RealGM 2023 Top 100 Project - #3 (Michael Jordan)

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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#201 » by WestGOAT » Mon Jul 10, 2023 9:04 pm

ShaqAttac wrote:

Yeah ngl, i got lost pretty quick. What's loog likelihood? Also idk what this means:

"i s designed to find the model that explains the most variation in the data, while penalizing for models that use an excessive number of parameters."


sorry I'm not that familiar with AIC either, just that's it used as a metric to compare predictive (regression) models. ChatGPT is actually does a decent job most of the time explaining these concepts, give it a try:
Spoiler:
me wrote:can you explain in simple terms what is AIC ( Akaike information criterion ), and log likelihood and how likelihood is related to probability


ChatGPT wrote:Certainly! Let's start by understanding likelihood and probability, and then we can delve into the Akaike Information Criterion (AIC).

Likelihood: In statistics, likelihood refers to the probability of observing a specific set of data given a particular statistical model. It represents how well the model explains the observed data. The likelihood is calculated using the parameters of the model and provides a measure of how likely the data is to have been generated by that model.

Probability: Probability is a measure of how likely an event or outcome is to occur. It is typically expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to quantify the uncertainty associated with an event.

Now, let's move on to the Akaike Information Criterion (AIC). The AIC is a statistical measure used to compare and select between different statistical models. It balances the goodness of fit of the model (how well it explains the data) with the complexity of the model (the number of parameters it has).

AIC (Akaike Information Criterion): The AIC is based on the concept of information theory and aims to find the model that provides the best trade-off between goodness of fit and model complexity. It is calculated as:

AIC = -2 * log likelihood + 2 * number of parameters

The AIC penalizes more complex models by adding twice the number of parameters to the value of the negative log likelihood. The lower the AIC value, the better the model is considered to be in terms of balancing goodness of fit and model complexity.

In summary, likelihood measures how well a statistical model explains observed data, while probability quantifies the likelihood of an event occurring. The AIC is a criterion used to compare models by balancing their goodness of fit and complexity, helping to select the model that best explains the data.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#202 » by trex_8063 » Mon Jul 10, 2023 11:36 pm

homecourtloss wrote:
ShaqAttac wrote:
trex_8063 wrote:I don't know how many wins/SRS added those^^^ things account for; but it is a non-zero sum.

And otherwise, most of the compensation is on the "bounce-back" of Pippen and Grant. Which---as per above---their down year in '93 is not on Jordan. Indeed, BOTH of them had their most efficient offensive seasons [plural] while playing next to him, and '94 [plus '95 for Pippen] rate out among the bottom half in terms of all-around efficiency.

If we want to say Kerr/Kukoc/Wennington account of NOTHING [again: I'd disagree], and focus only on what impact the loss of Jordan had, it would be more accurate [imo] to at least compare '94 to a year where Pippen/Grant were playing at a similar level as '94 (because they clearly were NOT in '93).
'92 (the other year that could be argued as peak for each of them, imo) comes to mind.

The difference there is: -12 wins, and a whopping -7.2 SRS change.

its only -7 with injuries tho. from that thing kd and rf been postin, its actually just -5 when everyones playin


Yes, the difference isn’t so stark at full health, which seems to keep getting ignored. At full-strength, the Bulls were +4.7 with Pippen annd and grant (55-win pace) and were +3.5 in 95 pre-Jordan without grant , a 52-win pace).



So......comparing to '92 (the other [outside of '94] peakish year for both Pippen and Grant) it's "only" an approximately +5 SRS lift [to an already semi-contender level team] that Jordan provides?
And that with an assumption that the Kukoc/Kerr/Wennington upgrades meant NOTHING (which again: I would argue that is NOT the case).

And in a far more competitive era than say......'69/'70.

idk, I think we're just reading the signals a fair bit differently.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#203 » by Moonbeam » Tue Jul 11, 2023 12:23 am

WestGOAT wrote:
ShaqAttac wrote:

Yeah ngl, i got lost pretty quick. What's loog likelihood? Also idk what this means:

"i s designed to find the model that explains the most variation in the data, while penalizing for models that use an excessive number of parameters."


sorry I'm not that familiar with AIC either, just that's it used as a metric to compare predictive (regression) models. ChatGPT is actually does a decent job most of the time explaining these concepts, give it a try:
Spoiler:
me wrote:can you explain in simple terms what is AIC ( Akaike information criterion ), and log likelihood and how likelihood is related to probability


ChatGPT wrote:Certainly! Let's start by understanding likelihood and probability, and then we can delve into the Akaike Information Criterion (AIC).

Likelihood: In statistics, likelihood refers to the probability of observing a specific set of data given a particular statistical model. It represents how well the model explains the observed data. The likelihood is calculated using the parameters of the model and provides a measure of how likely the data is to have been generated by that model.

Probability: Probability is a measure of how likely an event or outcome is to occur. It is typically expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to quantify the uncertainty associated with an event.

Now, let's move on to the Akaike Information Criterion (AIC). The AIC is a statistical measure used to compare and select between different statistical models. It balances the goodness of fit of the model (how well it explains the data) with the complexity of the model (the number of parameters it has).

