# Paper: Miscellaneous Statistics Projects 2018

How do you calculate the schedule strength metric? I’m assuming it’s at least partially based on the changes due to schedule numbers, but I don’t see any direct correlation (team A having a larger positive change in average rank than team B does not seem to imply that team A’s schedule strength will be lower than team B’s, or vice versa).

The schedule strength is the probability that the given team will seed higher with the actual schedule than they would have with a random schedule according to the simulator. This is found by the following formula:

Where r and q are ranks and are summed over all ranks and all ranks greater than r respectively. Changing the second summation to over all q>=r would provide a very similar metric, just that it would err on the high side instead of the low side.

For example, say that before the schedule is released a team is predicted to have a 20% chance of seeding first, 30% second, and 50% third. After the schedule is released, they have a 5% chance of seeding first, 25% second, and 70% third. Their schedule strength would then be:
0.05*(0.3+0.5)+0.25*(0.5)=0.04+0.125=0.165 or 16.5%.

Looks like a pretty strong correlation to me. Excepting the teams which are heavy favorites to seed first it seems to be doing it’s job.

As I’m delving more into schedule analysis, I decided I should probably do a proper comparison of the Cheesy Arena schedules, which is what I have been using instead of generating my own schedules, and the actual schedules used this year, generated according to the IdleLoop algorithm at each event. I am unfamiliar with exactly how this algorithm is run at each event, but I have heard that the scorekeeper generally will select a minimum match gap based on a number of factors, and then run the algorithm at the “best” (5 million attempts) setting. How exactly the minimum gap is selected is unknown to me, and likely varies across events.

For all 174 events which had qual matches, I compared the actual schedule for the event with the cheesy arena schedule for the same number of teams and the same number of matches per team. The metrics I was looking at to determine how good the schedule were:
number of surrogates used
red/blue balance for each team
gap between matches for all consecutive pairs of matches for all teams
repeated partners for all teams
repeated opponents for all teams

In some cases, these criteria will interfere with each other, most notably, a large minimum match gap will tend to cause more duplicate partners and opponents than a small minimum match gap. I also made the decision to treat surrogates the same as normal teams. Although for some metrics it might make sense to ignore surrogates, it seems to me that, if you were up against 254 in 4 different matches, it would be of little consolation to you if 254 was a surrogate in one of them, so I treated surrogates as normal teams.

The results show that overall, the cheesy arena schedules and the IdleLoop schedules are very similar. There were 11 events this season for which the Cheesy Arena schedules were as good or better than the IdleLoop schedules across all categories according to my metrics, and 6 events for which the IdleLoop schedules were as good or better than the Cheesy Arena schedules across all metrics. Here is a breakdown by category:
Surrogates: The number of surrogates used was identical for all events, this isn’t surprising since surrogate usage should be bounded above by 6 for any combination of teams and matches/team.
Red/blue balance: There were 80 events for which the red/blue balance was better achieved by the cheesy arena schedules than the Idle Loop schedules, and 64 for the reverse.
Match gap: There were 85 events for which the match gap was better in the Cheesy Arena schedules than the Idle Loop schedules, and 89 for the reverse.
Duplicate partners: There were 14 events for which the Cheesy Arena schedules were better at avoiding duplicated partners than the Idle Loop schedules, and 9 for the reverse.
Duplicate opponents: There were 70 events for which the Cheesy Arena schedules were better at avoiding duplicated opponents than the Idle Loop schedules, and 88 for the reverse.

Overall, it seems that the Cheesy Arena schedules might be slightly better at red/blue balance and avoiding duplicate partners, whereas the IdleLoop schedules might be slightly better at having larger match gaps and avoiding duplicate opponents, although the sample sizes might be too small to draw too much of a conclusion.

