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Guest article submitted by Ei-lara

Introduction

I have taken Daddio’s data, and added new variables to help understand what are the main factors contributing to victory in normal T99 games (not Invictus).

Here, I explain the new variables added, perform correlation analysis, and pathway analysis, to derive a reasonable theoretical model that is well-substantiated by both qualitative and quantitative data.

1) New Variables Considered

Minimum APM (Offensive Power)

APM (Attack Per Minute) is defined by the number of lines of garbage sent to your opponents every minute. Higher APM means more offensive power.

In this chart here, I have calculated the Minimum APM of some of the players on our sample. Mininum APM is the amount of garbage sent from Doubles, Triples, Tetrises, T-Spin Minis, T-Spin Singles, T-Spin Doubles, T-Spin Triples, and Back-to-Backs divided by Total Played Time in Minutes.

While negligible, it should be noted that there are 2 kinds of TSMs: TSM singles and doubles. TSM doubles are extremely rare – they are caused by using polymer T-spin methods, such as Neo TSD. For all practical purposes, they can be excluded. TSM doubles send 1 line of garbage inherently, and 2, if b2b is on.

Therefore, this is a “minimum” value as it does not take into account damage from combos, which cannot be inferred using T99’s stats.

Based on rough estimates and personal experience, mid-game combos constitute between 25 to 50% of a player’s APM. My experience with battling Misamino and Cold Clear bots is that my APM in Puyo Tetris is about 50 to 60, so one’s actual APM should be around 33 to 100% higher. Therefore, all of the APM values below are only *minimum* values – they underestimate the actual APM of players since combos are left out.

This chart does not factor in the attack multiplier from using things like Bait Strategy, as there is no data to infer.

T-Spin Efficiency

T-Spin Efficiency is defined by the Total number of T-spins divided by Lines Cleared (NOT lines sent!). The higher the value, the more efficient one is – that means, they use a greater percentage of their T pieces for T-spins.

T-Spin Efficiency correlates very highly with APL efficiency (Attack Per Line).

Of interest to note, is that, you can infer the rough percentage of T pieces used. Let’s assume using my data – 0.19611 T-spins per line cleared. Each line is 2.5 pieces. So 0.19611/2.5 = 0.078444 T-spins per piece. Multiply by 7 (each bag has 7 pieces) = about 0.6. This means I use 60% of all T pieces ever spawned to make T-spins.

Minimum APL (Overall Efficiency)

APL stands for Attack per Line Cleared (NOT line sent). So if your APL is 1.4, you send an average of 1.4 lines of garbage to your opponents per 1 line cleared.

APL is a measure of efficiency. The higher one’s value is, the more one can make use of limited pieces to create the most damage. The most efficient players in the world have an APL of around 1.2 or more.

“Minimum” APL is calculated using “Minimum APM” divided by Lines Cleared. It is a “Mininum” value as it cannot factor in damage from combos. Therefore, all values below are underestimations of the studied players’ true APL. From my experience (Ei’lara), I have around 1.7 to 1.8 APL, so the values below are probably around 20 to 30% less of actual values.

Also note: APP, or Attack Per Piece, matters MORE than APL. This is because, let’s say you receive 4 lines of clean garbage. You Tetris it. Your APP is 4. If you simply upstack all 4 rows, your APP is 4/10 = 0.4. Both has 1 APL. This matters when you downstack combos through free garbage. However, without any data on combos in the T99 stats, nothing of APP can be inferred. In fact, the game does not even record the number of pieces dropped.

Between 2 players – one with higher APL, but the other with higher APP, the 2nd person will win.

Tetramino Drop Distance Per Minute

Tetramino Drop Distance Per Minute is defined by the total Tetramino Drop Distance divided by Total Played time in minutes.

This may seem like ‘speed’, but it is not. For instance, a player playing at 3 pieces per second, but stays upstacked very high may get the same score as one who stays very low, and plays only at 1 piece per second. Therefore, this variable seems to indicate a combination of speed and the tendency to stay very low (Staying low means each piece drops more and inflates the player’s stats).

The hypothesis of staying low seems to be the more likely explanation, based on my observation of many of the studied players. Most of us have very similar speeds. Therefore, the variance seems more likely to be caused by staying low for some of the highest-scoring players.

2) General Correlations Found

The findings below use correlative methods to find the precise degrees of association between variables.

Legend

The charts below are arranged in ASCENDING order of correlation strength Coloring of Title indicates correlation extent

Green = STRONG correlation

Orange = Moderate

Red = Weak

In the above diagram, T-Spin efficiency seems to correlate very weakly with overall win-rate. This could partially be skewed due to my (Ei’lara) T-spin efficiency being 3 to 4 times everyone else’s. From my own experience, I never set my targeting to “KOs” or “Badges”, which may deflate my win-rate.

However, it is still substantial, and cannot be ignored. At the end of the day: T-spins still DO MATTER in deciding win-rate.

Minimum APL also seems to correlate very weakly with Win Rate. However, it is still substantial, and cannot be ignored.

After all, more efficiency x speed = raw attack power = more ability to offset enemy garbage, or top them out. So efficiency still DOES MATTER.

Again there is a weak to moderate correlation between the capacity to sustain Back-to-backs and Win Rate.

However, it is still substantial, and cannot be ignored. A Rho value of 0.5185 suggests that efficiency still plays a very important role in winning as it affects offensive power a lot.

As suspected by Daddio, Win rate correlates negatively with the number of rotations per line clear event. Rotations per line clear event can be interpreted as roughly the number of key presses per piece. The lower this is, the ‘smoother’ one’s gameplay is, and therefore, possibly the faster one is (or least, LESS encumbered by bad finesse faults or high key presses per piece). This seems to suggest, as Daddio said, that flow plays an important role in winning. However, the Rho value is weak to moderate only.

