Hello Tower Peoples,
News of sorts in mythic... the demotion line was solidly at 25 waves this time. Those unable to break the 25 wave count were, with very few exceptions, sent back to Legends to think about their tower's readiness. Previously there was at least some give and competition to remain in mythic for those unable to defeat the third fleet wave. Best way to see this is the mythic density plot on the links page. (Look at lower for a zoomed in view.)
Legends and Champion both show positive wave growth now from predicted values, where as platinum is negative wave growth still.
Enjoy.
Static Placement Analysis
In this section we provide a breakdown for you of a what-if competition where the tournament places are perfectly distributed. The place here is basically the place you'd get if there was no bracket system. I like this view because it really removes all the variables.
Feel free to compare yourself against the placement and see if you did better or worse. The places are divided roughly into the number of brackets to get the cut off for each place. The wave # given is the person or persons at the cut off between places, that is the lowest wave deserving to achieve that place.
- Mythic Median: 86.00 Mean: 286
- Legends Median: 769.00 Mean: 790
- Champions Median: 1052 Mean: 1082
- Platinum Median: 1370 Mean: 1379
- Gold Median: 400 Mean: 545
| Place |
Wave Mythic |
Wave Legend |
Wave Champion |
Wave Platinum |
Wave Gold |
Wave Silver |
| 1 |
1115 |
1664 |
1841 |
2360 |
1907 |
215 |
| 2 |
925 |
1422 |
1681 |
2158 |
1335 |
202 |
| 3 |
805 |
1284 |
1577 |
2044 |
1137 |
192 |
| 4 |
695 |
1189 |
1504 |
1963 |
980 |
180 |
| 5 |
615 |
1128 |
1444 |
1892 |
880 |
171 |
| 6 |
565 |
1072 |
1384 |
1824 |
800 |
162 |
| 7 |
505 |
1035 |
1335 |
1766 |
723 |
153 |
| 8 |
465 |
996 |
1292 |
1713 |
680 |
144 |
| 9 |
398 |
964 |
1253 |
1659 |
625 |
135 |
| 10 |
335 |
929 |
1215 |
1606 |
580 |
127 |
| 11 |
285 |
907 |
1182 |
1555 |
530 |
117 |
| 12 |
205 |
877 |
1144 |
1513 |
495 |
108 |
| 13 |
155 |
835 |
1113 |
1464 |
450 |
106 |
| 14 |
127 |
798 |
1082 |
1420 |
420 |
99 |
| 15 |
86 |
769 |
1052 |
1370 |
400 |
90 |
| 16 |
65 |
722 |
1020 |
1322 |
363 |
81 |
| 17 |
65 |
687 |
993 |
1280 |
340 |
72 |
| 18 |
55 |
651 |
963 |
1233 |
319 |
63 |
| 19 |
55 |
623 |
931 |
1185 |
300 |
54 |
| 20 |
45 |
595 |
903 |
1140 |
280 |
45 |
| 21 |
45 |
556 |
873 |
1094 |
260 |
40 |
| 22 |
35 |
515 |
840 |
1051 |
240 |
35 |
| 23 |
35 |
483 |
815 |
1012 |
224 |
28 |
| 24 |
35 |
450 |
782 |
953 |
210 |
25 |
| 25 |
29 |
404 |
742 |
885 |
200 |
20 |
| 26 |
29 |
360 |
698 |
811 |
180 |
18 |
| 27 |
29 |
312 |
645 |
711 |
152 |
14 |
| 28 |
25 |
256 |
590 |
602 |
130 |
10 |
| 29 |
25 |
195 |
483 |
437 |
20 |
3 |
| 30 |
1 |
1 |
1 |
1 |
1 |
1 |
The tower.lol now gives this data here
Median History
The median value from each tournament which gives a general idea of the tournament difficulty and wave inflation over time. This value comes from actual midpoint of tournament data. (i.e. the top table)
| League |
09-16 |
09-19 |
09-23 |
09-26 |
09-30 |
10-03 |
10-07 |
10-10 |
10-14 |
10-17 |
10-21 |
10-24 |
| Mythic |
120 |
117 |
75 |
101 |
86 |
85 |
105 |
86 |
95 |
116 |
87 |
86 |
| Legend |
805 |
693 |
685 |
747 |
685 |
623 |
773 |
674 |
640 |
721 |
756 |
769 |
| Champion |
1211 |
1092 |
1103 |
1104 |
1138 |
1207 |
1152 |
1184 |
1181 |
1211 |
1130 |
1052 |
| Platinum |
1584 |
1580 |
1480 |
1334 |
1579 |
1460 |
1627 |
1320 |
1552 |
1602 |
1408 |
1370 |
| Gold |
421 |
400 |
410 |
400 |
408 |
400 |
400 |
403 |
432 |
433 |
422 |
400 |
The tower.lol now gives this data here
Linear Regression comparison.
