Sabermetrics in HoSS - Ranking Figures

[Sheep]

If you're familiar with Baseball, or really any sport for that matter, advanced stats/analysis have taken a rise in how those sports look at players. I was wondering if we could use a similar system to rank figures in Heroscape (and since I work for HoSS and there aren't as many figures, yet, as there are in Classic 'Scape, I figured I'd start with HoSS figures ).

So if you aren't familiar with Sabermetrics, like I've stated, it's the advanced stats/analysis in sports. Examples include stats like WAR (Wins Above Replacement), OPS (On-base % + Slugging %), and FIP (Fielding Independent Pitching) in baseball, or QB Rating in football.

So let's get started with HoSS figures. The formula I'm using is this:

(Life + Move + Range + Attack + Defense) x Points* / 1000 x A1

= WBR (Wins Before Replacement)

A1 = If Common Squad, 9.143; If Unique Squad, N/A; If Common Hero, N/A; If Uncommon Hero, 1.875; If Unique Hero, 1 (These numbers are subject to change**)
*If Common or Unique Squad, Points / Number of Figures in Squad

Originally Posted by HoSS Units WBR (Highest to Lowest)

1. 7.13 AT-ST
2. 5.28 Darth Vader
3. 4.25 Boba Fett
4. 4.13 Wampa
5. 3.91 A-Zulmun
6. 3.60 IG-88B
7. 3.41 Rebel Snow Troopers
8. 3.25 Bossk
9. 3.20 Snowtroopers
10. 3.00 Han Solo
11. 2.92 Stormtroopers
12. 2.88 Grand Moff Tarkin
13. 2.87 Imperial Officer
14. 2.85 Obi-Wan Kenobi
15. 2.74 Death Star Troopers
16. 2.68 Rebel Troopers
17. 2.63 E-Web Trooper
18. 2.55 Average Unit
19. 2.44 Rebel Captain
20. 2.42 Dengar
21. 2.40 Chewbacca
22. 2.31 4-LOM
23. 2.20 Major Derlin
24. 2.10 General Veers
25. 2.10 Princess Leia Organa
26. 2.07 Rebel Heavy Gunner
27. 2.00 Zuckuss
28. 1.98 Luke Skywalker
29. 1.98 Tusken Raiders
30. 1.31 Atgar Cannon
31. 0.88 Jawas
32. 0.84 Probe Droid
33. 0.63 Greedo
34. 0.55 2-1B
35. 0.39 R2-D2
36. 0.09 C-3PO

WBR - A2

= WAR (Wins After Replacement)

A2 = Units Combined WBR / Number of Units (Currently 2.55)
(This number is subject to change)

Originally Posted by HoSS Units WAR (Highest to Lowest)

1. 4.58 AT-ST
2. 2.73 Darth Vader
3. 1.70 Boba Fett
4. 1.58 Wampa
5. 1.36 A-Zulmun
6. 1.05 IG-88B
7. 0.86 Rebel Snow Troopers
8. 0.70 Bossk
9. 0.65 Snowtroopers
10. 0.45 Han Solo
11. 0.37 Stormtroopers
12. 0.33 Grand Moff Tarkin
13. 0.32 Imperial Officer
14. 0.30 Obi-Wan Kenobi
15. 0.20 Death Star Troopers
16. 0.13 Rebel Troopers
17. 0.08 E-Web Trooper
18. 0.00 Average Unit
19. -0.11 Rebel Captain
20. -0.13 Dengar
21. -0.15 Chewbacca
22. -0.24 4-LOM
23. -0.35 Major Derlin
24. -0.45 General Veers
25. -0.45 Princess Leia Organa
26. -0.48 Rebel Heavy Gunner
27. -0.55 Zuckuss
28. -0.57 Luke Skywalker
29. -0.57 Tusken Raiders
30. -1.24 Atgar Cannon
31. -1.67 Jawas
32. -1.71 Probe Droid
33. -1.92 Greedo
34. -2.00 2-1B
35. -2.16 R2-D2
36. -2.46 C-3PO

**The way I figured out the numbers to multiply by for the units was this:

Common Squads (7):

6 = 2 x Death Star Troopers
8 = 2 x Jawas
6 = 2 x Rebel Snow Troopers
12 = 4 x Rebel Troopers
6 = 2 x Snowtroopers
8 = 2 x Stormtroopers
18 = 6 x Tusken Raiders