The full results can be seen in my IdleLoop_and_Cheesy_Arena_comparison.xlsx file. The “summary” page shows a quick look at which schedule was “better” according to my metric for each category. The “raw data” sheet shows a more in depth look at each event. I will walk through the results for the Great Northern Regional here in order to explain them. You can stop reading now if you’re not interested in a deeper dive into the data:
Columns 2-5 show information about the event. Columns 8-36 show data on the actual (Idle Loop) schedule used for this event. Columns 58-86 show data on the Cheesy schedule with the specified number of teams and matches/team. Columns 108-136 show the difference between the actual schedule and the cheesy schedule.
Starting in column 8, we see that the actual schedule had 5 surrogates used, and in column 58 we see the cheesy schedule also had 5 surrogates used. The difference between these in column 108 is 0.
In columns 9-17, we see the red/blue balance for teams in the actual schedule. There are 0 teams at this event that have an even number of red/blue matches, which is unsurprising given that each team had 11 matches. There are 40 teams that had either 1 more red matches than blue matches or 1 more blue matches than red matches, which are as balanced as you can get with 11 matches. There were 5 teams (the surrogate teams) that had a red/blue difference of 2 matches. Finally, there were 2 teams that had a 3 match red/blue difference. The cheesy schedule is similar, except that 4 of the surrogate teams had 0 red/blue difference (columns 59-67), this difference can be seen in cols 109-117, with the +4 value in the 2 match difference indicating that the actual schedule had 4 more instances of 2 match red/blue difference than the cheesy schedule did. Since the worst red/blue balance is worse for the actual schedule than the cheesy schedule, I mark in the “summary” sheet that the cheesy arena schedule is better for red/blue balance.
Moving on in a similar way to the next category of gap between matches, we see that with the actual schedule, no teams had back-to-back matches or consecutive matches with only a single match between their matches. There were however 38 occurrences of teams that had consecutive matches that were 3 matches apart. In the cheesy schedule though, there were only 34 of these occurrences. This gives the cheesy schedule the edge in “match gap” in my summary.
For pairs of partners, both schedules had 1044 occurrences of teams having another partner only once. There were no duplicated partners in either schedule. 1044 is to be expected since there are 87 matches, 2 alliances per match, 3 teams per alliance, and 2 partners per team, and 8723*2 = 1044. Neither schedule is superior by this metric.
Finally, looking at opponent pair occurrences, we see that the actual schedule had 2 instances where a team had to face another team in 3 separate matches (2500 facing 7257 and 7257 facing 2500). In contrast, the cheesy schedule has 6 such occurrences. This gives the Idle Loop schedule the edge in my summary sheet.

Anyway, let me know if you see any flaws in my analysis or have any questions.

In response to requests for more model validation, I decided to pull all of the top 4, top 8, and top 12 predictions my current simulator would have made on the week 3-4 events at 4 different points at the event, before the schedule was released, after the schedule was released, after 1/3 of qual matches had been played, and after 2/3 of qual matches had been played. The results can be seen in my “week3-4_calibration_results.xlsx” book. This book contains the raw data, a sheet that has calibration results, and a sheet of a bunch of graphs showing these results.

I’m still toying around with how best to represent the calibration results. I’ve done this format in the past, but this is limited by arbitrary bin sizes and inability to show how many of a type of prediction I make. One idea I had was to use my normal calibration curve format, but with smaller bins, and with dot sizes corresponding to the number of points that fall into the bin. This way, people can see how many of a type of prediction I make, as well as how well calibrated those predictions are. Here’s one of these graphs:

Although this is a pretty cool format to look at, there’s not much actionable information I can pull out of it. So I also made simple scatter plots of the predicted probabilities versus actual results, here’s one of those graphs:

This isn’t very visually intuitive, but the linear regression tells me both how much predictive power I have (according to the R^2 value) and how well calibrated my model is (looking at the slope of the line). In the shown graph, the R^2 value of 0.30 indicates that my model can explain about 30% of the variance in the top 12 seeds after the schedule is released, but before any matches have been played. The slope of 0.82 indicates that, if I wanted to be well calibrated for top 12 predictions, I would need to mean-revert all of the top 12 predictions at this point in the event by about 18%.

The results are pretty much what I would have expected. I’m aware that my model has a small but appreciable overconfidence problem, particularly early in the event, you can see though from the graphs that the calibration gets better and better as the event goes on. The main spots in my model that I need to inject more uncertainty are:
The non-WLT RPs, I threw together the predictions for these really quickly this year and didn’t get around to any proper calibration of them, so I expect them to be pretty overconfident
The second and third order RP sorts. I don’t have any uncertainty in these predictions at all, they are completely deterministic (that is, no variation from one simulation to another).
Simulations running “cold” instead of “hot”. I don’t have any accounting for the possibility that a team will consistently perform better or worse than their metrics would suggest. This is fine near the end of the event, since all of the team’s skill levels are pretty well known, but early on in the event this is a poorer assumption.

I could throw a blanket mean-reversion on my predictions to fix the over-confidence, but I’d prefer to fix the above problems first and the over-confidence should largely be taken care of as a result of the added uncertainty I introduce with the changes.

