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A Review of Zero-K Balance and Balance Design through the Lens of the 1v1 Environment, 2019-2026

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1 [size=5][b]Review: A Review of Zero-K Balance and Balance Design through the Lens of the 1v1 Environment, 2019-2026[/b][/size] 1 [size=5][b]Review: A Review of Zero-K Balance and Balance Design through the Lens of the 1v1 Environment, 2019-2026[/b][/size]
2 2
3 <wiki:toc /> 3 <wiki:toc />
4 4
5 = 1. Errors with no defence = 5 = 1. Errors with no defence =
6 6
7 These are internal contradictions, arithmetic errors, or undocumented methods. They need correcting regardless of what position the author takes on anything else. 7 These are internal contradictions, arithmetic errors, or undocumented methods. They need correcting regardless of what position the author takes on anything else.
8 8
9 == 1.1 Kodachi is described as both a nerf and a buff == 9 == 1.1 Kodachi is described as both a nerf and a buff ==
10 10
11 The prediction table reads: 11 The prediction table reads:
12 12
13 [quote]v1.9.1.0 Kodachi speed nerf → Tank Foundry WR ↓[/quote] 13 [quote]v1.9.1.0 Kodachi speed nerf → Tank Foundry WR ↓[/quote]
14 14
15 Figure 5's panel title confirms the direction: [q]v1.9.1.0: Kodachi speed nerf (117→108)[/q] The Steam patch note is titled [q]Slower Kodachi[/q] 15 Figure 5's panel title confirms the direction: [q]v1.9.1.0: Kodachi speed nerf (117→108)[/q] The Steam patch note is titled [q]Slower Kodachi[/q]
16 16
17 The discussion then says: 17 The discussion then says:
18 18
19 [quote]Both Kodachi and Hover displayed profound and statistically significant meta improvements after they were buffed.[/quote] 19 [quote]Both Kodachi and Hover displayed profound and statistically significant meta improvements after they were buffed.[/quote]
20 20
21 Kodachi was nerfed, the prediction was a win-rate decrease, and the observed result was a decrease. The sentence contradicts the table two pages earlier and the figure directly above it. 21 Kodachi was nerfed, the prediction was a win-rate decrease, and the observed result was a decrease. The sentence contradicts the table two pages earlier and the figure directly above it.
22 22
23 == 1.2 The Shipyard mirror-match argument is inverted == 23 == 1.2 The Shipyard mirror-match argument is inverted ==
24 24
25 [quote]It can be clearly observed that the win rate of Shipyard is entirely dependent on its high mirror match rate.[/quote] 25 [quote]It can be clearly observed that the win rate of Shipyard is entirely dependent on its high mirror match rate.[/quote]
26 26
27 Mirror matches contribute exactly 50% by construction — one Shipyard wins, one Shipyard loses. A high mirror rate pulls a factory's aggregate win rate [i]toward[/i] 50%. It cannot push it to 55.4%. 27 Mirror matches contribute exactly 50% by construction — one Shipyard wins, one Shipyard loses. A high mirror rate pulls a factory's aggregate win rate [i]toward[/i] 50%. It cannot push it to 55.4%.
28 28
29 Running the arithmetic with the paper's own numbers, at a mirror share of roughly 0.5: 29 Running the arithmetic with the paper's own numbers, at a mirror share of roughly 0.5:
30 30
31 {{{ 31 {{{
32 0.554 = 0.5(0.500) + 0.5(W_nonmirror) 32 0.554 = 0.5(0.500) + 0.5(W_nonmirror)
33 W_nonmirror ≈ 0.61 33 W_nonmirror ≈ 0.61
34 }}} 34 }}}
35 35
36 Shipyard wins roughly 61% of its non-mirror games. The mirror rate is [i]masking[/i] the imbalance, not producing it. 36 Shipyard wins roughly 61% of its non-mirror games. The mirror rate is [i]masking[/i] the imbalance, not producing it.
37 37
38 This matters because the correction supports the paper's own later position. The paper argues Shipyard is: 38 This matters because the correction supports the paper's own later position. The paper argues Shipyard is:
39 39
40 [quote]intentionally slightly overtuned in order to give it some advantage at sea[/quote] 40 [quote]intentionally slightly overtuned in order to give it some advantage at sea[/quote]
41 41
42 That claim is [b]strengthened[/b] by a mirror-excluded rate of ~61% and undercut by the current framing. As written, the two passages argue against each other. 42 That claim is [b]strengthened[/b] by a mirror-excluded rate of ~61% and undercut by the current framing. As written, the two passages argue against each other.
43 43
44 [b]Fix:[/b] recompute mirror-excluded win rates for all factories. It is a filter on the existing pipeline and it makes Figure 1 substantially more interpretable. 44 [b]Fix:[/b] recompute mirror-excluded win rates for all factories. It is a filter on the existing pipeline and it makes Figure 1 substantially more interpretable.