AIC (Akaike Information Criterion): The AIC is based on the concept of information theory and aims to find the model that provides the best trade-off between goodness of fit and model complexity. It is calculated as:

AIC = -2 * log likelihood + 2 * number of parameters

The AIC penalizes more complex models by adding twice the number of parameters to the value of the negative log likelihood. The lower the AIC value, the better the model is considered to be in terms of balancing goodness of fit and model complexity.

In summary, likelihood measures how well a statistical model explains observed data, while probability quantifies the likelihood of an event occurring. The AIC is a criterion used to compare models by balancing their goodness of fit and complexity, helping to select the model that best explains the data.


It's great to see a discussion of AIC here! I think ChatGPT has done a good job, but I think it might still be a bit obtuse if you aren't versed in statistical theory. I'll try to explain with a mock example.

Suppose we want to predict people's BMI based on other factors which we think might contribute to their BMI. In statistics, we can build a model (a mathematical equation) for predicting a variable of interest based on one or more predictor variables.

Suppose we sample 100 people and measure their BMI along with some other variables like the average number of calories they consume in a day, the average amount of exercise they do in a day, and their age. There may be other variables that are actually important, but I'll stick to these 3 for simplicity. We can then build a model for predicting the BMI based on calories, exercise, and age for these 100 people. I'll go with a linear model here for simplicity, though different types of model may be possible. So Model 1 would look like this.

Model 1: predicted BMI = b0 + b1*calories + b2*exercise + b3*age

In order to make predictions, we have to come up with estimates for the numbers b0, b1, b2, and b3. A common way to do this is through a procedure called maximum likelihood, which comes up with the combination of estimates for b0, b1, b2, and b3 which will maximize something called the likelihood function (related to probability). Essentially, the maximum likelihood estimates are those values of b0, b1, b2, and b3 that will maximize the probability of getting the observed 100 values of BMI in our sample based on calories, exercise, and age.

In Model 1, we used 3 predictor variables which for illustrative purposes I will consider to be meaningful (statistically useful) predictors. But we could use more. And the truth is that the likelihood will be higher whenever we add more variables, whether they are actually meaningful or not! So let's throw in some nonsense variables like the number of letters in the street name where the person lives, the number of Prince songs in their favorite playlist, and the length of their longest toenail, and call this Model 2.

Model 2: predicted BMI = b0 + b1*calories + b2*exercise + b3*age + b4*street name letters + b5*Prince songs in playlist + b6*longest toenail length

When we fit Model 2 using maximum likelihood, we'll get estimates for the numbers b0 through b6. Importantly, the values of b0, b1, b2, and b3 are likely to be different in Model 2 compared to what they were in Model 1, perhaps quite different.

Now, when we fit models using maximum likelihood, we get the calculated likelihood of the model. Suppose the log-likelihood of Model 1 (the natural logarithm of Model 1's likelihood) is -1000, and the log-likelihood of Model 2 is -999.8. Well, Model 2 has a higher log-likelihood, which means that we will get slightly better predictions overall of the 100 BMIs in our sample data using Model 2 as opposed to Model 1.

However, while making models more complex (i.e. having more predictor variables) makes them better at predicting the sample data, this can make them worse at predicting new data. Suppose we gather data on 200 new people and measure all of these variables. It is quite possible (I'd say probable) that predicting the BMI of these 200 new people with Model 1 will do a better job than using the more complex Model 2. This phenomenon is known as overfitting.

Enter AIC, and other metrics like BIC. AIC combines predictive performance of the sample data (in this case, our original 100 people which we used to estimate the numbers b0 through b3 in Model 1 and b0 through b6 in Model 2) and model complexity (the number of predictors). Here are the formulas:

AIC = -2*log-likelihood + 2*number of predictors
BIC = -2*log-likelihood + ln(sample size)*number of predictors

Essentially, AIC adds a penalty of 2 for every extra predictor, while BIC makes this penalty ln(sample size). These might seem like arbitrary numbers, but there is some mathematical theory behind them that justifies their choice.

Turning back to our 2 models, Model 1 had a log-likelihood of -1000 and Model 2 had a log-likelihood of -999.8.

The AIC of Model 1 is:

-2*(-1000) + 2*3 = 2006

The AIC of Model 2 is:

-2*(-999.8) + 2*6 = 2011.6

The BIC of Model 1 is:

-2*(-1000) + ln(100)*3 = 2013.82

The BIC of Model 2 is:

-2*(-999.8) + ln(100)*6 = 2027.23

Model 1 having the smaller AIC (and smaller BIC) means that it is preferred. Simply put, the extra 3 nonsense predictors in Model 2 didn't improve the log-likelihood enough to justify inclusion in the model.

This might not seem like a big deal to have 3 seemingly harmless predictors, but again note that including these predictors will also change the estimates of the useful parameters b1, b2, and b3 in comparison to what they were in Model 1. So not only do these nonsense predictors not help much in predicting the sample data, they change the estimates for the useful predictors!

Hopefully this makes some sense. :lol:
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#204 » by OhayoKD » Tue Jul 11, 2023 1:01 am

trex_8063 wrote:
homecourtloss wrote:
ShaqAttac wrote:its only -7 with injuries tho. from that thing kd and rf been postin, its actually just -5 when everyones playin


Yes, the difference isn’t so stark at full health, which seems to keep getting ignored. At full-strength, the Bulls were +4.7 with Pippen annd and grant (55-win pace) and were +3.5 in 95 pre-Jordan without grant , a 52-win pace).