Not really sure how to respond to accusations that I personally am overconfident, since my model isn’t particularly overconfident in a statistical sense. Any major uncertainties I have are either already introduced into my model, or listed above and planned to be improved upon in the future. I don’t see my posting of my predictions as any different from predicting a coin flip has a 50% chance of heads. Sure, if you knew more properties of the coin, the surrounding air, the person flipping the coin, and the local gravitational field, you could make a prediction that is better than the 50% prediction, but that doesn’t mean the 50% prediction is bad. It’s just a well calibrated prediction that recognizes what it knows and doesn’t know. That’s all I try to do with my predictions, to maximize predictive power given the known bounds of the metrics available to me. I’m nowhere remotely close to predicting everything perfectly, but I’m doing the best I can with the information I have available.

I’m going to try soon to add some normalization between years for my Elo ratings. Presently, I find start of season Elos by taking 70% of the previous season’s Elo + 30% of the end of season Elo from 2 seasons ago. I then revert this sum toward 1550 by 20%. My concern with this method is that I don’t think it’s fair to directly sum Elos from different seasons since the Elo distributions vary so greatly year to year based on the game. If we had the same game every year, this wouldn’t be a problem.

To start, I measured the average, stdev, skew, and kurtosis for the end of season Elo distributions in each year. The results are shown in this table:

The average hovers right around 1500 each year, but this is due to how I designed my Elo ratings, and doesn’t actually tell us much. Some actual measure of “true skill” would probably have higher averages in recent years, since most would agree the average robot in 2018 is much better than the average robot was in 2002.
stdevs move around each year, likely due to the game structure. 2018 had the highest stdev on record by a pretty solid margin. I have previously speculated that this could be due to the snowballing scoring structure of powerup.
The skewness is interesting, for those of you unfamiliar with skewness, a positive skewness indicates a larger positive “tail” on the distribution than the negative “tail”. Every year on record has had a positive skew, which indicates that there are always more “outlier” good teams than “outlier” bad teams. Some years have had much higher skews than others though. For example, 2015 had an incredibly positive skew, which means there were a large number of very dominant teams. 2017 in contrast had one of the smallest skews on record. This is probably due to the severely limited scoring opportunities for the strong teams after the climb and 3 rotors, as well as the fact that the teams that lacked climbing ability were a severe hindrance to their alliances. The difference in skews between 2015 and 2017 can be seen in histograms of their Elo distributions. Notice how much longer the 2015 positive tail is than the 2017 one.

I also threw in kurtosis, kurtosis is a rough measure of how “outlier-y” or “taily” a distribution is. Kurtosis tracks very closely with skew every year. This means that the “outlier” teams driving the high kurtosis in some years are “good team” outliers and not “bad team” outliers. A high kurtosis with low skew would indicate that there are lots of good team and bad team outliers. Plots of stdev vs skew and skew vs kurtosis can be seen below.

Next, I’ll be trying to normalize end of season Elos so that I can get better start of season Elos. We’ve now had two years in a row of games that have low skew/kurtosis, which means that without adjustment the 2019 start of season Elos will also have low skew/kurtosis even though the 2019 game likely will not. It’ll all come down to predictive power though, if I can get enough predictive power increase I’ll add it in, otherwise I won’t.

I’m currently working on analyzing the awesome timeseries data from TBA. I’ll have plenty more to come, but I’m at a point where I got some really sweet graphs, so I thought I’d share, and describe a rough outline of my live model at the same time.

I am currently analyzing the ~1500 matches that have the best timeseries data. It’s possible that I’ll go back later and clean up the messier data, but I wanted to focus my early analysis on data I could have high trust in. What I’m currently working on is a way to predict the match winner in real-time based on this data. Here is a Brier score graph of my current model:

The first five seconds of the match just use my pre-match Elo win probability, but from then on, I begin incorporating the real-time scoring (in conjunction with the pre-match Elo prediction) to create win probabilities. The Brier score is basically steady for the first 5 seconds (when I’m not incorporating match data) but also from ~19 to ~23 seconds, which is probably because teams have by this point scored their first set of cubes and are picking up the second set. Also, note that even at t = 150 seconds, the Brier score is not zero because the actual final score can differ from the last score shown on the screen.

I mentioned that I incorporate Elo ratings into the predictions, here is a graph showing how much weight I give to Elo versus live match data at each second:

This and the following graphs you will see were created by tuning my prediction model, so the values that you see were the most predictive ones I found. After the first 5 seconds, the importance of Elo drops sharply down to ~65% by the end of auto, where it holds roughly steady for the same 19-23 second interval described above. This makes sense, since if there isn’t much scoring, we wouldn’t expect the live scoring to increase in importance much. After that, the Elo weight decays roughly exponentially down to 0.