45 45
46 == 1.3 The b ≤ 0 case is mischaracterised == 46 == 1.3 The b ≤ 0 case is mischaracterised ==
47 47
48 [quote]If b≤0 , the system is set to overshoot and over correct balance.[/quote] 48 [quote]If b≤0 , the system is set to overshoot and over correct balance.[/quote]
49 49
50 b = 0 is [i]perfect[/i] single-period correction: the entire deviation is eliminated in one step. Overshoot begins at b < 0. As written, the paper's own criterion classifies ideal correction as failure. 50 { { { b = 0} } } is [i]perfect[/i] single-period correction: the entire deviation is eliminated in one step. Overshoot begins at b < 0. As written, the paper's own criterion classifies ideal correction as failure.
51 51
52 The same passage also contains a transcription error — [q]If b=1, no corrections are made ( no deviation) [/q] — where the parenthetical should read something like "deviation persists. " 52 The same passage also contains a transcription error — { { { If b=1, no corrections are made ( no deviation) } } } — where the parenthetical should read something like "deviation persists. "
53 53
54 == 1. 4 The p = 0. 83 test is never specified == 54 == 1. 4 The patch-direction test is never specified ==
55 55
56 This value appears three times and carries roughly half the thesis: 56 This value appears three times and carries roughly half the thesis:
57 57
58 [quote]we would end up with p value of around 0.83[/quote] 58 [quote]we would end up with p value of around 0.83[/quote]
59 59
60 [quote]shows no significant relationship between a factory's win rate and whether it subsequently gets buffed or nerfed ( p = 0. 83) [/quote] 60 [quote]shows no significant relationship between a factory's win rate and whether it subsequently gets buffed or nerfed { { { ( p = 0. 83) } } } [/quote]
61 61
62 [quote]Regarding patches directly affecting win rate, the evidence is much weaker ( p = 0. 83) [/quote] 62 [quote]Regarding patches directly affecting win rate, the evidence is much weaker { { { ( p = 0. 83) } } } [/quote]
63 63
64 The paper never states the unit of observation, the number of patches examined, how "documented nerfs or buffs" were coded, the test statistic, the effect size, or a confidence interval. 64 The paper never states the unit of observation, the number of patches examined, how "documented nerfs or buffs" were coded, the test statistic, the effect size, or a confidence interval.
65 65
66 This is more serious than an omission because the argument [b]affirms a null[/b]. "No significant relationship" only supports "balance is not mechanistic" if the test had power to detect a relationship that exists. With a small hand-coded patch set, power may be near zero, in which case p = 0. 83 is uninformative rather than evidence. 66 This is more serious than an omission because the argument [b]affirms a null[/b]. "No significant relationship" only supports "balance is not mechanistic" if the test had power to detect a relationship that exists. With a small hand-coded patch set, power may be near zero, in which case { { { p = 0. 83} } } is uninformative rather than evidence.
67 67
68 Report n, the estimate, and the CI. If the interval is wide, say so — a wide interval is an honest and still-interesting result. The GitHub repository is already cited; automated extraction of signed stat changes per version would turn this into the strongest section of the paper rather than its weakest. 68 Report n, the estimate, and the CI. If the interval is wide, say so — a wide interval is an honest and still-interesting result. The GitHub repository is already cited; automated extraction of signed stat changes per version would turn this into the strongest section of the paper rather than its weakest.
69 69
70 == 1.5 The case study claims significance without reporting any test == 70 == 1.5 The case study claims significance without reporting any test ==
71 71
72 The method is described as: 72 The method is described as:
73 73
74 [quote]we arranged a z-test where we are looking for change to justify the path within a close time from (here we set values to be measured at various increments of 30/45/90 days)[/quote] 74 [quote]we arranged a z-test where we are looking for change to justify the path within a close time from (here we set values to be measured at various increments of 30/45/90 days)[/quote]
75 75
76 No z-statistic, p-value, or confidence interval appears anywhere in Figure 5 or the surrounding text. The discussion nonetheless concludes: 76 No z-statistic, p-value, or confidence interval appears anywhere in Figure 5 or the surrounding text. The discussion nonetheless concludes:
77 77
78 [quote]These two examples are statistically significant enough where it is likely acceptable to call them strong examples that would support our theory.[/quote] 78 [quote]These two examples are statistically significant enough where it is likely acceptable to call them strong examples that would support our theory.[/quote]
79 79
80 Either report the test statistics or remove the significance language. Also state the selection rule for the four patches — with hundreds of candidates and no stated rule, a reader cannot distinguish these from cases chosen after inspecting the outcome. 80 Either report the test statistics or remove the significance language. Also state the selection rule for the four patches — with hundreds of candidates and no stated rule, a reader cannot distinguish these from cases chosen after inspecting the outcome.
81 81
82 == 1.6 Strider Hub violates the paper's own inclusion criterion == 82 == 1.6 Strider Hub violates the paper's own inclusion criterion ==
83 83
84 [quote]we only include year data from factories that have over 100 games in that year[/quote] 84 [quote]we only include year data from factories that have over 100 games in that year[/quote]
85 85
86 Strider Hub appears in Figure 1 with n = 72 across the entire 2019-2026 period, so no single year can clear the threshold. Either the rule has an unstated exception for the aggregate figure, or the row should be dropped. 86 Strider Hub appears in Figure 1 with n = 72 across the entire 2019-2026 period, so no single year can clear the threshold. Either the rule has an unstated exception for the aggregate figure, or the row should be dropped.