So......comparing to '92 (the other [outside of '94] peakish year for both Pippen and Grant) it's "only" an approximately +5 SRS lift [to an already semi-contender level team] that Jordan provides?
And that with an assumption that the Kukoc/Kerr/Wennington upgrades meant NOTHING (which again: I would argue that is NOT the case).



idk, I think we're just reading the signals a fair bit differently.

I'd say it's rather weak-looking relative to who he's compared with or placed over. Would also say that if you're using 1992, someone like Cartwright being a downgrade isn't as clear.
And in a far more competitive era than say......'69/'70.

I mean, I suppose it matters how you factor era-relativity vs league-strength/"in a vacuum", but if you're going by the former, +5 is actually worth alot more in 69/70(and I may as well point out there was a 8-point drop-off with a retiring Russell):

Well, and I have pointed this out before, by such a standard, the Celtics are very clearly ,more advantaged than the Bulls:

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(1996)

Image
(1962)

At the height of their dynasty, the Celtics were comically dominant. From 1962-65, their average margin-of-victory (MOV) was over 8 points per game. During the same time span, only two other teams even eclipsed 4 points per game – the ’64 Royals and the ’64 Warriors. And all of Boston’s separation was created by its historic defense, anchored by Russell:

Anenigma wrote:But par for the course I suppose. Jordan’s case pathologically needs to be a matter of him being the best. 6 needs to be greater than 11. A supporting cast that looks like a top quartile team without you needs to be worse than a cast that ends up looking like a bottom quartile one. Having a regular season SRS three points clear of the next best team on three occasions needs to be better than doing so on six occasions. Being theoretically maybe a conceivably comparable impact standout if we squint needs to put you on the same impact level of a clear and repeatedly demonstrated standout. Or in the tidiest summary, no matter what, if it is inconvenient to this image of an infallible Jordan, lesser separation from the pack needs to be reframed as better than greater separation.

Assuming you buy that the Bulls cast did not degrade between 1984 and 1988, we can give Jordan all the credit for the Bulls team-wide improvement and that gets him to...+8. On a worse team. In an era where 8-points of srs is worth substantially less.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#205 » by trex_8063 » Tue Jul 11, 2023 3:57 pm

OhayoKD wrote:
trex_8063 wrote:

idk, I think we're just reading the signals a fair bit differently.

I'd say it's rather weak-looking relative to who he's compared with or placed over. Would also say that if you're using 1992, someone like Cartwright being a downgrade isn't as clear.


And King was a pinch better in '92, so.......fair enough, I'll give you the Wennington swap as negligible.

Note, however, that I'd indicated we were ignoring the other swaps in the '92 comparison anyway:
If we want to say Kerr/Kukoc/Wennington account of NOTHING [again: I'd disagree], and focus only on what impact the loss of Jordan had, it would be more accurate [imo] to at least compare '94 to a year where Pippen/Grant were playing at a similar level as '94 (because they clearly were NOT in '93).
'92 (the other year that could be argued as peak for each of them, imo) comes to mind.


......as including them only helps the arguments in Jordan's favour (because they generally benefit the '94 squad).


As to the other swaps, in comparing the '94 team with the '92 team (instead of with '93)........
Rookie Toni Kukoc's minutes are now replacing those of Cliff Levingston and maybe a tiny bit of one or both of Scott Williams and Bobby Hansen. This no longer appears much of an upgrade (vs when he was primarily replacing the washed up Rodney McCray). So we'll call that a nil exchange, too (though again: I'd indicated we were ignoring these other moving pieces in the '92 comparison anyway).

Steve Kerr, in comparing '94 to '92, is primarily replacing Craig Hodges, whatever portion of Paxson's lost minutes that weren't consumed by Armstrong, and maybe a tiny bit bit of Bobby Hansen.
That's still an upgrade in the backcourt, imo.

How much is that worth? idk, probably not much, but a non-zero amount.


OhayoKD wrote:
And in a far more competitive era than say......'69/'70.

I mean, I suppose it matters how you factor era-relativity vs league-strength/"in a vacuum", but if you're going by the former, +5 is actually worth alot more in 69/70


I'm never quite sure how to treat years that have a greater degree of parity vs years that do not.

I mean, if we say it was "worth a lot more" in '69/'70, are we saying wasn't possible (or at least was FAR more difficult) for teams to so differentiate themselves from the mean?

Or was it possible......but there just weren't [by happenstance] any teams capable of doing so in one or both of those years?

The SRS difference between the BEST team and WORST team in both '69 and '70 [in a 14-team league] is smaller than the difference seen in '93 by a long shot (gap is 13.74 in '69, 12.57 in '70, and 21.34 in '93).
HOWEVER, the difference between the BEST team and the 26th-place team in '93 is pretty similar to the gap of '69 or '70. Things are just skewed by the outlier bad Dallas Mavericks (they were not only last, but in '93 they were multiple standard deviations from the 26th-placed team). The gap from 1st to 26th is just 14.28 (fairly similar to that seen in '69 or '70).

I also note that the best team [by SRS] of all three of these years is the '70 Knicks (a team that still toiled through TWO 7-game series's [including one that was before Reed got injured]).