Minimum APM, the best indicator of offensive power, correlates moderately with Win Rate, suggesting that the more garbage one produces, the better one’s chances of winning. This is obvious, as you need more garbage to overpower your opponents or to defend, so as to win the uphill struggle in the late-game.

This is when things get super interesting. Win Rate correlates very highly with the capacity to downstack or skim generously with non-T-spin Singles, Doubles, and Triples. This suggests that playing defensively by downstacking generously to stay low correlates with winning more. Perhaps, it allows one to survive longer, get more badges and KOs, and thus outlast opponents.

Win Rate correlates even more highly with total KOs per game. The exact mechanics cannot be known, but I hypothesize the following: more KOs = more offensive power to outlast your opponent later since each badge gives +25% more damage (up to 4 x 25% = 100%). Also, killing more opponents prune the field of other strong, high-offensive players, so you can more easily survive later.

Regardless, setting your targeting to “KOs” or “Badges” mid-game probably does matter A LOT. I myself, Ei’lara’, set only to target “Attackers”, which deflates my KOs a lot despite having the highest APM amongst all players in the study by more than 50% of the second highest, and 3 times the average. The irony is that my KOs is only slightly above average in the samples studied.

Lesson learned: I’m setting to target “KOs” mid-game from now on!

Lines per minute here is NOT lines sent. Rather, it is lines downstacked. The super high correlation again, suggests that a defensive playstyle to downstack generously to survive correlates highly with winning.

Same as the previous variable, except Total Lines cleared is an absolute value rather than as a rate, per time.

This again suggests that having more Badges gives one more offensive power, whether from stealing badges or by having high KOs. Each badge gives +25% more attack power. Therefore, Divinehere, who has 60% of Ei’lara’s APM, can do 20% more damage than the latter if he gets 4 badges. Badges thus make a super huge difference in winning. Also, if you happen to steal badges from 4-badge holders, you free yourself from facing a powerful enemy in the late-game. So it is both offensive and defensive, in a way, to grab more badges.

This is by far the most important factor in determining win rate. Tetramino drop distance per minute, as mentioned many times earlier, suggests heavily that staying low equates to higher win rates. This seems qualitatively supported by the idea that in the late game, the pieces drop and lock almost instantly. If you are stacked high up, not even using DAS preservation can allow you to move some pieces to the required places. So you wish to stay low to prevent that. Staying low, instead of making reckless and fancy T-spin setups like DT cannon, seems like the more important thing to do. Probably the meta late-game strategy is to just downstack, wait for opponents to send clean garbage, and you just send it back.

3) Derived Theoretical Model using Pathway Analysis

The above model seems to be the most likely one that explains victory rate in normal T99 games.

Qualitative Support:

1) Players with heavy downstack focus, but are balanced with decent offensive pressure, like Divine, Tetri, and Icy, have the highest win rates. This is done by staying low, so as to avoid being knocked out by spikes, have more room to stack, and avoid instant-lock if stacked too high.

2) Offensive power is magnified by Kos and Badges, which then leads to a self-fulfilling prophecy where it leads to higher offense to top out people + create lines for garbage offsetting/blocking + get even more Kos and badges to amplify it further.

3) In the late-game, having more badges is crucial, as it makes it easier to attack and defend = you survive longer = higher chances of victory. Killing more players with high badge-counts also prunes the late-game of very strong opponents.

4) Ei’lara, who has the most extreme T-spin efficiency and highest offensive pressure at 3 to 5 times the average player’s in this study, has only an average win-rate as he (me of course) heavily prioritises heavy upstacking to sustain b2b over downstacking or skimming and does not switch to target Kos or badges mid-game (sets only to target “attackers” ALL the time)

5) Also, I watched the Twitch channels of many players like Cfillot, Derpy, Tenktenks – they all follow this defensive playstyle and have high win rates, even if their offensive pressure from b2bs + T-spins is not very high. They stayed low and prioritised survivability = higher win rates.

Limitations of Study

• This is a strictly quantitative study

• Unless there is qualitative data about how each player plays (like info on whether they use mid-game 4ws a lot, or baiting at the start, or generally build with a well around a hole hold for combos + Tetris for defense), we cannot infer much about the specifics

• This is a nomothetic/general study – rather than an idiographic/contextual/ethnographic/specific study

• I suspect that players who use meta methods like 4w and baiting have a very inflated win-rate, but cannot confirm or disprove with given data in this study

4) Conclusion and Summary

Given the current data, it seems that the “Holistic but Primarily Downstack-Heavy Defensive Strategy Model” is the most promising theory and model.

1) Players who prioritise defensive downstacking over offense have the highest win rate, by purposely staying low.

2) However, offensive pressure also do matter, like T-spins, B2Bs, APM, but should be given less weight compared to defensive downstacking and staying low. If you can’t survive, your APM drops to zero!

3) This then leads to higher survivability = higher Kos + Badges = more offensive power = Higher win rate. Set “target” to “badges” or “Kos” mid-game to accelerate the process. Also higher badge steals = kills off stronger opponents to even the late-game uphill battle vs other strong opponents later

4) Due to study and data inadequacies, it is not known how baiting, opening and mid-game 4w, mid-game combos factor in.

Super Short Summary

In summary, it’s better to fight more with a shield more so than use a sword; but the sword is also important too

Prioritise survival first, before offence.

5) Appendix: Other Interesting Descriptive Statistics

These histograms are just for fun. I tabulated the data for all studied players, worked out their means and standard deviations, and other stuff.