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LALLAREN_1 · 12-17-2024, 05:22 PM

Hello, I am back with the product of wasting more of my time making stuff, this time nerd stuff. I had free time this week and I really need a new game to play, I’ll take tips and maybe I can find something else to do than theoretical mathematical breakdowns in an online simulation-based forum hockey league. Anyway, enough with the breakdown of my mental status.

IF YOU ONLY WANT THE RESULTS SCROLL TO THE “RESULTS” BELOW.
If you want the full background, methodology, and mental rambling I went through just keep reading.

For the analytically inclined in sports ya’ll may have run into this before.
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[Image: AD_4nXdlVkX83IGeCb-s0sEs1zPo-ak0YAH_frIr...LjEULtPwfF]

This is a draft value chart. The one shown above is the original, made by Michael Vernon McCoy in the late 80's. McCoy was a minority shareholder in the Dallas Stars and some time there in the late ’80s (yeah I wish I knew the exact time too) he made this chart for the then-head coach Jimmy Johnson. This chart was made by analyzing previous trades over decades to attempt to ascertain the “perceived value” of each pick. This was not made to be a definitive value guide, it was only showing the historical trends and perceived value of the picks. If you are a Cowboys fan or follow NFL history you are likely aware of the Herschel Walker trade. Tl;dr, Cowboys trade superstar Herschel Walker to the Vikings for a boatload of picks. They used these picks to select several Hall-of-Famers and build their little dynasty in the ‘90s from this trade more or less. Success has the funny ability to create copycats and mimicry (They do say mimicry is the more sincere form of flattery). Other teams caught on to how this was achieved and the value chart went from a little guidebook to help Johnson, to an established definitive chart. As it spread in the NFL similar have been made over the years for all the big American sports that have drafts. So that leads us to here and now. SHL has a draft, we have picks sooooooo why not try my hand at making a chart like this? This is for the SMHJL, I may very well do the same for the SHL someday, but not today.

So where to start? The NFL, NHL, and all the rest are made by analyzing trades involving known picks and forming a graph based on it. You can read about how an NHL one is made here. Ok, not too hard there is an archived forum section for all transactions including trades. Just go on there, yoink a good sample, and plug it in, right? Well, I wish it was that easy. The issue you immediately run into is that a vast VAST majority of trades involve futures. The goal I am setting out to find is the PERCEIVED value and futures make that kinda impossible cause they are so uncertain. What I, you, or a GM values a team’s 2nd round pick 3 drafts from now will differ so wildly that it is impossible to try to build anything cohesive. So that makes the sample of in-draft trades very small. I need trades that are only made up of picks and all those picks are contained in the same draft. I went back to S68 looking through trades and I found 7 instances of in-draft trades. That’s cool but making a value chart on 7 trades is not a lot to work off of. But that ain’t stopping me, here is what I have to work with if just use in-draft trades.
Numbers are what picks they are if it wasn’t somehow clear
2 = 6 + 31
5 = 10 + 38
7 = 14 + 46
24 = 33 + 45
26 = 38 + 40
32 = 37 + 40
42 = 54 + 66

So here comes the math part. Draft charts are all kinda “Exponential Decay Functions”, a fancy way of saying each pick is worth less than the one that came before by a certain amount. I’m useless at math so I can’t tell you too much but here is the formula: V(n) = a * b^{-n}
V(n) = value of the pick
a = is the initial value
b = is the decay factor
n = is the pick we are measuring
I’m setting a = 100 which is a fancy way of saying I'm making pick 1 worth 100. For the b which is the the decay factor, imma need to keep it real with you. I just brute-forced this one trying stuff until I found one I felt was the best. I concluded 0.95 was best which you’ll soon see why. So here is the graph this makes:
[Image: AD_4nXc0NC38vhJdekBUNL9HhnuOJs1v83s7BGdw...LjEULtPwfF]

[Image: AD_4nXc0NC38vhJdekBUNL9HhnuOJs1v83s7BGdw...LjEULtPwfF]

Just looking at it, it looks, plausible, yet there are definitely some faults here. The issue lies with the “Exponential Decay Function”. It makes the graph with this set slope. The very limited data I have just doesn't make for a very useful interpolated graph. So despite the limitations, I really like this. How does this graph value the actual trades above? These are real trades so we expect it to be decently close.

The left equation is the combined value as shown from the graph. In the ( ) is the trade itself again.
95 = 98 (2 = 6 + 31)
81 = 78 (5 = 10 + 38)
73 = 62 (7 = 14 + 46)
31 = 31 (24 = 33 + 45)
28 = 28 (26 = 38 + 40)
20 = 28 (32 = 37 + 40)

Not bad, it’s actually closer to reality than I thought it would be ngl. So this is the graph then showing value? Well kinda yeah but it’s a darn shame that we’re limited to so little data.