OhayoKD wrote:(and I may as well point out there was a 8-point drop-off with a retiring Russell):


OK. But I think you'd agree that [generally speaking] adding +5 to the SRS of a team that is around -2 is not the same as adding +5 to a that was already around +5. The latter is a much more impressive feat.

Russell appears to add 14 wins and +7.95 SRS..........to a starting point of 34 wins and -1.59 SRS.

Even accounting for health/injuries on the '94 Bulls, if comparing to '92 it appears Jordan adds 12 wins and +5 [or so] SRS (that assuming [dubiously] that the Kerr upgrade means nothing).........to a starting point of 55 wins and circa +5 SRS.

I'm not sure I'm willing to crown the former as more impressive than the latter, and perhaps definitely not when considering strength of respective eras.


But again, maybe I just read the tea leaves differently. Which is fine; we can agree to disagree.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#206 » by WestGOAT » Tue Jul 11, 2023 5:39 pm

Moonbeam wrote:
WestGOAT wrote:
ShaqAttac wrote:Yeah ngl, i got lost pretty quick. What's loog likelihood? Also idk what this means:

"i s designed to find the model that explains the most variation in the data, while penalizing for models that use an excessive number of parameters."


sorry I'm not that familiar with AIC either, just that's it used as a metric to compare predictive (regression) models. ChatGPT is actually does a decent job most of the time explaining these concepts, give it a try:
Spoiler:
me wrote:can you explain in simple terms what is AIC ( Akaike information criterion ), and log likelihood and how likelihood is related to probability


ChatGPT wrote:Certainly! Let's start by understanding likelihood and probability, and then we can delve into the Akaike Information Criterion (AIC).

Likelihood: In statistics, likelihood refers to the probability of observing a specific set of data given a particular statistical model. It represents how well the model explains the observed data. The likelihood is calculated using the parameters of the model and provides a measure of how likely the data is to have been generated by that model.

Probability: Probability is a measure of how likely an event or outcome is to occur. It is typically expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to quantify the uncertainty associated with an event.

Now, let's move on to the Akaike Information Criterion (AIC). The AIC is a statistical measure used to compare and select between different statistical models. It balances the goodness of fit of the model (how well it explains the data) with the complexity of the model (the number of parameters it has).

AIC (Akaike Information Criterion): The AIC is based on the concept of information theory and aims to find the model that provides the best trade-off between goodness of fit and model complexity. It is calculated as:

AIC = -2 * log likelihood + 2 * number of parameters

The AIC penalizes more complex models by adding twice the number of parameters to the value of the negative log likelihood. The lower the AIC value, the better the model is considered to be in terms of balancing goodness of fit and model complexity.

In summary, likelihood measures how well a statistical model explains observed data, while probability quantifies the likelihood of an event occurring. The AIC is a criterion used to compare models by balancing their goodness of fit and complexity, helping to select the model that best explains the data.


It's great to see a discussion of AIC here!


Thanks for introducing it, I hadn't heard about it before. I've mainly used AUC/sensitivity/specificity metrics to evaluate cross-validated classification models, so it's nice to add something extra to the toolbox!
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#207 » by OhayoKD » Tue Jul 11, 2023 9:19 pm

Going to go a bit out of order because I don't want to bury the lede
trex_8063 wrote:
OhayoKD wrote:I mean, if we say it was "worth a lot more" in '69/'70, are we saying wasn't possible (or at least was FAR more difficult) for teams to so differentiate themselves from the mean?

No. It's not about difficulty, it's about championships. Remember, the goal is to be the best team(ideally by a large margin), not to blow-out team #23. Let's say 1962 Russell was only worth 4-points of srs on a random team. Let's say 1991 Jordan was worth 8-points on a random team. Here's the thing
Image
Image

In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.
idk, I think we're just reading the signals a fair bit differently.

Nothing wrong with that :D
I'd say it's rather weak-looking relative to who he's compared with or placed over. Would also say that if you're using 1992, someone like Cartwright being a downgrade isn't as clear.


And King was a pinch better in '92, so.......fair enough, I'll give you the Wennington swap as negligible.

Note, however, that I'd indicated we were ignoring the other swaps in the '92 comparison anyway:
If we want to say Kerr/Kukoc/Wennington account of NOTHING [again: I'd disagree], and focus only on what impact the loss of Jordan had, it would be more accurate [imo] to at least compare '94 to a year where Pippen/Grant were playing at a similar level as '94 (because they clearly were NOT in '93).

'92 (the other year that could be argued as peak for each of them, imo) comes to mind.


......as including them only helps the arguments in Jordan's favour (because they generally benefit the '94 squad).

Perhaps, though I think a replacement like Pete Myers might be more of factor than you do. After all, there were stretches where Pippen was played at shooting-guard(he was not a fan). And then there's the matter of the growing acrimony between Scottie and management. Kukoc and Pippen had beef of their own...all in all I do not think it is clear one version of the team was better than the other, but If you would curve things a few wins up or down, I won't protest. :D
OhayoKD wrote:(and I may as well point out there was a 8-point drop-off with a retiring Russell):


OK. But I think you'd agree that [generally speaking] adding +5 to the SRS of a team that is around -2 is not the same as adding +5 to a that was already around +5. The latter is a much more impressive feat.

Russell appears to add 14 wins and +7.95 SRS..........to a starting point of 34 wins and -1.59 SRS.