87 87
88 == 1.7 The stated confound is not applied consistently == 88 == 1.7 The stated confound is not applied consistently ==
89 89
90 The paper correctly flags a pre-existing trend for Spider: 90 The paper correctly flags a pre-existing trend for Spider:
91 91
92 [quote]Spider was already on an uptrend before the buff, which makes it quite hard to point to that as the sole affecting factor in this situation.[/quote] 92 [quote]Spider was already on an uptrend before the buff, which makes it quite hard to point to that as the sole affecting factor in this situation.[/quote]
93 93
94 Figure 5 shows Tank Foundry falling from roughly 60% (Aug '20) to roughly 56% (Jan '21) [i]before[/i] the Kodachi nerf. The identical confound applies and is not mentioned. Tank also recovers to roughly 53% within five months, which reads as a transient dip rather than a durable correction. 94 Figure 5 shows Tank Foundry falling from roughly 60% (Aug '20) to roughly 56% (Jan '21) [i]before[/i] the Kodachi nerf. The identical confound applies and is not mentioned. Tank also recovers to roughly 53% within five months, which reads as a transient dip rather than a durable correction.
95 95
96 The Amphbot explanation has a related problem: 96 The Amphbot explanation has a related problem:
97 97
98 [quote]this can likely be attributed to players experimenting and thus playing worse for a short period of time[/quote] 98 [quote]this can likely be attributed to players experimenting and thus playing worse for a short period of time[/quote]
99 99
100 As stated this is unfalsifiable — it would explain any post-patch decline. It becomes testable if you commit to a timescale and show recovery within it. 100 As stated this is unfalsifiable — it would explain any post-patch decline. It becomes testable if you commit to a timescale and show recovery within it.
101 101
102 ---- 102 ----
103 103
104 = 2. Statistical claims that do not survive as stated = 104 = 2. Statistical claims that do not survive as stated =
105 105
106 == 2.1 Slope 0.87 does not describe active self-correction == 106 == 2.1 Slope 0.87 does not describe active self-correction ==
107 107
108 [quote]1v1 balance does in fact exhibit a statistically significant rate of mean reversion of balance in regards to factory win rate ( slope = 0. 87, 95% CI [0. 77, 0. 97], p = 0. 009) , consistent with an actively self-correcting balance environment[/quote] 108 [quote]1v1 balance does in fact exhibit a statistically significant rate of mean reversion of balance in regards to factory win rate { { { ( slope = 0. 87, 95% CI [0. 77, 0. 97], p = 0. 009) } } } , consistent with an actively self-correcting balance environment[/quote]
109 109
110 At b = 0. 87, the half-life of a deviation is ln( 0. 5) /ln( 0. 87) ≈ [b]5 years[/b]. A factory sitting 10 points off 50% takes half a decade to close half the gap. That is distinguishable from a random walk; it is not "active" correction in any ordinary sense. 110 At { { { b = 0. 87} } } , the half-life of a deviation is ln( 0. 5) /ln( 0. 87) ≈ [b]5 years[/b]. A factory sitting 10 points off 50% takes half a decade to close half the gap. That is distinguishable from a random walk; it is not "active" correction in any ordinary sense.
111 111
112 The slower reading is also the one that fits the paper's own conclusion — that [q]meaningful imbalance can persist[/q] — considerably better than the current wording does. 112 The slower reading is also the one that fits the paper's own conclusion — that [q]meaningful imbalance can persist[/q] — considerably better than the current wording does.
113 113
114 == 2.2 The regression's leverage comes from points the paper exempts from reverting == 114 == 2.2 The regression's leverage comes from points the paper exempts from reverting ==
115 115
116 Figure 4's caption identifies the influential observations: 116 Figure 4's caption identifies the influential observations:
117 117
118 [quote]note outliers Air and Gunship at bottom left[/quote] 118 [quote]note outliers Air and Gunship at bottom left[/quote]
119 119
120 The paper elsewhere argues these factories should not revert: 120 The paper elsewhere argues these factories should not revert:
121 121
122 [quote]Some factories, such as a Gunship or Airplane, actually are intentionally balanced in a way where they primarily function as support factories, so their low win rate is intentional[/quote] 122 [quote]Some factories, such as a Gunship or Airplane, actually are intentionally balanced in a way where they primarily function as support factories, so their low win rate is intentional[/quote]
123 123
124 The points at −20 to −28 carry nearly all the leverage behind r = 0. 90 and R² = 0. 81. But for a factory that is [i]designed[/i] to sit below 50%, "low in year t, low in year t+1" measures [b]persistence, not reversion[/b]. Including them in a mean-reversion test while separately arguing they are exempt from it is not a defensible combination. 124 The points at −20 to −28 carry nearly all the leverage behind { { { r = 0. 90} } } and { { { R² = 0. 81} } } . But for a factory that is [i]designed[/i] to sit below 50%, "low in year t, low in year t+1" measures [b]persistence, not reversion[/b]. Including them in a mean-reversion test while separately arguing they are exempt from it is not a defensible combination.
