BuzzerBeater Forums

TL; DR: I think the two players are similar.

It seemed that the discussion went into a debate, but I just want to try to answer the OP's question by some simulation.

The OP's situations is to choose among two candidates.
Candidate 1: 18yo, 3/5/C+, 6'7", SF
Candidate 2: 19yo, 5/5/A+, 6'7", PF
Goal: Find the best strategy to pick a good candidate who eventually grows as a SF.

My assumptions:
1. The ten player skills are independently (to other skill and height/potential) and uniformly distributed between 1.00 to 7.99 for 18 yo and 1.00 to 8.99 for 19 yo (could be argued, especially that for MVP+ potentials, skill distribution might be leaning toward the high end side, but no one except Marin knows the actual distribution).
2. C+ means 2000-2200 in salary and A+ means 3400+. I made this assumption from another guy's draft data in season 48.
3. I don't have the updated salary formula. Used CoachParrot plus a simple scaling on my own so that it should be within 2% most of the time from BuzzerManager's estimation.
4. The OP wants a SF prospect, so only the TSP matters.

The simulation:
1. Randomly generate players until salary/ position fall in the right range.
2. Round the skills to integers (anyway, no one sees the decimal from the draft ;) ).
3. Repeat 10k times, make histograms.

The results:

The 1%/5%/10%/20%/30%/40%/50%/60%/70%/80%/90%/95%/99% percentiles for the two situations are:

For the 18yo: 33/36/38/39/41/42/43/44/45/46/48/49/52; average=42.87.
For the 19yo: 42/45/47/49/51/53/54/55/57/59/61/63/67; average=54.04.

Picture:

Analysis:
How much difference in TSP from a 18 and a 19 equalizes the value of the two player? It's probably true that the 18yo will get 15p+ in his first year with good training, but there is a training cost... So the expected market value of the two players might be quite close!

Personal thought:
1. I would probably pick whomever, sell him, and buy a real good one from the TL. The OP is from the U.S. so it should be easy to find the right man with the right flag!
2. If you want to change something in the generation, please suggest, maybe I can do one or two when I have the time ;).

Last edited by Feizai Passing by at 8/24/2020 7:34:16 PM

You don't need to go through all this trouble though: the minimum TSP of a SF in that range is 31 and the maximum is 54. So yeah, if it was completely random you'd expect a TSP of around 43.

The 19yo however is probably incorrect, because the theoretical minimum for a 5.5k PF is 39, but the maximum is actually 80.

How many of your simulations fell within the salary range and in the correct salary formula?

Last edited by Lemonshine at 8/24/2020 9:57:45 PM

It's his assumption, not mine.

Last edited by Lemonshine at 8/25/2020 4:56:53 AM

Glad you liked it!

First I want to make a remark before the reply. Yesterday after the post, someone told me that Joey Ka reverse engineered BuzzerManager's formula in season 48, (160760.16), which should be much reliable than what I was doing. Maybe I will implement that when I have time, but below is based on what was on my post.

(1) I don't know how you rounded the numbers. It is very important because if you rounded them to the closest integer, the player will look on average 5 points better than what you look on the webpage. But if you use the floor function, the salary will be understimated.

Since I need to make my own estimate on the salary by re-calibrating CoachParrot's formulas, I scaled it so that my estimated salaries. It goes in the way that, when estimating skills as integers, are close to BuzzerManager's estimation, which seemed to estimate skills as half integers. And skills are indeed randomized between [0.5, 7,49] and [0.5, 8.49] for 18yo and 19yo, respectively (you caught me). By doing so there is neither the 5-point-average problem or the salary underestimate problem as you stated; the main issue is the reliability of the formula.

(2) Just as a theoretic question, I don't know if a Monte Carlo simulation is necessary or if you can be exhaustive.

When we have to round the player skill to integers {1, ...,, it is already a equal-distanced sampling rather than an exhaustive search, so it only provides another good estimate.

Skipping all the details, I'd say the full 8^10 searches will take probably 12-24 hours in my configuration, and maybe in minutes in a high spec computer and optimized code. But again, that is still only a good estimation since the actual parameter space is in floating numbers.

Below is for your older reply.

A second point is that 15 pops seems too optimistic.

15 points in the first season is based on the fact that most people train One to one for their SF trainee these days. So when I say what is the TSP difference for a 18yo and a 19yo to have the same market value, I'd say 15 is an upper bound. But it certainly should be lower. I would refrain for saying more since I didn't really made an investigation on the marker value for 9p+, so it is up to all of you to interpret anything from my last post.

How many of your simulations fell within the salary range and in the correct salary formula?

That's a good question. I don't know, since I didn't make a counter and just discarded everything not meeting the criteria. I think it should be something in the magnitude like 50-100 player generated to get one qualified.

You don't need to go through all this trouble though: the minimum TSP of a SF in that range is 31 and the maximum is 54. So yeah, if it was completely random you'd expect a TSP of around 43.

The 19yo however is probably incorrect, because the theoretical minimum for a 5.5k PF is 39, but the maximum is actually 80.

My assumption is that every skill is i.i.d. uniform distribution in the interval [1.0, 7.99] or [1.0, 8.99], but the TSP will not be a uniform distribution in the interval [10, 79.9] or [10, 89.9].

Here is a discrete version of the problem. Suppose you throw 10 identical 6-faced dices. Suppose you know that the sum of dices are >=40, what is the expected value of the sum of dices? The answer is indeed lower than 50.

Your estimation relies on the fact that the distribution of the TSP is symmetric within the range of the TSP, which is not guaranteed (although it seemed to be more symmetric than the dice situation above). So I would say that at most it is a reasonable estimation.

But anyway, I tried to emulate the total distribution, and hope it helps those who have different criteria when making their decision: some might be conservative and look at the 30% percentile, while some others may look into the extreme case and bet for the top 1% guy. Your call