Even accounting for health/injuries on the '94 Bulls, if comparing to '92 it appears Jordan adds 12 wins and +5 [or so] SRS (that assuming [dubiously] that the Kerr upgrade means nothing).........to a starting point of 55 wins and circa +5 SRS.

Well the initial target of that +8 mark was 1988 Jordan who was lifting a worse team(1984 Bulls were 27-win pace) to worse(far worse in a CORP sense), but again, if we are sticking to era-relativity(and maybe you are not), the 1993 Bulls are not really better than the 1969 Celtics who were a tenth of a point shy of the srs-leaders(that is not full-strength) and ahead of team #3 by nearly a full-point. The 1993 Bulls were behind three separate teams and barely ahead of the Knicks. And that's just going by the regular-season. In the playoffs I'd say the Celtics are substantially more impressive beating that Knicks side that posted +8, the following year and a Lakers team that(when healthy) was on-pace to be the strongest team in league history before they added Wilt Chamberlain.

I would say the Celtics were both better and Russell was probably worth more to them. That's a winning combination, especially when you're a player-coach whose on his last legs.
But again, maybe I just read the tea leaves differently. Which is fine; we can agree to disagree.

Sure! Though I do wonder if we were disagreeing so much as misunderstanding each other.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#208 » by lessthanjake » Tue Jul 11, 2023 11:15 pm

OhayoKD wrote:Going to go a bit out of order because I don't want to bury the lede
trex_8063 wrote:
OhayoKD wrote:I mean, if we say it was "worth a lot more" in '69/'70, are we saying wasn't possible (or at least was FAR more difficult) for teams to so differentiate themselves from the mean?

No. It's not about difficulty, it's about championships. Remember, the goal is to be the best team(ideally by a large margin), not to blow-out team #23. Let's say 1962 Russell was only worth 4-points of srs on a random team. Let's say 1991 Jordan was worth 8-points on a random team. Here's the thing
Image
Image

In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.


So I get this point to some degree, but doesn’t that ultimately amount to arbitrarily crediting a player with more or less value depending on whether the rest of the league has more or less parity? Like, to use a stylized example, if a guy is a +4 to his team and therefore makes them go from a 0 SRS team to a +4 SRS team, does it really make him a better player if the rest of the league is filled with really even teams such that they’re all hovering around 0 SRS? Or is the level of parity in the rest of the league just an exogenous variable that doesn’t really bear on how good a player is?

Relatedly, doesn’t this just work to artificially advantage players in smaller leagues? The fewer teams there are, the more likely it probably is that there won’t be any more than one really good team. Basically, if each team that exists has a certain probability of being a high SRS team, you’ll tend to have more high SRS teams the more teams there are in the league. Looking at it the way you are, it basically ends up amounting to saying that SRS boosts are not worth as much if there are more high SRS teams, because in that scenario an SRS boost doesn’t distinguish a team as much from the next best teams in the league. But that ends up just artificially penalizing players who played in a larger league, because there’s almost certainly going to be more high SRS teams.

In a sense, I get the point. It actually may be true that a player in a smaller league where there’s not another really good team actually increased their team’s chances of winning the title more than someone in a much larger league with multiple really good teams—even if the latter player actually provided a larger SRS boost. But I don’t really think that that means the player is better. It might actually have made them more *valuable* in the context of their era, but not better IMO. And perhaps one can validly measure greatness by looking at how valuable someone was in the context of their era—it’s not a totally illogical way to think about things—but I think that that would unduly advantage guys for the simple fact of playing in a smaller league.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#209 » by OhayoKD » Wed Jul 12, 2023 12:14 am

lessthanjake wrote:
OhayoKD wrote:Going to go a bit out of order because I don't want to bury the lede
trex_8063 wrote:

No. It's not about difficulty, it's about championships. Remember, the goal is to be the best team(ideally by a large margin), not to blow-out team #23. Let's say 1962 Russell was only worth 4-points of srs on a random team. Let's say 1991 Jordan was worth 8-points on a random team. Here's the thing
Image
Image

In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.


So I get this point to some degree, but doesn’t that ultimately amount to arbitrarily crediting a player with more or less value depending on whether the rest of the league has more or less parity?

Well theoretically, more parity may be an indication that it's materially harder to generate srs. If i take the a similarly talented league but there are more teams, srs will suddenly go up. Does that actually mean the teams with high srs are better than the teams with "near nuetral" srs were in the smaller league? The 60's were weaker than the 90's, but SRS isn't how you go about showing that.

Like, to use a stylized example, if a guy is a +4 to his team and therefore makes them go from a 0 SRS team to a +4 SRS team, does it really make him a better player if the rest of the league is filled with really even teams such that they’re all hovering around 0 SRS? Or is the level of parity in the rest of the league just an exogenous variable that doesn’t really bear on how good a player is?

It makes him better relative-to-era assuming your definition of better is tied to championships. There is no rule against breaking era-relativity(and I have repeatedly defended the validity of that approach), but if you are using an era-relative framework or saying your criteria is or factors in "CORP"...

(Note: "era" is also subjectively defined, you could just apply this year by year in which case Lebron's "corp" would just drop naturally in 2017 irregardless of his own quality as a player. 2019 Giannis can have a higher corp than a more polished 2022 giannis as the league hasn't figured him out yet, ect)
Relatedly, doesn’t this just work to artificially advantage players in smaller leagues? The fewer teams there are, the more likely it probably is that there won’t be any more than one really good team.