125 125
126 Rerun the regression excluding designated support factories. The dense cloud within ±5 of the origin is what remains, and its slope may well have an interval spanning 1. 126 Rerun the regression excluding designated support factories. The dense cloud within ±5 of the origin is what remains, and its slope may well have an interval spanning 1.
127 127
128 == 2.3 A slope below 1 is expected even with zero real correction == 128 == 2.3 A slope below 1 is expected even with zero real correction ==
129 129
130 The predictor (win rate in year t) is measured with error, which biases the slope toward zero by a factor of var(true)/(var(true) + var(noise)). At the stated 100-game threshold, the standard error on a win rate is roughly 5 percentage points — and Airplane Plant averages about 130 games per year, so the highest-leverage points are also the noisiest. 130 The predictor (win rate in year t) is measured with error, which biases the slope toward zero by a factor of var(true)/(var(true) + var(noise)). At the stated 100-game threshold, the standard error on a win rate is roughly 5 percentage points — and Airplane Plant averages about 130 games per year, so the highest-leverage points are also the noisiest.
131 131
132 A slope of 0. 87 is consistent with b = 1 plus sampling noise. This needs either an explicit attenuation correction or an instrument: split each factory-year's games into random halves and use one half to predict the other. 132 A slope of 0. 87 is consistent with { { { b = 1} } } plus sampling noise. This needs either an explicit attenuation correction or an instrument: split each factory-year's games into random halves and use one half to predict the other.
133 133
134 == 2.4 The 74 observations are not independent == 134 == 2.4 The 74 observations are not independent ==
135 135
136 Each factory contributes roughly seven transitions, and within any year the deviations are mechanically constrained by the zero-sum property the paper itself raises: 136 Each factory contributes roughly seven transitions, and within any year the deviations are mechanically constrained by the zero-sum property the paper itself raises:
137 137
138 [quote]win rates are zero-sum in aggregate[/quote] 138 [quote]win rates are zero-sum in aggregate[/quote]
139 139
140 Both inflate precision. Cluster standard errors by factory; the interval [0. 77, 0. 97] will widen and may well cross 1. 140 Both inflate precision. Cluster standard errors by factory; the interval { { { [0. 77, 0. 97]} } } will widen and may well cross 1.
141 141
142 == 2.5 Figure 3 has a multiple-comparisons problem == 142 == 2.5 Figure 3 has a multiple-comparisons problem ==
143 143
144 Twelve correlations at n = 8 each, of which one reaches p = 0. 02 ( Shieldbot) . At α = 0. 05 across twelve tests, roughly 0. 6 false positives are expected by chance. The caption already warns about power; it should also note multiplicity, or apply a correction. 144 Twelve correlations at { { { n = 8} } } each, of which one reaches { { { p = 0. 02} } } ( Shieldbot) . At { { { α = 0. 05} } } across twelve tests, roughly 0. 6 false positives are expected by chance. The caption already warns about power; it should also note multiplicity, or apply a correction.
145 145
146 The surrounding prose also conflates two distinct questions. Figures 1-2 concern the [i]between-factory[/i] relationship ("do popular factories win more?"); Figure 3 concerns the [i]within-factory over time[/i] relationship ("when a factory gets more popular, does it win more?"). The claim 146 The surrounding prose also conflates two distinct questions. Figures 1-2 concern the [i]between-factory[/i] relationship ("do popular factories win more?"); Figure 3 concerns the [i]within-factory over time[/i] relationship ("when a factory gets more popular, does it win more?"). The claim
147 147
148 [quote]there is no strong correlation with pick to win rate[/quote] 148 [quote]there is no strong correlation with pick to win rate[/quote]
149 149
150 is the first question, but the evidence offered is the second. The between-factory version is one rank correlation across twelve points and should be reported directly. 150 is the first question, but the evidence offered is the second. The between-factory version is one rank correlation across twelve points and should be reported directly.
151 151
152 ---- 152 ----
153 153
154 = 3. What the win-rate variable actually measures = 154 = 3. What the win-rate variable actually measures =
155 155
156 This section is the most consequential, because it applies to every number in the paper. 156 This section is the most consequential, because it applies to every number in the paper.
157 157
158 == 3.1 The unit of observation is the opening factory, and is never stated == 158 == 3.1 The unit of observation is the opening factory, and is never stated ==
159 159
160 Factory counts in Figure 1 sum to roughly 178,400 across 90,024 matches — almost exactly two observations per match, i.e. one factory per player. Since players routinely build additional factories, the dataset cannot be "factories used." It is the [b]opener[/b]. 160 Factory counts in Figure 1 sum to roughly 178,400 across 90,024 matches — almost exactly two observations per match, i.e. one factory per player. Since players routinely build additional factories, the dataset cannot be "factories used." It is the [b]opener[/b].
161 161
162 Figure 1 is therefore an opening-viability chart, not a factory-strength chart. These are different objects and the paper treats them as one. 162 Figure 1 is therefore an opening-viability chart, not a factory-strength chart. These are different objects and the paper treats them as one.