The general form of my model (excluding Elo) is red win probability = 1-1/(1+10^((current red winning margin)/scale)) where “scale” is how much of a lead red would need to have a 10/11 ~=91% chance of winning the match at that point in the match. Let’s call this “scale” the “big lead” amount so as not to be confused with the scale on the field. If a team is up by 40 at a point in the match where the “big lead” value is 40, that team has a 91% chance of winning, but if they are up by 80 (two big leads), that team has a 99% chance of winning. Obviously, what is considered a big lead will vary over the match, so here is a graph showing that change over time:

I mentioned that the form of my model uses the red winning margin, but that’s not precisely true. In fact, I use an adjusted red winning margin where I account for ownership of the scale and of the switch. Basically, I found how much “value” to give to switch and scale ownership at each point in the match. What I mean by “value” is this, if red is down by X points but controls the scale, what is the value of X such that red and blue have an equal chance of winning the match? Here is a graph of value versus time for the scale:

Again, skipping the first 10 seconds of auto, we see scale ownership to be worth ~30 points after auto. It then drops in value to a min of 25 points at 23 seconds. This drop might be due to the initial scuffle for the scale. By 45 seconds, the scale has peaked in value at 49 points, and then it has a jittery drop until the end of the match. The same dip seen in “big lead” also appears in scale value at around 120 seconds. Interestingly, scale value does not go to 0 at the end of the match, but rather ends at 8 points. Perhaps scale ownership provides some indication of climb success?

Here is a similar graph for switch value:

Most of the same trends as in the previous graph also appear in this one. The biggest difference though is that switch value actually does go to 0 by the end of the match.

Let me know if you have any questions. I’ll have more to come soon, including win probability graphs and match “excitement” and “comeback/upset” scores.

I’ve just uploaded a sheet called “live_win_probabilities” which has win probabilities at every second of the match for each match in my data set. Only about 10% of matches are in this data set, I still might go back and clean up the messier ones if people are interested, but idk. I also calculated a couple of other metrics which could be used to determine how “good” a match is, here’s a summary of them:
team quality: this is just the pre-match average Elo of the competing teams
stakes: This is just a simple combination of the match type and the match number, qual matches have values of zero, and the first matches in the quarterfinals have values of 1, and the second matches of the quarterfinals have values of 2. This continues up until the highest stakes of final 3, which have values of 9. This is just a rough measurement obviously.
upset/comeback score: This is the probability that the winning alliance will win at their weakest point in the match. A value of 98% indicates the wining team had, at their worst point in the match, a 2% chance of winning.
excitement score: This looks at how much the win probability changes for an alliance over the course of a match. The units are a bit hard to grasp, but essentially a value of 1 indicates that, during the match, there was a full swing from a red win to a blue win or vice versa. So a value of 5 indicates 5 full swings of the expected match outcome.

According to these metrics, here are the matches in my data set that had the most excitement:
Tesla Division qm 1 29
Tesla Division qf 2 3
San Francisco Regional qm 1 33
Finger Lakes Regional qm 1 68
Idaho Regional qm 1 35

Here are the matches that had the biggest comeback or upset:
PNW District SunDome Event qf 2 2
Canadian Rockies Regional qm 1 64
ONT District Western University, Western Engineering Event f 1 1
Tesla Division qm 1 105
Minnesota North Star Regional qm 1 41

I also added a “lookup” sheet to the workbook which can be used to generate win probability graphs. For example, here’s the win probability graph for the last comeback I mentioned, Minnesota North Star Regional qm 1 41:

I had a lot of fun looking at this data. Live win probabilities are something I’ve been dreaming about for FRC ever since I saw them for other sports. I hope to be able to analyze the 2019 data before the season ends, but no promises.