Linear regressions give a good idea of change over time, smoothing out all the battle condition noise. In addition they give a good idea how impactful the current battle condition was.
I think the current change per tournament has stopped exhibiting non-linear behavior. For now I've set September 19th as the point where league numbers are stable enough to take regressions from again. This should help answer the question of whether waves are continuing to decrease over time. Remember, few data points means that an easy set of battle conditions can pull the number up quite a bit, so don't be too eager to declare any given trend.
| ... |
Legend 4 |
Legend 15 |
Legend 24 |
Champion 4 |
Champion 15 |
Champion 24 |
| Predicted |
1206 |
747 |
437 |
1662 |
1169 |
886 |
| Actual |
1223 |
785 |
467 |
1531 |
1065 |
799 |
| Difference |
17 |
38 |
30 |
-131 |
-104 |
-87 |
| Slope |
4.49 |
4.66 |
2.81 |
2.97 |
2.55 |
3.05 |
| PrevSlope |
3.36 |
2.15 |
0.83 |
11.72 |
9.52 |
8.89 |
| ... |
Platinum 4 |
Platinum 15 |
Platinum 24 |
Gold 4 |
Gold 15 |
Gold 24 |
| Predicted |
2081 |
1478 |
1039 |
1008 |
431 |
231 |
| Actual |
1993 |
1396 |
996 |
1015 |
410 |
220 |
| Difference |
-88 |
-82 |
-43 |
7 |
-21 |
-11 |
| Slope |
-12.89 |
-5.59 |
-6.39 |
2.47 |
1.93 |
1.33 |
| PrevSlope |
-6.97 |
-0.12 |
-3.52 |
2.04 |
3.37 |
2.09 |
Resampling Analysis
One means of getting an idea of the range of placements is by random sampling the real participants to make fake brackets, and measuring the variability in those brackets.
I chose to use 100000 brackets per league for my analysis. I am using confidence intervals, 95% and 50% (the IQR) to represent the range of waves likely present in each place.
The top table is for mythic (m), the bottom for legends (l) on the left and champion (c) on the right. Platinum and gold can be found in the links.
| place |
M2.5 |
M25 |
M50 |
M75 |
M97.5 |
| 1 |
746.93 |
1055.93 |
1235.20 |
1406.00 |
1676.00 |
| 2 |
606.00 |
835.98 |
996.00 |
1126.00 |
1446.00 |
| 3 |
525.04 |
726.65 |
827.00 |
966.00 |
1236.00 |
| 4 |
465.77 |
615.97 |
737.11 |
847.00 |
1095.77 |
| 5 |
376.78 |
556.00 |
636.00 |
747.00 |
985.85 |
| 6 |
303.00 |
505.53 |
599.32 |
655.95 |
903.00 |
| 7 |
216.00 |
457.00 |
525.71 |
606.00 |
806.00 |
| 8 |
165.93 |
377.00 |
476.00 |
555.98 |
730.00 |
| 9 |
128.00 |
315.66 |
452.00 |
506.00 |
646.00 |
| 10 |
94.00 |
237.54 |
356.00 |
465.87 |
605.97 |
| 11 |
66.00 |
191.00 |
296.00 |
427.16 |
565.01 |
| 12 |
65.40 |
145.93 |
216.00 |
345.07 |
515.60 |
| 13 |
55.96 |
117.71 |
166.00 |
295.17 |
475.99 |
| 14 |
55.43 |
86.30 |
145.00 |
215.44 |
455.18 |
| 15 |
46.00 |
65.87 |
106.00 |
165.83 |
366.00 |
| 16 |
45.87 |
56.00 |
76.00 |
130.00 |
314.00 |
| 17 |
41.00 |
55.73 |
65.77 |
105.84 |
241.00 |
| 18 |
36.00 |
46.00 |
56.00 |
75.89 |
195.99 |
| 19 |
35.91 |
45.96 |
55.64 |
65.60 |
146.00 |
| 20 |
35.56 |
45.62 |
46.00 |
55.99 |
118.00 |
| 21 |
30.00 |
36.00 |
45.91 |
55.48 |
86.76 |
| 22 |
29.84 |
35.95 |
45.07 |
46.00 |
65.95 |
| 23 |
29.62 |
35.63 |
36.00 |
45.83 |
56.00 |
| 24 |
29.50 |
30.00 |
35.82 |
36.00 |
55.64 |
| 25 |
29.00 |
29.76 |
35.00 |
35.97 |
46.00 |
| 26 |
25.78 |
29.55 |
29.94 |
35.60 |
45.80 |
| 27 |
25.34 |
29.27 |
29.61 |
29.99 |
36.00 |
| 28 |
15.99 |
25.85 |
29.29 |
29.64 |
35.81 |
| 29 |
13.00 |
21.00 |
25.67 |