I'll stop teasing you. There is another way unique to the SHL and similar online stuff that isn’t possible in real life I can use here to gain many more data points that are accurate. Remember the reason we use known draft picks, it’s cause we don’t want the uncertainty unknown picks add. What else is known at the time of a trade? Well, the other point trades exist for, players! In real life using players' values is kinda hard outside baseball, baseball has WAR that is good enough to gauge individual value. We have game score! I AM KIDDING, game score is fakking useless. We have TPE. Rental players in their 2nd, 3rd, and 4th seasons are all at known caps, especially 3rd and 4th season players. So this gives me a new data point to use, how much is a single season of a 425 TPE player worth in draft picks?

Now, while there are many trades involving players. I want trades where all assets are known, no futures. That actually cut down on the sample by a significant amount but I still got a few.
Picks = TPE
16 + 18 + 42 + 48 = 4x 425 players (it’s 2 players for 2 seasons but for the math making it 4 players is better)
31 = 425
42 = 425
32 = 425
40 = 350
47 = 300

I think it’s rather easy to see that 30-32 area is what it takes to get a 425 TPE player for one season. I am discarding that 42 one cause it’s an outlier and I am making the graph so sue me. I am also taking the executive decision to combine that first trade like this (16 + 48 = 2x 425) AND (18 + 42 2x 425), then bake these into 17 = 2x425. Yes, I know I might lose some detail but shush this is close enough, and I am not a math guy so I am allowed to do whatever I want.
Aight so let's plug these into a graph and see what it looks like:
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Yes, I got a new graph site, the old one wanted money and they can f*** right off.

Looks good and similar to the other one. That could be because this one has a decay factor of 0.9544, only 0.0044 more than the arbitrary one I used for the other graph.
I don’t like that it focuses more on the later picks than the 17 and 31 ones. Tweaking the formula ever so slightly to .9566, improves the accuracy. So with a formula in hand, here is the chart:
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Now, invoking the crackpot hypothesis which says “Does your outcome look real, if not you probably fucked something up” and ehhhhhhh. Don’t get me wrong it correctly has what the real trades have gone for, so there is a lot of real value in here. The fundamental issue in this chart is simply that the largest pick traded is 16. The issue is that the value of the picks tends to go up exponentially around 10ish so this likely does not capture how much TPE in theory you could buy with the 1OA pick. So while I’d take anything before 16ish with a heavy dose of salt, this still does very well capture the value of 15 <.

We have the multipliers from the first graph I made so if I insert those in the top picks to adjust for the exponential nature we could generate something else. The picks chart has a higher multiplication factor for the top 5 picks than this TPE chart has. If I change the multiplication factor using the same as the picks chart, we get this instead:

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[Image: AD_4nXfm8mpib8phskWGzBfbRpvYok7iFeJ_IXfq...LjEULtPwfF]

This looks better, it has the value correct from the trades and also takes into account the exponential value we expect from the higher picks. So using the historical precedent, you could trade for about 2300 TPE worth of player(s). I know that this will never happen. The teams that have Top5 picks likely are not looking to buy rental players. But for fun and theory, this is what taking the precedent and running with it could yield.

So now comes the big challenge, creating the final, unified chart for pick value. Taking what we’ve learned from all the chart-making and spreadsheet writing, I have made my pick value chart. Without too much difficulty, here it is:
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[Image: AD_4nXe3Afm4P9ZuRVDC2P-DSqSYSB20r8B61gpt...LjEULtPwfF]

While having a chart is cool and all, we need to field-test this thing to know if it is actually rooted in reality.
Here are a few real trades done by GMs as gone through above in the first graph with their value:

2 = 6 + 31 (400 = 389)
5 = 10 + 38 (300 = 313)
7 = 14 + 46 (280 = 267)
24 = 33 + 45 (153 = 127)
26 = 38 + 40 (135 = 124)
32 = 37 + 40 (94 = 124)

It’s almost damn spot on with the big trades and once we hit the 3rd round I don’t even think it is wrong that some of those are probably “overpays”. So it works for picks, now let's try for players (TPE).

We established in the core of this article that pick 31 = 1 season of a 425 rental. 17 = 2 seasons of a 425 player or 2 425 players for one season. By this logic then my draft chart should value 2 31st picks close to a 17th pick. Does it? 17 = 196, 31 = 99 (x2 = 198). I’ll be damned that is spot on. The value to TPE is basically translatable now too.

RESULT
So once again, here is the final graph that has both pick-to-pick and pick-to-TPE values in one.
Open image in new tab to get a much more readable version
[Image: AD_4nXe3Afm4P9ZuRVDC2P-DSqSYSB20r8B61gpt...LjEULtPwfF]

I STRESS ONCE AGAIN, THIS IS BASED ON THE HISTORY OF TRADES BY SMJHL GMs. IT’S HISTORICAL AND USE IT FOR PERSPECTIVE, NOT GOSPEL TO BASE AND VALUE ALL FUTURE TRADES ON!

(1912 words) + charts