For anyone that already wants to start thinking about 2019, I’ve uploaded a book which shows the 2019 start of season Elo ratings for all teams. I’m not currently planning to change my Elo model again before next season (although note that I’m bad at evaluating myself). Results are copied here:

``````Team	2019 start of season Elo
254	1900
2056	1876
1678	1865
118	1828
2481	1820
195	1817
1114	1817
2046	1817
694	1806
148	1801
3310	1791
2590	1789
3309	1788
2767	1785
1323	1782
125	1778
2910	1778
1574	1775
1538	1774
2122	1774
225	1770
1619	1768
1986	1767
3130	1764
842	1761
5406	1760
1241	1760
217	1758
971	1756
1796	1755
16	1751
4613	1750
133	1750
27	1749
4539	1744
5172	1744
180	1742
25	1741
4003	1740
3538	1740
624	1740
3357	1740
2168	1740
1690	1739
987	1739
67	1739
230	1738
3478	1737
2471	1734
340	1732
1629	1732
179	1731
3452	1730
1806	1728
319	1727
1318	1727
3005	1725
330	1724
399	1722
5050	1722
141	1722
2337	1721
494	1721
85	1719
3476	1718
2614	1718
2791	1718
2478	1715
1519	1715
5460	1715
3707	1715
33	1714
4488	1714
3339	1713
1325	1712
1747	1712
3512	1711
365	1709
4028	1708
4917	1708
4237	1706
1756	1705
177	1705
4910	1705
176	1705
2642	1704
3959	1704
1706	1703
1425	1703
5818	1703
973	1703
5687	1701
610	1701
1640	1700
1918	1700
5190	1699
291	1695
525	1693
1876	1692
5895	1692
1533	1692
868	1691
604	1690
56	1690
2403	1690
233	1690
2834	1689
234	1689
1712	1689
2059	1689
3937	1689
3539	1688
359	1688
4451	1686
2052	1685
4362	1685
302	1684
269	1683
71	1683
1506	1683
1024	1683
865	1681
364	1680
1923	1680
95	1679
6329	1679
3015	1678
4564	1678
3255	1678
384	1678
910	1677
303	1676
1259	1676
5199	1676
3674	1675
1731	1675
4513	1675
5985	1675
1730	1674
6763	1673
2992	1673
1023	1673
1741	1672
2557	1672
1648	1672
744	1671
341	1671
175	1670
870	1669
1102	1669
379	1668
2848	1668
5987	1668
2410	1668
4253	1668
3098	1668
2630	1667
4618	1667
4265	1666
1726	1666
4946	1665
1492	1665
4063	1665
4143	1664
346	1663
1011	1663
876	1663
4476	1663
3683	1663
1736	1663
294	1663
3802	1662
2130	1661
1391	1660
4911	1660
3646	1660
1305	1659
957	1659
3663	1659
3128	1659
6705	1659
3990	1659
832	1659
5803	1658
368	1658
846	1658
2451	1658
78	1657
4655	1657
2075	1657
1477	1656
188	1656
4188	1656
4334	1655
1025	1655
3641	1655
3616	1655
4976	1654
4678	1654
1746	1654
503	1654
862	1654
5505	1654
1339	1653
5802	1653
5254	1653
456	1652
1622	1652
5472	1651
4522	1651
2877	1651
488	1651
5053	1651
4272	1651
772	1651
5012	1651
2522	1650
20	1650
3546	1650
3824	1650
639	1650
2013	1649
3316	1649
1507	1649
2974	1649
2502	1649
1723	1649
4587	1648
2383	1648
1559	1648
5572	1648
3230	1648
1018	1648
1983	1647
1065	1647
1772	1646
1296	1646
4561	1646
2826	1646
2194	1645
70	1645
2960	1645
1577	1645
1684	1645
3314	1644
2485	1644
314	1644
6672	1643
4004	1643
1262	1643
2706	1643
115	1643
1885	1642
1197	1642
135	1642
5842	1640
6579	1640
5883	1640
649	1639
3536	1639
88	1639
5436	1639
3656	1639
3620	1638
5501	1638
4388	1638
4405	1638
1073	1638
2200	1638
4189	1638
2771	1637
4635	1637
834	1637
2137	1637
930	1637
4145	1636
3750	1636
1414	1636
2996	1636
333	1636
3547	1636
2708	1635
3847	1635
3542	1635
5567	1635
6201	1635
2930	1635
2976	1634
2231	1634
1836	1634
2054	1633
2556	1633
4776	1632
3419	1632
5036	1632
6025	1631
5813	1631
2655	1631
2987	1631
5026	1631
245	1631
3835	1631
2659	1630
1421	1630
6090	1630
1718	1630
469	1629
4980	1629
2363	1629
1156	1629
2175	1629
1255	1629
2682	1629
2474	1629
386	1628
5404	1628
2338	1628
5046	1628
1360	1628
103	1628
4213	1628
2990	1628
4541	1627
6328	1627
1572	1627
5152	1627
3276	1627
2144	1627
66	1627
6334	1627
3489	1626
4391	1626
5675	1626
6418	1626
1322	1625
1744	1625
4469	1625
1599	1625
1058	1625
5817	1625
687	1624
3534	1624
3250	1623
316	1623
4967	1623
5155	1623
4944	1623
4855	1623
829	1623
1100	1622
5603	1622
4146	1622
597	1622
3929	1622
5509	1622
2783	1622
1710	1621
708	1621
2486	1621
422	1621
1218	1621
4290	1621
3481	1621
1319	1621
3770	1621
4959	1621
2202	1621
997	1620
5114	1620
1987	1620
578	1619
3461	1619
237	1619
1189	1619
2611	1619
3328	1618
5431	1618
1732	1618
238	1618
2164	1617
2468	1617