163 163
164 This is clearest with Airplane Plant at 27%. The paper reads the wiki as evidence of intentional weakness: 164 This is clearest with Airplane Plant at 27%. The paper reads the wiki as evidence of intentional weakness:
165 165
166 [quote]Cf. Zero-K wiki, describes Airplane Plant units as "more like a support force, as opposed to combat units"[/quote] 166 [quote]Cf. Zero-K wiki, describes Airplane Plant units as "more like a support force, as opposed to combat units"[/quote]
167 167
168 But that describes air's [i]role in a composition[/i] — something added alongside a ground factory — not weak units. The 27% measures the cost of spending an opening on a factory that doesn't contest map or answer an early raider push. It contains essentially no information about air unit statistics. 168 But that describes air's [i]role in a composition[/i] — something added alongside a ground factory — not weak units. The 27% measures the cost of spending an opening on a factory that doesn't contest map or answer an early raider push. It contains essentially no information about air unit statistics.
169 169
170 Which means the damping model cannot apply to this factory even in principle: 170 Which means the damping model cannot apply to this factory even in principle:
171 171
172 [quote]V t+1=V t−k ( Rt−Rtarget) [/quote] 172 { { { V t+1=V t−k ( Rt−Rtarget) } } }
173 173
174 There is no adjustment to air unit stats that makes [i]opening[/i] Air correct. The failure is one of timing and structure, not numbers — which is precisely the insight the paper reaches in its conclusion for Shipyard and misses for Air. 174 There is no adjustment to air unit stats that makes [i]opening[/i] Air correct. The failure is one of timing and structure, not numbers — which is precisely the insight the paper reaches in its conclusion for Shipyard and misses for Air.
175 175
176 == 3.2 Rating absorbs strategy strength into the player number == 176 == 3.2 Rating absorbs strategy strength into the player number ==
177 177
178 Matchmaking equilibrates players, not strategies. A player who mains a strong factory climbs until facing opponents who beat them half the time — at which point their games with that factory read ~50% regardless of how strong it is. The factory's advantage has been laundered into MMR. 178 Matchmaking equilibrates players, not strategies. A player who mains a strong factory climbs until facing opponents who beat them half the time — at which point their games with that factory read ~50% regardless of how strong it is. The factory's advantage has been laundered into MMR.
179 179
180 So a factory's deviation from 50% is not its strength; it is roughly the [i]within-player delta[/i] between that factory and whatever the player's rating was calibrated on. The paper's own data shows the signature. Sorting by sample size: 180 So a factory's deviation from 50% is not its strength; it is roughly the [i]within-player delta[/i] between that factory and whatever the player's rating was calibrated on. The paper's own data shows the signature. Sorting by sample size:
181 181
182 || [b]Factory (n)[/b] || [b]Absolute deviation from 50%[/b] || 182 || [b]Factory (n)[/b] || [b]Absolute deviation from 50%[/b] ||
183 || Cloak (46,482) || ~0.4 || 183 || Cloak (46,482) || ~0.4 ||
184 || Rover (28,475) || ~1.5 || 184 || Rover (28,475) || ~1.5 ||
185 || Tank (19,449) || ~1 || 185 || Tank (19,449) || ~1 ||
186 || Spider (19,443) || ~0.5 || 186 || Spider (19,443) || ~0.5 ||
187 || Shield (15,722) || ~3 || 187 || Shield (15,722) || ~3 ||
188 || Hover (14,897) || ~1 || 188 || Hover (14,897) || ~1 ||
189 || Amphbot (12,285) || ~3 || 189 || Amphbot (12,285) || ~3 ||
190 || Jumpbot (12,029) || ~0.5 || 190 || Jumpbot (12,029) || ~0.5 ||
191 || Shipyard (4,634) || ~5.4 || 191 || Shipyard (4,634) || ~5.4 ||
192 || Gunship (3,857) || ~10 || 192 || Gunship (3,857) || ~10 ||
193 || Air (1,055) || ~23 || 193 || Air (1,055) || ~23 ||
194 || Strider (72) || ~29 || 194 || Strider (72) || ~29 ||
195 195
196 Nearly monotonic. Every common factory is pinned near 50; every deviation lives in the rare tail — and in [b]both directions[/b], since Shipyard and Amphbot deviate upward. The support-factory explanation covers only the downward cases. Rarity predicting distance from 50 regardless of sign is the signature of rating absorption, not of design intent. Sampling noise contributes, but noise alone would not produce this clean a rank ordering. 196 Nearly monotonic. Every common factory is pinned near 50; every deviation lives in the rare tail — and in [b]both directions[/b], since Shipyard and Amphbot deviate upward. The support-factory explanation covers only the downward cases. Rarity predicting distance from 50 regardless of sign is the signature of rating absorption, not of design intent. Sampling noise contributes, but noise alone would not produce this clean a rank ordering.