If SRS is the measure it is also less likely(all else equal) for you to be on the good team. The actual advantage of smaller-leagues is having to beat less opponents, but the degree of that advantage is overstated when you focus on srs because a team having higher srs(a natural outcome in a bigger league) doesn't necessarily mean they've increased their likelihood of beating you directly. Assuming equal talent-levels, a bigger league will produce higher srs, that does not mean the higher srs teams are actually better in a vacuum.
In a sense, I get the point. It actually may be true that a player in a smaller league where there’s not another really good team actually increased their team’s chances of winning the title more than someone in a much larger league with multiple really good teams—even if the latter player actually provided a larger SRS boost. But I don’t really think that that means the player is better. It might actually have made them more *valuable* in the context of their era

Sure. But that is how era-relativity works(unless you're using different "objective" than championship-winning)
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#210 » by lessthanjake » Wed Jul 12, 2023 12:45 am

OhayoKD wrote:
lessthanjake wrote:
OhayoKD wrote:Going to go a bit out of order because I don't want to bury the lede

No. It's not about difficulty, it's about championships. Remember, the goal is to be the best team(ideally by a large margin), not to blow-out team #23. Let's say 1962 Russell was only worth 4-points of srs on a random team. Let's say 1991 Jordan was worth 8-points on a random team. Here's the thing
Image
Image

In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.


So I get this point to some degree, but doesn’t that ultimately amount to arbitrarily crediting a player with more or less value depending on whether the rest of the league has more or less parity?

Well theoretically, more parity may be an indication that it's materially harder to generate srs. If i take the a similarly talented league but there are more teams, srs will suddenly go up. Does that actually mean the teams with high srs are better than the teams with "near nuetral" srs were in the smaller league? The 60's were weaker than the 90's, but SRS isn't how you go about showing that.

Like, to use a stylized example, if a guy is a +4 to his team and therefore makes them go from a 0 SRS team to a +4 SRS team, does it really make him a better player if the rest of the league is filled with really even teams such that they’re all hovering around 0 SRS? Or is the level of parity in the rest of the league just an exogenous variable that doesn’t really bear on how good a player is?

It makes him better relative-to-era assuming your definition of better is tied to championships. There is no rule against breaking era-relativity(and I have repeatedly defended the validity of that approach), but if you are using an era-relative framework or saying your criteria is or factors in "CORP"...

(Note: "era" is also subjectively defined, you could just apply this year by year in which case Lebron's "corp" would just drop naturally in 2017 irregardless of his own quality as a player. 2019 Giannis can have a higher corp than a more polished 2022 giannis as the league hasn't figured him out yet, ect)
Relatedly, doesn’t this just work to artificially advantage players in smaller leagues? The fewer teams there are, the more likely it probably is that there won’t be any more than one really good team.

If SRS is the measure it is also less likely(all else equal) for you to be on the good team. The actual advantage of smaller-leagues is having to beat less opponents, but the degree of that advantage is overstated when you focus on srs because a team having higher srs(a natural outcome in a bigger league) doesn't necessarily mean they've increased their likelihood of beating you directly. Assuming equal talent-levels, a bigger league will produce higher srs, that does not mean the higher srs teams are actually better in a vacuum.
In a sense, I get the point. It actually may be true that a player in a smaller league where there’s not another really good team actually increased their team’s chances of winning the title more than someone in a much larger league with multiple really good teams—even if the latter player actually provided a larger SRS boost. But I don’t really think that that means the player is better. It might actually have made them more *valuable* in the context of their era

Sure. But that is how era-relativity works(unless you're using different "objective" than championship-winning)


I don’t think taking an “era-relative” lens requires one to look at it this way. To me, being “era-relative” is about not discounting a player’s individual skills by measuring them against modern players’ skills. So it would mean not looking at tape of Bill Russell and saying something like “He’s just Bam Adebayo without a jump shot,” and instead acknowledging that within the context of his era he was extremely athletic and very skilled. I don’t think an “era-relative” lens requires measuring how much a player increased his team’s chances of winning titles in his era, because then that “era-relative” lens will just systematically favor players in earlier eras, where, with fewer teams, any great player was going to naturally increase their team’s title chances by more than a player would now.

Of course, one could still take the approach you’re describing. It’s not inherently invalid. But I do think it’s inherently biased in favor of players in earlier eras, and I also think there’s ways to take an “era-relative” lens without thinking about it in this way.
OhayoKD wrote:Lebron contributes more to all the phases of play than Messi does. And he is of course a defensive anchor unlike messi.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#211 » by trex_8063 » Wed Jul 12, 2023 1:07 pm

OhayoKD wrote:In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.