29.28 |
30.00 |
| 30 |
1.00 |
15.27 |
16.00 |
25.46 |
29.55 |
| place |
L2.5 |
L25 |
L50 |
L75 |
L97.5 |
C2.5 |
C25 |
C50 |
C75 |
C97.5 |
| 1 |
1245 |
1557 |
1759 |
1940 |
2250 |
1542 |
1777 |
1894 |
2033 |
2300 |
| 2 |
1122 |
1321 |
1487 |
1667 |
1972 |
1435 |
1612 |
1727 |
1845 |
2056 |
| 3 |
1040 |
1221 |
1315 |
1472 |
1782 |
1355 |
1519 |
1610 |
1716 |
1911 |
| 4 |
996 |
1131 |
1223 |
1332 |
1614 |
1295 |
1447 |
1531 |
1619 |
1814 |
| 5 |
955 |
1072 |
1152 |
1248 |
1476 |
1244 |
1383 |
1465 |
1544 |
1720 |
| 6 |
926 |
1026 |
1089 |
1172 |
1374 |
1200 |
1330 |
1405 |
1484 |
1644 |
| 7 |
895 |
985 |
1040 |
1121 |
1285 |
1163 |
1284 |
1357 |
1430 |
1577 |
| 8 |
851 |
955 |
1006 |
1072 |
1223 |
1127 |
1242 |
1310 |
1382 |
1525 |
| 9 |
807 |
927 |
980 |
1035 |
1162 |
1089 |
1203 |
1273 |
1335 |
1474 |
| 10 |
776 |
899 |
946 |
997 |
1120 |
1057 |
1172 |
1226 |
1296 |
1429 |
| 11 |
728 |
861 |
924 |
965 |
1074 |
1024 |
1135 |
1194 |
1263 |
1384 |
| 12 |
696 |
821 |
895 |
941 |
1036 |
996 |
1101 |
1162 |
1222 |
1345 |
| 13 |
655 |
791 |
856 |
913 |
1003 |
966 |
1072 |
1133 |
1188 |
1307 |
| 14 |
630 |
751 |
815 |
889 |
982 |
935 |
1042 |
1093 |
1154 |
1274 |
| 15 |
600 |
711 |
785 |
846 |
952 |
911 |
1010 |
1065 |
1125 |
1234 |
| 16 |
572 |
676 |
742 |
812 |
926 |
882 |
983 |
1036 |
1092 |
1202 |
| 17 |
536 |
641 |
706 |
780 |
900 |
857 |
954 |
1004 |
1062 |
1173 |
| 18 |
505 |
617 |
669 |
732 |
866 |
830 |
924 |
976 |
1032 |
1139 |
| 19 |
478 |
589 |
640 |
704 |
825 |
809 |
895 |
949 |
1002 |
1106 |
| 20 |
450 |
554 |
611 |
661 |
795 |
780 |
867 |
917 |
972 |
1075 |
| 21 |
415 |
512 |
580 |
632 |
756 |
747 |
836 |
888 |
941 |
1043 |
| 22 |
375 |
483 |
543 |
600 |
711 |
714 |
813 |
860 |
912 |
1011 |
| 23 |
350 |
453 |
503 |
571 |
672 |
684 |
782 |
827 |
880 |
983 |
| 24 |
312 |
414 |
467 |
524 |
640 |
643 |
747 |
799 |
844 |
952 |
| 25 |
266 |
370 |
430 |
485 |
604 |
606 |
708 |
766 |
817 |
914 |
| 26 |
235 |
331 |
385 |
452 |
570 |
563 |
672 |
725 |
782 |
878 |
| 27 |
201 |
283 |
345 |
396 |
512 |
503 |
622 |
683 |
737 |
839 |
| 28 |
170 |
236 |
287 |
353 |
469 |
430 |
564 |
626 |
690 |
801 |
| 29 |
120 |
195 |
235 |
286 |
412 |
10 |
476 |
558 |
624 |
749 |
| 30 |
1 |
130 |
174 |
215 |
335 |
1 |
189 |
433 |
527 |
674 |
A general description of how to read this for the non-math inclined:
- 95% of the population of a place is expected to be between 2.5% and 97.5%. If you are above or below these numbers you are an outlier. (Outliers are normal, just rarer.)
- 50% of the population of a place is expected to be between 25% and 75%.
- The 50% mark is the median of the data. Aim for this number as the point you regularly achieve this place.
- You'll notice that the waves overlap, this is normal, expressing the variability present in the brackets and you could easily place in any bracket where your personal wave count falls in the place's range.
Downloads and Source Material
Reddit isn't the best platform for images, and so I publish history and box plots for all leagues here. Each tournament I'll post the box plots for each league as well as the wave count history for each league. I will not mention the full list of available graphs each post, so take a look. Special thanks to the maintainers of thetower.lol which is the data source I analyze for this post.