6 + 8 + 6 + 12 + 6 + 8 + 18 = 64 / 7 = 9.143

Unique Squads (0):

N/A

Common Heroes (0):

N/A

Uncommon Heroes (8):

1 x Atgar Cannon
1.5 x AT-ST
2 x E-Web Trooper
2 x Imperial Officer
1.5 x Probe Droid
2 x Rebel Captain
3 x Rebel Heavy Gunner
2 x Wampa

1 + 1.5 + 2 + 2 + 1.5 + 2 + 3 + 2 = 15 / 8 = 1.875

This is basically saying that there are an average of 9.143 Common Squad figures and 1.875 Uncommon Heroes in a 500pt Army. Obviously, since you can only have one Unique Hero in an army, that's why you only multiply a Unique Hero's WBR by 1.

That's why the AT-ST is way above Vader. Because it's pretty much combining the WBR of about 2 AT-STs.

Hope you guys enjoyed this! Thoughts and concerns/criticism are greatly welcomed! It's not perfect.

[Tai-Pan]

Uh.... Cool....

What exactly does this tell me?

I'm leaning towards, "Statistically best units" (statistically meaning the numbers alone, exluding special abilities), but I'm not sure.

[Dysole]

Theoretically. I've thought about applying sabermetrics to Scape before but it's significantly harder to come to how well a figure provides a Scape win. hs2010's system assumes that an extra point of move, range, attack, and defense are equally weighted. I find this assumption tenuous at best. It's debatable whether these stats are even equally weighted within themselves. In baseball a single counts for the same value no matter who hits it. However, here the jump from say 4 to 5 move is greater than the jump from 6 to 7 move. It is further complicated by attack and defense values not seeming to take into account things that subtract dice, add auto skulls or shields, or double the value of skulls or shields. It is not a bad initial effort but it has a lot of assumptions built into it that I don't think help with what it's trying to accomplish. I think a better starting place would be something like KAR (Kills Above Replacement). That is significantly easier to sort out than figuring out WAR for Scape since so many factors contribute to that including positioning and maps that WAR is going to be a titch more complicated for Scape.

~Dysole, who has a spreadsheet with all Scape figures (parsed out in sections of Classic, Classic - DND, and Classic + VC) and when he tried to just do a simple regression started running into these issues

[Killometer]

Originally Posted by Dysole

However, here the jump from say 4 to 5 move is greater than the jump from 6 to 7 move.

Excellent point. Any ideas on the maths for diminishing returns?

[Dysole]

Originally Posted by Killometer

Excellent point. Any ideas on the maths for diminishing returns?

I think what might be better is to figure out the "average distance" on tournament maps and then you can see where the jump is more useful. You could probably make something like "average distance" with and without elevation included so we could compare fliers to other fliers.

Barring that and wanting to put it in isolation you could assign weights to move beyond a certain value. Not too certain precisely what to do but that's my initial stab at it.

~Dysole, glad at least someone appreciates one of his quirks

[Killometer]

Originally Posted by Dysole

I think what might be better is to figure out the "average distance" on tournament maps and then you can see where the jump is more useful. You could probably make something like "average distance" with and without elevation included so we could compare fliers to other fliers.

Interesting idea, but then what about distance to glyphs and high ground and paths that rely on cover, etc., not to mention alternate styles of play like HoB, or atypical maps, or goal-oriented/scenario objectives, or...

Unless it's something that's on the card (Deadly Strike, for example), Master Stats are probably best considered in a vacuum, imo.

[Dysole]

This is another reason why sabermetrics will have to be modified a fair bit transitioning from baseball to Heroscape. The rules of baseball are fairly uniform with really the only difference being needing to account for park effects. But that slight adjustment isn't the same as the vast majority of maps being different and different formats. It'd be more akin to having baseball where some stadiums had 60 feet between bases and others had 100 feet or there was a format of baseball where you only started with three guys on the field but could add players in as the game went on. It's not an easy transition but I'm not saying it's impossible. I do think the vacuum approach is probably better.