197 197
198 The consequence for the headline result: rating recalibration is [i]itself[/i] a mean-reverting process operating on roughly the timescale of the regression. A player who switches to a strong factory wins, gains rating, and returns to 50% with no patch involved. The slope of 0.87 may be measuring the matchmaker re-equilibrating. 198 The consequence for the headline result: rating recalibration is [i]itself[/i] a mean-reverting process operating on roughly the timescale of the regression. A player who switches to a strong factory wins, gains rating, and returns to 50% with no patch involved. The slope of 0.87 may be measuring the matchmaker re-equilibrating.
199 199
200 The paper gestures at this but characterises it as human learning: 200 The paper gestures at this but characterises it as human learning:
201 201
202 [quote]player meta-adaptation that happens independent of any patch[/quote] 202 [quote]player meta-adaptation that happens independent of any patch[/quote]
203 203
204 Rating absorption is mechanical — it occurs even if no player adapts, learns, or notices. It is a null model that produces the paper's central finding for free, and it needs to be stated and ruled out rather than folded into meta-adaptation. It is arguably corroborated by the paper's own p = 0. 83: patches fail to predict correction because much of the correction is the ladder. 204 Rating absorption is mechanical — it occurs even if no player adapts, learns, or notices. It is a null model that produces the paper's central finding for free, and it needs to be stated and ruled out rather than folded into meta-adaptation. It is arguably corroborated by the paper's own { { { p = 0. 83} } } : patches fail to predict correction because much of the correction is the ladder.
205 205
206 == 3.3 The opener tag decays exactly where balance matters most == 206 == 3.3 The opener tag decays exactly where balance matters most ==
207 207
208 In high-level play, neither player is typically eliminated in the opening window; games become macro contests with multiple factories, static defence, and silos on both sides. The tagged factory is then a label on a transient, and the win credited to it may have been produced by a composition built twenty minutes later. 208 In high-level play, neither player is typically eliminated in the opening window; games become macro contests with multiple factories, static defence, and silos on both sides. The tagged factory is then a label on a transient, and the win credited to it may have been produced by a composition built twenty minutes later.
209 209
210 This creates an asymmetry the paper never addresses: the tag is most informative in low-rated games, where openers actually decide outcomes, and least informative at the top. The aggregate is a weighted average across that gradient with no stratification. 210 This creates an asymmetry the paper never addresses: the tag is most informative in low-rated games, where openers actually decide outcomes, and least informative at the top. The aggregate is a weighted average across that gradient with no stratification.
211 211
212 It can also invert. If Cloak is the safest opener into an unknown, players intending a long macro game open Cloak [i]because[/i] it survives to reach the macro phase — and Cloak is then credited with wins that Tank or Air produced. Cloak's 49.6% across 46,482 games is close to uninformative for this reason. 212 It can also invert. If Cloak is the safest opener into an unknown, players intending a long macro game open Cloak [i]because[/i] it survives to reach the macro phase — and Cloak is then credited with wins that Tank or Air produced. Cloak's 49.6% across 46,482 games is close to uninformative for this reason.
213 213
214 This bears directly on the case study. Kodachi, Venom, Bulkhead, and the hover units all appear in mid-game armies, which is the window in which the opener tag has stopped describing the game. The measurement instrument and the effect being measured are misaligned by several minutes of game time. 214 This bears directly on the case study. Kodachi, Venom, Bulkhead, and the hover units all appear in mid-game armies, which is the window in which the opener tag has stopped describing the game. The measurement instrument and the effect being measured are misaligned by several minutes of game time.
215 215
216 == 3.4 The paper cites a matchup-level claim and presents marginal win rates == 216 == 3.4 The paper cites a matchup-level claim and presents marginal win rates ==
217 217
218 The quoted patch rationale is explicitly about matchups: 218 The quoted patch rationale is explicitly about matchups:
219 219
220 [quote]Rover is dominating the vehicle matchups... We took this to mean that Rovers feel fun and well balanced... Instead, we took a look at Hover and Tank.[/quote] 220 [quote]Rover is dominating the vehicle matchups... We took this to mean that Rovers feel fun and well balanced... Instead, we took a look at Hover and Tank.[/quote]
221 221
222 Aggregate win rates cannot represent this. Specific matchups also behave very differently from one another — Jumpbot against Cloak is a well-known and highly snowbally pairing, and pairings like that are precisely where the opener tag [i]stays[/i] valid at high level, because the game resolves inside the raid window. 222 Aggregate win rates cannot represent this. Specific matchups also behave very differently from one another — Jumpbot against Cloak is a well-known and highly snowbally pairing, and pairings like that are precisely where the opener tag [i]stays[/i] valid at high level, because the game resolves inside the raid window.
223 223
224 Aggregation hides the distinction that matters. A factory with two brutal matchups and otherwise even results averages to roughly the same number as a factory that is mildly ahead everywhere. Those are entirely different balance problems. 224 Aggregation hides the distinction that matters. A factory with two brutal matchups and otherwise even results averages to roughly the same number as a factory that is mildly ahead everywhere. Those are entirely different balance problems.
