really lend itself to the non-press team, even though most folks traditionally think of this as a press advantage. of course, the better team also benefits from the higher possession count inherent in press, so really amazing press teams (who are really amazing overall but also press), get an extra boost here.

anyway, i am guessing the sheet is not capturing the 3 main aspects of press defense there, the fg/3pt defense, the turnover generation, and the fatigue - but you can certainly start watching those. without question, a full depth team running press is going to have a substantial overall defensive edge over any other defense, assuming similar-ish ath/def. the idea typically has been, its harder to have a balanced 12 deep team like the press needs, so hopefully the man/zone teams have more talent and can gain an advantage elsewhere, like on offense, or rebounding. however, this often has not translated, and as a result, for most of HD history, at most levels, at the high end of competition (top 5 teams in the nation and up or so), press is the pre-eminent system. today's d1 is the most balanced HD has ever been in this regard, because getting 12 players almost always requires substantial sacrifice, and is VERY far from guaranteed even when getting 12 players is the coach's top priority. d2/d3 are much easier to fill up to 12 players, so press remains the ultimate top-tier defense at those levels.

Thanks Gil - I agree with all of this. The goal here is how do we put some aspects of the above into a formula to give us a quick gauge of what to expect.

I agree two defensive scores would be useful (if it's possible to arrive at the appropriate ratios for determining each). One for the turnover generation (think backcourt) and another for the half court defense (sometimes results in a turnover as well but is mostly for suppressing field goal percentage). The turnover generation factor would apply to all defenses but we would see much higher ability scores for a press team with high SPD than for zone with similar ratings.

For the press/stamina, I think the reason it is perceived as a "press strength" is because the turnovers can skyrocket when the opposing team starts to fatigue. If I were to rank the abilities of which are most impacted by fatigue, I would say 1. ballhandling (more turnovers), 2. scoring (lower FG%), 3. Defense (more fouls), 4. Rebounding (I have never seen a team rebound much worse because they were tired--or at least its impact is marginalized compared to the other factors above).
It's tough to see in the PBP how much each player is fatigued at any given moment but I suspect even some fatigue can be very detrimental. But with the 1st ability above resulting in more turnovers, this means more easy shots for the press team, and the 2nd ability leading to more missed shots, this lends itself to more possessions without stoppage/substitutions and more fatigue (again favoring the press team). This is where I perceive even more advantage for the press team--if they can generate some fatigue in the opposing team, especially at one of the guard positions. Whereas if the the press team gets tired and they're facing a zone, they're still not going to turn it over that much and their FG% won't suffer as bad if they can continue to cause turnovers to create easy shots.

hey guys - thanks for all the additional feedback and food for thought here!

just wanted to give you a heads up that i've been experimenting with some alternate models that better encompass the impact of FB/Press. as you both illustrated well in your commentary, capturing this effect "accurately" is quite challenging, but something that i recognize the current model comes too far short in doing.

just a note: a team with very strong stamina, in particular amongst its best players, as well as top-tier depth, will still score better in my system on FB/Press vs the alternative schemes. i.e. there is a mechanism in the current model that provides a boost for teams running such schemes, so long as they have the stamina + depth to do so effectively. however, i believe i've set this bar a little too high at the moment, so that perhaps only 1 in 5 programs running any variation of FB or Press schemes actually receives a positive impact from this choice of scheme that offsets the negative impact of higher bench utilization. i'd like for this to be closer to 1 in 2 programs.

separately, i'm also aiming to improve the logic for advised offensive +/-, as the current system is highly rudimentary and doesn't account for relative skill, only your opponent's defensive strengths and weaknesses.

look out for an update here later this month! thanks again for all the feedback - please keep it coming :)

This is tremendous, trail. Appreciate you sharing with the community.

Version 1.1 is now ready! Details below:

• Key Update: FB + Press are now modeled much better. Teams with poor depth and stamina will be penalized when running these sets, but teams with strong depth and stamina will be rewarded with higher scores than they would see if they were running less depth-utilizing sets.
• Other updates:
  • "Driving" as a method of scoring has been tuned down a bit, in addition to other minor optimizations to the scoring calculations.
  • You'll know find offensive ratings distinguished from defensive ratings for individuals.
  • True Shooting % has been added a stock metric in the stats section.

Edit: There was a minor bug in how depth ratings were being calculated that has been corrected.

Additional minor update: Recommended offensive +/- settings have now been updated to consider both your opponent's defensive skills as well as your own team's skills. If the overall skillset gap is large, the system will tend to push you to take more 3-point shots, which tend to be more efficient. However, as your opponent skill reaches or surpasses your own team's, the system will push you away from such shots which tend to be harder to convert efficiently at scale at the highest levels of competition. The system will generally be contained by a -2 to +2 scale, but there might be exceptions in extreme cases.