OK, I see what you mean now. The strictly CORP principle and analysis is something I've only just begun toying with (and I've been more just assessing the player's quality in a given season sort of "in a vacuum" [i.e. is it MVP-level, or only weak-MVP level, etc]). I admit I've not gone to this level of granularity (looking at league parity in each year), where [for example] I might find that a "weak-MVP level" season might get you further in '62 or '69 [or whatever] than it would in '93 [or whatever]--->because you don't need as much of a shift in the point differential to become the favourite.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#212 » by OhayoKD » Wed Jul 12, 2023 1:32 pm

trex_8063 wrote:
OhayoKD wrote:In 1991, being +8 on an average team only makes your team a solid contender. In 1962, being +4 on an average team makes you the clear championship favorite. Even though Jordan is worth twice as many-points of srs(in this hypothetical), Bill Russell gives you a better shot at a title. Not so relevant if you're breaking era-relativity, but if you are assessing something like CORP(which seems to play a factor in your rankings), it's not really the raw srs you should be looking at.


OK, I see what you mean now. The strictly CORP principle and analysis is something I've only just begun toying with (and I've been more just assessing the player's quality in a given season sort of "in a vacuum" [i.e. is it MVP-level, or only weak-MVP level]). I admit I've not gone to this level of granularity (looking at league parity in each year), where [for example] I might find that a "weak-MVP level" season might get you further in '62 or '69 [or whatever] than it would in '93 [or whatever]--->because you don't need as much of a shift in the point differential to become the favourite.

FWIW, I do think it's standard to be a little looser and establish "thresholds" based on an extended period of time(thus era-relative rather than season-relative). Ultimately though it's about how you define "weak mvp" or "mvp" and then the process emerges from there. If you're Ben Taylor and you are literally establishing goodness by "likelihood of picking up a title in your era", then this should be getting factored in(as far as I know he doesn't). If it's "in a vacuum"(though I'd be curious what goodness is to you "in a vacuum"), then obviously this doesn't neccesarily apply.
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#213 » by ShaqAttac » Wed Jul 12, 2023 4:07 pm

trex_8063 wrote:
homecourtloss wrote:
ShaqAttac wrote:its only -7 with injuries tho. from that thing kd and rf been postin, its actually just -5 when everyones playin


Yes, the difference isn’t so stark at full health, which seems to keep getting ignored. At full-strength, the Bulls were +4.7 with Pippen annd and grant (55-win pace) and were +3.5 in 95 pre-Jordan without grant , a 52-win pace).



So......comparing to '92 (the other [outside of '94] peakish year for both Pippen and Grant) it's "only" an approximately +5 SRS lift [to an already semi-contender level team] that Jordan provides?
And that with an assumption that the Kukoc/Kerr/Wennington upgrades meant NOTHING (which again: I would argue that is NOT the case).

And in a far more competitive era than say......'69/'70.

idk, I think we're just reading the signals a fair bit differently.

i mean the league def got more competitive after the 90's
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#214 » by ShaqAttac » Fri Jul 14, 2023 4:00 pm

Moonbeam wrote:
WestGOAT wrote:
ShaqAttac wrote:Yeah ngl, i got lost pretty quick. What's loog likelihood? Also idk what this means:

"i s designed to find the model that explains the most variation in the data, while penalizing for models that use an excessive number of parameters."


sorry I'm not that familiar with AIC either, just that's it used as a metric to compare predictive (regression) models. ChatGPT is actually does a decent job most of the time explaining these concepts, give it a try:
Spoiler:
me wrote:can you explain in simple terms what is AIC ( Akaike information criterion ), and log likelihood and how likelihood is related to probability


ChatGPT wrote:Certainly! Let's start by understanding likelihood and probability, and then we can delve into the Akaike Information Criterion (AIC).

Likelihood: In statistics, likelihood refers to the probability of observing a specific set of data given a particular statistical model. It represents how well the model explains the observed data. The likelihood is calculated using the parameters of the model and provides a measure of how likely the data is to have been generated by that model.

Probability: Probability is a measure of how likely an event or outcome is to occur. It is typically expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. Probability is used to quantify the uncertainty associated with an event.

Now, let's move on to the Akaike Information Criterion (AIC). The AIC is a statistical measure used to compare and select between different statistical models. It balances the goodness of fit of the model (how well it explains the data) with the complexity of the model (the number of parameters it has).

AIC (Akaike Information Criterion): The AIC is based on the concept of information theory and aims to find the model that provides the best trade-off between goodness of fit and model complexity. It is calculated as:

AIC = -2 * log likelihood + 2 * number of parameters

The AIC penalizes more complex models by adding twice the number of parameters to the value of the negative log likelihood. The lower the AIC value, the better the model is considered to be in terms of balancing goodness of fit and model complexity.

In summary, likelihood measures how well a statistical model explains observed data, while probability quantifies the likelihood of an event occurring. The AIC is a criterion used to compare models by balancing their goodness of fit and complexity, helping to select the model that best explains the data.


It's great to see a discussion of AIC here! I think ChatGPT has done a good job, but I think it might still be a bit obtuse if you aren't versed in statistical theory. I'll try to explain with a mock example.

Suppose we want to predict people's BMI based on other factors which we think might contribute to their BMI. In statistics, we can build a model (a mathematical equation) for predicting a variable of interest based on one or more predictor variables.

Suppose we sample 100 people and measure their BMI along with some other variables like the average number of calories they consume in a day, the average amount of exercise they do in a day, and their age. There may be other variables that are actually important, but I'll stick to these 3 for simplicity. We can then build a model for predicting the BMI based on calories, exercise, and age for these 100 people. I'll go with a linear model here for simplicity, though different types of model may be possible. So Model 1 would look like this.