225 225
226 There is also a selection effect: openers are chosen with some read on the opponent, so any cell is filtered by who was willing to enter it. Pairwise rates don't remove that filtering, but they localise it to one cell where it can be reasoned about instead of smearing it across every factory. 226 There is also a selection effect: openers are chosen with some read on the opponent, so any cell is filtered by who was willing to enter it. Pairwise rates don't remove that filtering, but they localise it to one cell where it can be reasoned about instead of smearing it across every factory.
227 227
228 Snowballiness is measurable with data the paper already has. If match duration is available, the signature is a left-shifted or bimodal length distribution in that cell, plus a win rate that moves sharply with small rating differences — a snowbally matchup amplifies a skill edge more than a grindy one does. Either would be a novel result. 228 Snowballiness is measurable with data the paper already has. If match duration is available, the signature is a left-shifted or bimodal length distribution in that cell, plus a win rate that moves sharply with small rating differences — a snowbally matchup amplifies a skill edge more than a grindy one does. Either would be a novel result.
229 229
230 == 3.5 The map taxonomy cannot capture the mechanism the paper describes == 230 == 3.5 The map taxonomy cannot capture the mechanism the paper describes ==
231 231
232 [quote]In general, Flat (39.66%) and Light Hills (36.58%) account for over 75% of all games.[/quote] 232 [quote]In general, Flat (39.66%) and Light Hills (36.58%) account for over 75% of all games.[/quote]
233 233
234 Flat / Light Hills / Hills / Mixed / Sea is a roughness scale. The terrain features that decide these matchups are [b]discrete[/b]: a cliff either blocks a raider path or it doesn't; a ridge either lets a Spider cross where a Tank can't, or a ramp exists and the advantage vanishes; Jumpbots care whether there is a gap worth jumping. Two maps in the same bucket can have entirely opposite implications for the same matchup, because what matters is the arrangement of chokes, ramps, and impassable edges — topology, not a scalar. 234 Flat / Light Hills / Hills / Mixed / Sea is a roughness scale. The terrain features that decide these matchups are [b]discrete[/b]: a cliff either blocks a raider path or it doesn't; a ridge either lets a Spider cross where a Tank can't, or a ramp exists and the advantage vanishes; Jumpbots care whether there is a gap worth jumping. Two maps in the same bucket can have entirely opposite implications for the same matchup, because what matters is the arrangement of chokes, ramps, and impassable edges — topology, not a scalar.
235 235
236 There is a testable puzzle here the paper doesn't notice. Figure 6 shows Flat swinging from roughly 31% to roughly 49% of games — a large shift in the terrain mix — while factory win rates barely move. Two readings: the buckets are too coarse to track it, or players re-pick openers in response to the map so the effect is absorbed by the [i]pick distribution[/i] rather than the win rate. The second is checkable directly — pick share conditioned on map type, by year. If Spider's share rises with Hills' share, players are compensating and the flat win rate is an artifact of adaptation. 236 There is a testable puzzle here the paper doesn't notice. Figure 6 shows Flat swinging from roughly 31% to roughly 49% of games — a large shift in the terrain mix — while factory win rates barely move. Two readings: the buckets are too coarse to track it, or players re-pick openers in response to the map so the effect is absorbed by the [i]pick distribution[/i] rather than the win rate. The second is checkable directly — pick share conditioned on map type, by year. If Spider's share rises with Hills' share, players are compensating and the flat win rate is an artifact of adaptation.
237 237
238 The more serious structural point: the paper builds a full section arguing maps matter and then never conditions a single win rate on map type. Map needs to enter as a control on the matchup cell, not as a standalone descriptive section. 238 The more serious structural point: the paper builds a full section arguing maps matter and then never conditions a single win rate on map type. Map needs to enter as a control on the matchup cell, not as a standalone descriptive section.
239 239
240 Given that maps rotate but popular ones recur, per-map rates for the fifteen or twenty highest-volume maps would be better than any taxonomy — a map is a fixed object with fixed chokes, so a per-map matchup rate removes the proxy entirely. 240 Given that maps rotate but popular ones recur, per-map rates for the fifteen or twenty highest-volume maps would be better than any taxonomy — a map is a fixed object with fixed chokes, so a per-map matchup rate removes the proxy entirely.
241 241
242 ---- 242 ----
243 243
244 = 4. What to do instead = 244 = 4. What to do instead =
245 245
246 Cell counts get thin fast, so the recommendation is depth over coverage: pick the high-volume matchups and do them properly rather than reporting one number per factory. 246 Cell counts get thin fast, so the recommendation is depth over coverage: pick the high-volume matchups and do them properly rather than reporting one number per factory.
247 247
248 * [b]A matchup matrix.[/b] 12x12, per-cell Wilson intervals, mirror cells greyed, ideally split by map class and rating band. Most cells will be too thin — Strider Hub disappears entirely — but the top eight factories against each other should have real sample. This is the object balance actually operates on, and it is what the cited patch note is talking about. 248 * [b]A matchup matrix.[/b] 12x12, per-cell Wilson intervals, mirror cells greyed, ideally split by map class and rating band. Most cells will be too thin — Strider Hub disappears entirely — but the top eight factories against each other should have real sample. This is the object balance actually operates on, and it is what the cited patch note is talking about.