1625	1617
1540	1616
6502	1616
75	1616
4533	1616
5584	1616
1418	1616
4499	1615
4276	1615
3997	1615
4550	1615
4415	1615
1816	1615
3197	1615
222	1615
343	1615
4795	1614
5986	1614
3374	1614
2811	1613
3695	1613
226	1613
4027	1613
1778	1613
4908	1613
4039	1613
236	1612
3256	1612
3042	1612
63	1612
2537	1612
5530	1612
6117	1611
5434	1611
4061	1611
3623	1611
5499	1610
3010	1610
2199	1610
1595	1610
3218	1609
1002	1609
968	1609
3647	1609
5576	1609
342	1609
3360	1609
58	1608
348	1608
2102	1608
1592	1608
4525	1608
3635	1607
5338	1607
888	1607
4020	1606
1523	1606
5654	1606
4087	1606
207	1606
4623	1606
2152	1606
3737	1606
167	1606
287	1605
1658	1605
6077	1605
5663	1605
4472	1605
358	1605
1071	1605
3277	1605
5614	1604
3667	1604
159	1604
120	1604
59	1603
614	1603
5846	1603
4198	1603
2851	1603
1807	1603
3313	1602
2377	1602
51	1602
1511	1602
670	1602
836	1602
1596	1602
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``````
1 Like

Well, I guess a DQ after time expires is one way to get a big point swing.

After a break, I’m back at it again looking at schedule strengths, I’ll have a more thorough post soon, but I thought I would just share this quick. Here is a summary of the best and worst schedules of 2018. I decided just to look at when partners and opponents were picked in order to validate my model, and I think my model’s doing a pretty good job.

I have 2096’s Hopper schedule as the worst schedule of 2018:

They had to play against 6 of the top 10 teams (top 5 captains and top 5 picks) and got to play with 0 of them. Tough luck guys.

On the flipside, we have 2220’s schedule on Archimedes as the best schedule:

They get to play with all of the top 4 robots, and don’t have to face a single one. The with/against lists are the same size though, which doesn’t sound great until you realize you play against 50% more teams than you play with.

More to come shortly

I haven’t read everything entirely in-depth, but in a game like this years averaging scores isn’t as accurate a measurement of how good a robot is. Do you account for this in any way? To me it seems to accurately predict matches better data would be required.

Are you referring specifically to any of my books or just speaking generally?

I’m assuming the latter here. My general match prediction algorithm is a raw average of predicted contribution win probability and Elo win probability. Neither of these methods “average scores” like you seem to be saying. Both of them only incorporate raw match scores though, not any scouting data or detailed score breakdowns. I’m looking to make a second more advanced Elo model soon which incorporates some aspects of the published score breakdowns, that will hopefully be noticeably more predictive than my current Elo model.

Not sure I answered your question though, so let me know if you were asking something else.

I’ve uploaded a new book, called “CC Ranking Comparison.xlsx”. I’m trying something new though, instead of making a long post here, for my next few projects I’m going to be explaining them on a site I just made called https://frcstats.blog/. We’ll see how this goes, feel free to give me feedback either here or there on which format you prefer or what I could do differently in either medium to improve my content.

Thanks for the shout out in the blog post! I’m glad my predictions were actually helpful for something other than placating my boredom.

I’m looking forward to see where this takes you next, and please let me know if there’s anything else of help I can do.

I’ve got another post up, this one regarding finding the best way to “measure” strength of schedule. I’ve decided to use a metric I’m calling “average rank difference” moving forward, which is found by:
Averaging the sum of all opponent ranks and subtracting out all partner ranks, and then also subtracting ((# of teams + 1)/2) and then dividing by the number of teams.

Another post is up talking about schedule strengths from 2005-2018.

All teams’ average schedule strengths (higher = harder, 0 = neutral):

