Health of banner items

[KerrAvon]

@dr_ishmael Congratulations. I am glad my numbers make sense. I was having trouble finding the points in my data where I moved up levels. I will need to think further on your table and do some calculations to maker sure I understand.

I also have 2 new items, one of which I thought was odd. But maybe not. They are emblems and cross over one of the bonuses.
Diamond league, lvl 16, 2-star, 713
Diamond league, lvl 16, 3-star, 813

I presume you are still working on the calculations for the emblems. No rush.

[dr_ishmael]

@kerravon This goes back to my previous post, where I talked about @killerkea’s 2/15 factor.

• Emblems have 3/8 (0.375) of the base stat of a top/flag at the same level.
• Emblems receive 5%, or 1/20, of the wood-league top/flag base stat per league above wood. For diamond league, which is 5 leagues above wood, the total bonus is 25% (0.25).
• 3/8 * 1/20 = 2/15 – This is the per-league bonus if you calculate from the emblem’s base stat. Below, I work entirely from the top/flag base stat, so 2/15 doesn’t show up there.

Working this through for your two items, then…

Diamond league, lvl 16, 2-star, 713 – The relevant base stat from my table is level 16, which is 1140.
1140 * 0.375 + 1140 * 0.25 = 427.5 + 285 = 712.5 =~ 713

Diamond league, lvl 16, 3-star, 813 – The relevant base stat from my table is level 17 (since this is a 3* item), which is 1300.
1300 * 0.375 + 1300 * 0.25 = 487.5 + 325 = 812.5 =~ 813

[KerrAvon]

@dr_ishmael So all the information I needed was there. But it’s good to have worked examples.

[Edit] I just set up a table on excel using your values. Like @killerkea, I find it much easier to work with calculations starting with a 0-star item. So I just shifted the stats and bonuses down 2 lines.

Now it is quite simple to calculate stats for each combination of level, league and stars.

[KillerKea]

@dr_ishmael I haven’t visited this site for a few days. Congratulations on finding a formula to work for each level. I thought it would take a long time to collect enough data to figure one out. One small correction 3/8 * 1/20 does not equal 2/15. It is much simpler to say that all emblems are equal to 3/8 of the same type of top/flag. In other words a 3 star gold emblem is equal to 3/8 of a 3 star gold top/flag.

[KerrAvon]

@killerkea Sorry for butting in here @dr_ishmael.

That calculation was a typo. dr_ishmael had it correct in an earlier post. It should be 1/20 divided by 3/8 or 1/20 x 8/3.

The 3/8 multiplier only works for wood league items. The multiplier applied to tops/flags and emblems when you move up a league are different (x1.0, x1.1, x1.2, x1.3 etc vs x15/15, x17/15, x19/15, 21/15 etc), which affects this relationship. You can confirm this by looking at the data in the initial post.

[dr_ishmael]

@killerkea Sorry, I didn’t explain that part very well. I’ll write out all the calculation steps this time to make sure I don’t goof anything up.

We know the emblem base stat (wood league) is 3/8 of the top/flag base stat.
1. emblem_base = 3/8 * top_flag_base

Turn that around to get:
2. top_flag_base = 8/3 * emblem_base

We know that the per-league bonus on emblems is 1/20 = 5% of the top/flag base stat.
3. emblem_league_bonus = 1/20 * league_diff * top_flag_base

Substituting for top_flag_base from equation 2, we can rewrite that in terms of emblem_base:

4.  emblem_league_bonus = 1/20 * league_diff * 8/3 * emblem_base
                        = 8/60 * league_diff * emblem_base
                        = 2/15 * league_diff * emblem_base

There’s the 2/15.

Because the per-league bonus for emblems is 1/2 that for tops/flags, while the base stat is 3/8, your final statement doesn’t hold up.

A level 41 2* Gold League top has the following stat:

3740 + 3740 * 0.1 * 3 =
3740 + 3740 * 0.3 =
3740 * 1.3 =
4862

A level 41 2* Gold League emblem has:

3740 * 0.375 + 3740 * 0.05 * 3 =
3740 * 0.375 + 3740 * 0.15 =
3740 * 0.525 =
1963.5

The numbers reported and then recorded in the OP are 4862 and 1964, so I know I got those right.

Is this 3/8?
1963.5 / 4862 = 0.4038...

Nope. If the emblem’s per-league bonus had been 3/8 of the top/flag per-league bonus (3/8 * 1/10 = 3/80 = 0.0375), then that logic would work, but it’s not.

[KillerKea]

You’re right. I quickly wrote what I thought you were trying to say, but didn’t check the math. It is not 3/8 for anything but the Wood league since the league bonus increases at 10% for tops/flags and increases by 2/15 or 13.33% for emblems. However now that you know the wood emblem is 3/8 the wood top/flag you will get accurate numbers when rounding since the 1339 number for the wood emblem now becomes 1338.75.

Therefore the 5 missing numbers for the diamond emblems should be

2231, 2284, 2338, 2391, 2444

[Abyssuss]

After the latest update health of all Set items have been decreased.

Edit: Set items from for example golden league are actually weaker than some regular items from the same league…

[t_russell]

Diamond;Set;5279;41
Platinum;Set;5083;41
Gold;Set;4888;41
Silver;Set;4692;41
Stone;Set;4497;41
Wood;Set;4301;41

Made it through stone and silver on the wood items. Didn’t see the need to pursue them. Thanks @dr_ishmael for the Stone and Silver numbers.

[dr_ishmael]

@tigerussell Level 41 Stone set items are 4497. The per-league bonus is 1/22, so Silver set items are 4692.

This means diamond set items are weaker than 0* diamond items (5279 vs 5355). This has got to be a bug.

[t_russell]

@dr_ishmael — The diamond set items are weaker than platinum three star items. Don’t know if it’s a bug but I suspect so as well. I do know that I now have a roughly 1000 point advantage in most arena matches due to my three star items beating all the saved teams with sets. Changes the whole dynamic.