249 * [b]Condition on rating.[/b] Rating absorption inflates both players' ratings symmetrically within a matchup, so the relative result at matched Elo still carries signal even though the marginal rate does not. 249 * [b]Condition on rating.[/b] Rating absorption inflates both players' ratings symmetrically within a matchup, so the relative result at matched Elo still carries signal even though the marginal rate does not.
250 * [b]Mirror-excluded win rates[/b] throughout. 250 * [b]Mirror-excluded win rates[/b] throughout.
251 * [b]State the unit of observation[/b] — opening factory — in the Data Set section, and treat off-pick rates as off-pick deltas. Air's 27% is meaningful as "what it costs to switch to Air," which is a legitimate design question, just not the one the paper asks. 251 * [b]State the unit of observation[/b] — opening factory — in the Data Set section, and treat off-pick rates as off-pick deltas. Air's 27% is meaningful as "what it costs to switch to Air," which is a legitimate design question, just not the one the paper asks.
252 * [b]Stratify by rating band[/b] wherever the opener tag's validity varies. 252 * [b]Stratify by rating band[/b] wherever the opener tag's validity varies.
253 253
254 ---- 254 ----
255 255
256 = 5. Smaller items = 256 = 5. Smaller items =
257 257
258 [b]The damping equation is decorative. [/b] V( t+1) = V( t) − k( R( t) − R_target) is never estimated or reused. It also cannot cover both quantities named in [q]( cost, power, or spawn rate) [/q] with one sign — if win rate is above target, power should fall but cost should rise — and k carries unspecified units converting win-rate points into cost. Either fit k from actual stat changes against prior-year deviation ( the git history supports this) or cut it. 258 [b]The damping equation is decorative. [/b] { { { V( t+1) = V( t) − k( R( t) − R_target) } } } is never estimated or reused. It also cannot cover both quantities named in [q]( cost, power, or spawn rate) [/q] with one sign — if win rate is above target, power should fall but cost should rise — and k carries unspecified units converting win-rate points into cost. Either fit k from actual stat changes against prior-year deviation ( the git history supports this) or cut it.
259 259
260 [b]Sample sizes don't reconcile. [/b] Factory counts sum to ~178, 400 against 2 x 90, 024 = 180, 048 factory-slots. State that each match contributes two factory observations and account for the ~1, 648 excluded slots. 260 [b]Sample sizes don't reconcile. [/b] Factory counts sum to ~178, 400 against { { { 2 x 90, 024 = 180, 048} } } factory-slots. State that each match contributes two factory observations and account for the ~1, 648 excluded slots.
261 261
262 [b]Limitations opens on the wrong word.[/b] [q]we have some limitations in our data regarding time zone[/q] — the paragraph then discusses matchmaking-only coverage. Presumably "time frame." 262 [b]Limitations opens on the wrong word.[/b] [q]we have some limitations in our data regarding time zone[/q] — the paragraph then discusses matchmaking-only coverage. Presumably "time frame."
263 263
264 [b]Garbled methodology sentence.[/b] [q]we will regress next years win rate deviation by 50%[/q] — presumably "regress next year's deviation on the current year's deviation." 264 [b]Garbled methodology sentence.[/b] [q]we will regress next years win rate deviation by 50%[/q] — presumably "regress next year's deviation on the current year's deviation."
265 265
266 [b]Abstract and Introduction share a near-verbatim opening paragraph.[/b] Cut one. 266 [b]Abstract and Introduction share a near-verbatim opening paragraph.[/b] Cut one.
267 267
268 [b]The Abstract reports no findings.[/b] It should carry n, the slope, and both p-values. 268 [b]The Abstract reports no findings.[/b] It should carry n, the slope, and both p-values.
269 269
270 [b]Byline.[/b] [q]Sam Kincer (Qrow) et al.[/q] — "et al." isn't used in an author line. List coauthors or drop it. 270 [b]Byline.[/b] [q]Sam Kincer (Qrow) et al.[/q] — "et al." isn't used in an author line. List coauthors or drop it.
271 271
272 [b]Uncited entry in Works Cited.[/b] v1.12.1.1 "Ship Shape" doesn't appear in the text. 272 [b]Uncited entry in Works Cited.[/b] v1.12.1.1 "Ship Shape" doesn't appear in the text.
273 273
274 [b]Access dates.[/b] All sources are listed as accessed 10 Aug. 2026 in a paper dated August 2026 — check these are correct. 274 [b]Access dates.[/b] All sources are listed as accessed 10 Aug. 2026 in a paper dated August 2026 — check these are correct.
275 275
276 [b]Typos:[/b] "accurate distinguish" → accurately; "eachother" → each other; "after a path" → patch; "in our introduction.." (double period); "considerably less micro-intensive game on average than TA-like games on average" (repeated phrase). 276 [b]Typos:[/b] "accurate distinguish" → accurately; "eachother" → each other; "after a path" → patch; "in our introduction.." (double period); "considerably less micro-intensive game on average than TA-like games on average" (repeated phrase).