Model 1: predicted BMI = b0 + b1*calories + b2*exercise + b3*age

In order to make predictions, we have to come up with estimates for the numbers b0, b1, b2, and b3. A common way to do this is through a procedure called maximum likelihood, which comes up with the combination of estimates for b0, b1, b2, and b3 which will maximize something called the likelihood function (related to probability). Essentially, the maximum likelihood estimates are those values of b0, b1, b2, and b3 that will maximize the probability of getting the observed 100 values of BMI in our sample based on calories, exercise, and age.

In Model 1, we used 3 predictor variables which for illustrative purposes I will consider to be meaningful (statistically useful) predictors. But we could use more. And the truth is that the likelihood will be higher whenever we add more variables, whether they are actually meaningful or not! So let's throw in some nonsense variables like the number of letters in the street name where the person lives, the number of Prince songs in their favorite playlist, and the length of their longest toenail, and call this Model 2.

Model 2: predicted BMI = b0 + b1*calories + b2*exercise + b3*age + b4*street name letters + b5*Prince songs in playlist + b6*longest toenail length

When we fit Model 2 using maximum likelihood, we'll get estimates for the numbers b0 through b6. Importantly, the values of b0, b1, b2, and b3 are likely to be different in Model 2 compared to what they were in Model 1, perhaps quite different.

Now, when we fit models using maximum likelihood, we get the calculated likelihood of the model. Suppose the log-likelihood of Model 1 (the natural logarithm of Model 1's likelihood) is -1000, and the log-likelihood of Model 2 is -999.8. Well, Model 2 has a higher log-likelihood, which means that we will get slightly better predictions overall of the 100 BMIs in our sample data using Model 2 as opposed to Model 1.

However, while making models more complex (i.e. having more predictor variables) makes them better at predicting the sample data, this can make them worse at predicting new data. Suppose we gather data on 200 new people and measure all of these variables. It is quite possible (I'd say probable) that predicting the BMI of these 200 new people with Model 1 will do a better job than using the more complex Model 2. This phenomenon is known as overfitting.

Enter AIC, and other metrics like BIC. AIC combines predictive performance of the sample data (in this case, our original 100 people which we used to estimate the numbers b0 through b3 in Model 1 and b0 through b6 in Model 2) and model complexity (the number of predictors). Here are the formulas:

AIC = -2*log-likelihood + 2*number of predictors
BIC = -2*log-likelihood + ln(sample size)*number of predictors

Essentially, AIC adds a penalty of 2 for every extra predictor, while BIC makes this penalty ln(sample size). These might seem like arbitrary numbers, but there is some mathematical theory behind them that justifies their choice.

Turning back to our 2 models, Model 1 had a log-likelihood of -1000 and Model 2 had a log-likelihood of -999.8.

The AIC of Model 1 is:

-2*(-1000) + 2*3 = 2006

The AIC of Model 2 is:

-2*(-999.8) + 2*6 = 2011.6

The BIC of Model 1 is:

-2*(-1000) + ln(100)*3 = 2013.82

The BIC of Model 2 is:

-2*(-999.8) + ln(100)*6 = 2027.23

Model 1 having the smaller AIC (and smaller BIC) means that it is preferred. Simply put, the extra 3 nonsense predictors in Model 2 didn't improve the log-likelihood enough to justify inclusion in the model.

This might not seem like a big deal to have 3 seemingly harmless predictors, but again note that including these predictors will also change the estimates of the useful parameters b1, b2, and b3 in comparison to what they were in Model 1. So not only do these nonsense predictors not help much in predicting the sample data, they change the estimates for the useful predictors!

Hopefully this makes some sense. :lol:

im still kinda confused but... does it basically test which models are on point and which models are doing too much? also what do u mean by b0 b1 b2 and b3.

thanks for writing all this tho
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Re: RealGM 2023 Top 100 Project - #3 (Deadline 7/9 11:59pm) 

Post#215 » by Moonbeam » Sat Jul 15, 2023 1:20 am

ShaqAttac wrote:im still kinda confused but... does it basically test which models are on point and which models are doing too much? also what do u mean by b0 b1 b2 and b3.

thanks for writing all this tho


Sort of. AIC (and other measures like BIC) weigh up the balance between how good a model predicts the input data and how complex the model is. Making a model more complex by adding additional predictors to the current set of predictors will ALWAYS increase predictive performance of the input data even if these new predictors are nonsense, so AIC and BIC measure how much better these predictions are, and if they aren't that much better, those more complex models are accordingly penalised and appear worse.

In terms of b0, b1, b2, b3, b4, b5, and b6, these are just numbers. So for instance, my hypothetical Model 1 looks like this:

predicted BMI = b0 + b1*calories + b2*exercise + b3*age.

If we let b0 = 12, b1 = 0.02, b2 = -0.7, and b3 = 0.3, the model becomes:

predicted BMI = 12 + 0.02*calories - 0.7*exercise + 0.3*age.

If we instead let b0 = 15, b1 = 5, b2 = -2, b3 = 1.5, the model becomes:

predicted BMI = 15 + 5*calories + -2*exercise + 1.5*age.

These different values of b0, b1, b2, and b3 will yield different predictions of BMI for the people in our data set. Maximum likelihood will find the values of b0, b1, b2, and b3 which best fit the data set.

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