``````team	average schedule strength
1	-0.03
4	0.03
5	0.00
7	-0.12
8	-0.04
9	0.14
11	-0.06
16	-0.16
19	0.26
20	-0.10
21	-0.02
22	-0.23
23	0.06
25	-0.14
27	-0.12
28	-0.09
31	0.05
33	-0.10
34	-0.05
38	-0.05
39	-0.08
40	-0.13
41	0.05
42	0.18
45	-0.07
47	-0.01
48	-0.06
49	-0.01
51	-0.10
53	0.01
56	-0.19
57	-0.06
58	-0.03
59	-0.03
60	-0.08
61	-0.03
63	-0.03
64	-0.25
65	-0.03
66	-0.04
67	-0.17
68	-0.10
69	-0.12
70	-0.09
71	-0.16
73	0.15
74	-0.04
75	-0.04
78	-0.14
79	-0.11
81	0.04
84	-0.06
85	-0.09
86	-0.04
87	0.01
88	-0.07
92	0.14
93	-0.11
94	-0.04
95	0.00
96	-0.01
97	-0.01
100	-0.01
101	0.00
102	-0.03
103	-0.11
104	0.21
107	-0.07
108	-0.03
111	-0.13
114	-0.11
115	-0.01
116	0.04
117	0.08
118	-0.12
120	0.05
121	-0.10
122	-0.01
123	-0.03
125	-0.12
126	-0.15
128	-0.02
131	-0.09
133	-0.05
134	0.03
135	-0.04
136	0.18
138	-0.05
141	0.00
144	-0.08
145	-0.02
148	-0.19
151	0.07
155	-0.04
156	0.03
157	0.06
158	-0.04
159	-0.05
165	-0.12
166	-0.10
167	-0.06
168	0.13
171	-0.06
172	0.00
173	-0.03
174	-0.02
175	-0.09
176	-0.04
177	-0.11
178	0.08
179	-0.12
180	-0.13
181	0.00
184	0.18
188	-0.13
190	-0.06
191	-0.09
192	-0.06
193	-0.05
195	-0.16
199	0.13
201	-0.04
203	0.12
204	0.07
207	-0.09
211	0.09
213	-0.04
216	-0.01
217	-0.15
219	-0.01
222	-0.03
223	0.03
224	0.04
225	-0.09
226	-0.06
228	0.02
229	-0.10
230	-0.07
231	-0.09
233	-0.16
234	-0.10
236	-0.05
237	-0.09
238	-0.05
240	-0.06
241	0.02
244	0.00
245	-0.08
246	-0.02
247	-0.03
250	-0.01
253	0.18
254	-0.17
256	0.04
263	-0.02
265	0.08
269	-0.04
270	0.07
271	-0.04
272	-0.07
274	-0.15
276	-0.04
279	-0.03
280	0.00
281	-0.02
283	-0.10
284	0.04
287	0.01
288	0.08
291	-0.03
292	-0.01
293	-0.11
294	-0.11
295	-0.06
296	0.02
299	0.09
300	0.34
301	-0.10
302	-0.06
303	-0.08
304	0.01
306	-0.01
308	-0.02
312	-0.07
313	0.14
314	-0.03
316	-0.07
319	-0.05
321	0.05
322	-0.01
323	-0.12
326	-0.03
329	-0.10
330	-0.14
331	-0.10
333	-0.01
334	-0.05
335	0.01
337	-0.07
339	-0.02
340	-0.08
341	-0.09
342	0.01
343	-0.12
345	-0.07
346	-0.05
348	-0.06
350	0.31
352	0.03
353	-0.06
354	-0.05
357	0.04
358	-0.12
359	-0.10
360	-0.10
362	0.11
364	-0.10
365	-0.13
368	-0.23
369	-0.03
371	0.06
372	0.03
375	-0.07
378	-0.10
379	-0.01
380	-0.02
381	0.06
382	0.46
383	-0.07
384	-0.05
386	0.00
388	0.11
391	0.12
393	0.05
395	-0.06
397	-0.03
398	0.00
399	-0.14
401	-0.04
404	0.11
405	0.07
406	0.10
408	0.17
414	0.11
415	-0.11
416	0.12
417	0.11
418	-0.08
421	0.08
422	-0.07
423	0.05
424	0.00
425	0.03
433	0.03
434	0.05
435	-0.05
437	0.08
440	0.08
441	-0.07
442	0.04
443	0.00
444	0.04
447	0.06
448	0.18
449	0.00
451	0.01
453	0.01
456	-0.23
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494	-0.11
496	-0.02
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514	-0.13
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804	0.04
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810	-0.02
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812	0.03
814	0.15
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816	-0.01
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820	0.18