~Dysole, running possibilities

[Agent Minivann]

I think the biggest issue with applying sabermetrics principles to Heroscape is that the Heroscape minis are closer to skills of the "sport", and the Heroscape player is what the stats should track. The player is a big variable, and I'm not talking about the relative size of player vs minis. The problem there is data. We have the stats for the minis, but less so for the players.

[Dysole]

Originally Posted by Agent Minivann

I think the biggest issue with applying sabermetrics principles to Heroscape is that the Heroscape minis are closer to skills of the "sport", and the Heroscape player is what the stats should track. The player is a big variable, and I'm not talking about the relative size of player vs minis. The problem there is data. We have the stats for the minis, but less so for the players.

Excellent point. It does mean that something like dok's analysis of Gencon players or someone doing something similar with the OHS rankings would be more akin to sabermetrics. I'll have to think on this.

~Dysole, finding it funny how many people can kind of sort of disagree on numbers

[Sheep]

Yeah, Dysole, this definitely doesn't account for everything. Which is what I was hoping discussion would help with. I was hoping multiplying by the points would somewhat incorporate the powers side of it (without going into major depth), though.

It also doesn't account for any of the left card stats (Species, Uniqueticity, Class, Personality, and Size), which is a bust.

As far as Sabermetrics would be better if applied to the players, instead of the units, I think you could say that for anything. Just because a bad player drafts A+ Q9, doesn't mean that bad player can use Q9 to his A+ value.

Using sabermetrics to measure HS Units is basically a different way of going about the Power Rankings, IMO. I debated to myself before making this thread on how different it would be compared to the Power Rankings, but I guess you can't know unless you try.

As far as improving on this system, I think making a 1-5 (maybe 1-10) scale on how useful a specific power or left card stat is would up the usefulness of the Sabermetrics.

[Seraph]

When it comes to adding the value for stats, perhaps you could use a chart to give each value of each stat a point value.
These numbers are totally just for example:

Move: 1=1pt, 2=2pt, 3=3pt, 4=5pt, 6=7pt, 7=10pt, 8=12pt, 9=14pt, 10=15pt
Range: 1=5pt, 2=6pt, 3=7pt, 4=10pt, 5=13pt, 6=16pt...

This type of valuing could account for both hitting the magic number of a stat, as well as getting diminishing returns above a certain point. The point values could then be added together. Or perhaps relevant numbers would be multiplied together or averaged (like range and attack - maybe even move). You could get really crazy like SQROOT{MOVE*[SQROOT(RANGE*ATTACK)+DEFENSE]+LIFE^2}. Putting in the point values for the stats and not the actual raw stat values.

[Dysole]

Originally Posted by heroscaper2010

Yeah, Dysole, this definitely doesn't account for everything. Which is what I was hoping discussion would help with. I was hoping multiplying by the points would somewhat incorporate the powers side of it (without going into major depth), though.

It also doesn't account for any of the left card stats (Species, Uniqueticity, Class, Personality, and Size), which is a bust.

As far as Sabermetrics would be better if applied to the players, instead of the units, I think you could say that for anything. Just because a bad player drafts A+ Q9, doesn't mean that bad player can use Q9 to his A+ value.

Using sabermetrics to measure HS Units is basically a different way of going about the Power Rankings, IMO. I debated to myself before making this thread on how different it would be compared to the Power Rankings, but I guess you can't know unless you try.

As far as improving on this system, I think making a 1-5 (maybe 1-10) scale on how useful a specific power or left card stat is would up the usefulness of the Sabermetrics.

I set up a spreadsheet wherein I have all the figures with average values calculated out and how each figure is at or above that average value (although I really need to parse it out so unique heroes are compared with unique heroes, common squads with common squads et al.)

However, this information while useful is only okay in a vacuum. It sounds like you were attempting to discover a similar thing wherein I had this data set up and ran a regression on it (and then would later incorporate things). My model had the base stats including life (actually it was more life units per card), points, attacks per card, uniqueness, hero/squad, flight, disengage, and a few other things that were fairly easy to build a model off of. I left it a little while back simply because life got hectic but my goal with it was similar to yours.

Improvement in this particular area may be weights of some sort as previously mentioned. There might be some other areas but Heroscape is such a hard game to apply consistent and viable mathematical values to. (considering others have tried stuff like this before)

~Dysole, who really should revisit this stuff