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830	0.03
832	-0.06
833	-0.21
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840	-0.12
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843	-0.06
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846	-0.13
847	-0.02
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852	-0.10
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876	-0.11
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888	-0.06
892	0.42
894	-0.01
896	0.14
900	-0.03
903	-0.03
904	0.00
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907	-0.01
909	-0.08
910	-0.10
912	0.20
913	-0.19
919	-0.03
922	-0.03
926	-0.13
928	-0.08
930	0.02
931	-0.10
932	0.03
935	-0.06
937	0.07
938	0.01
939	0.07
945	-0.06
948	-0.17
949	0.03
955	-0.04
956	0.03
957	0.06
961	0.05
963	-0.17
964	0.20
966	0.14
967	-0.03
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970	0.33
971	-0.17
972	0.03
973	-0.13
974	0.01
975	0.13
977	-0.03
980	-0.04
981	-0.05
987	-0.19
988	-0.01
989	0.03
990	0.03
991	0.01
995	-0.02
996	0.02
997	-0.01
999	0.03
1000	0.01
1001	-0.11
1002	-0.09
1006	-0.04
1007	0.01
1008	0.14
1009	0.10
1011	0.00
1013	0.05
1014	-0.01
1015	0.18
1018	0.00
1019	0.05
1022	-0.16
1023	-0.08
1024	-0.12
1025	-0.09
1026	-0.01
1027	-0.01
1028	0.01
1029	0.08
1031	-0.47
1033	0.05
1034	0.05
1038	-0.06
1039	0.00
1040	-0.18
1047	0.12
1048	0.33
1049	0.20
1051	-0.01
1053	0.26
1054	-0.05
1056	-0.13
1057	-0.05
1058	-0.04
1062	-0.09
1065	-0.14
1068	0.02
1070	-0.01
1071	-0.04
1072	0.12
1073	-0.03
1075	0.03
1076	0.00
1079	-0.24
1080	0.00
1083	-0.07
1084	0.02
1085	0.06
1086	-0.02
1087	0.21
1089	-0.11
1091	-0.01
1093	0.28
1094	-0.05
1095	-0.11
1097	0.04
1098	0.00
1099	0.04
1100	-0.06
1101	0.04
1102	-0.08
1103	-0.01
1108	-0.07
1110	0.08
1111	0.02
1112	0.19
1113	-0.35
1114	-0.16
1120	-0.16
1123	0.12
1124	-0.09
1126	-0.12
1127	-0.10
1130	0.20
1132	0.15
1135	0.31
1137	-0.04
1138	-0.11
1139	-0.06
1140	-0.04
1141	0.06
1143	0.04
1144	-0.03
1147	0.14
1148	0.12
1152	0.13
1153	-0.08
1155	-0.03
1156	-0.03
1157	-0.04
1158	-0.13
1159	0.02
1160	0.04
1163	0.04
1164	0.04
1165	0.03
1167	-0.06
1168	0.12
1172	0.28
1178	0.08
1180	0.03
1182	-0.04
1183	-0.13
1184	-0.20
1187	-0.02
1188	0.00
1189	-0.03
1190	0.05
1195	0.10
1197	-0.08
1203	-0.13
1205	0.00
1208	-0.14
1209	0.09
1211	0.01
1212	-0.13
1213	-0.08
1214	0.29
1216	-0.09
1218	-0.16
1219	-0.03
1221	0.06
1222	0.09
1224	0.41
1225	0.00
1227	0.37
1228	0.01
1230	-0.17
1232	0.15
1236	-0.07
1237	0.09
1240	0.35
1241	-0.12
1242	0.36
1243	-0.03
1244	0.28
1245	-0.05
1246	0.13
1247	0.01
1248	0.22
1249	-0.09
1250	-0.03
1251	-0.06
1254	0.01
1255	-0.01
1256	0.01
1257	-0.06
1258	0.02
1259	-0.08
1260	-0.11
1261	-0.11
1262	-0.03
1263	0.15
1266	0.03
1268	0.18
1270	0.05
1272	0.01
1274	0.08
1275	0.02
1276	-0.02
1277	0.09
1278	-0.14
1279	-0.05
1280	-0.09
1281	0.08
1284	0.06
1285	-0.10
1286	-0.08
1287	-0.08
1288	-0.09
1289	0.13
1290	-0.04
1292	-0.07
1293	0.06
1294	0.01
1296	-0.08
1301	-0.02
1302	-0.01
1303	0.03
1304	0.03
1305	-0.08
1306	0.04
1307	0.03
1308	-0.04
1310	-0.08
1311	-0.03
1312	-0.12
1315	-0.26
1317	-0.01
1318	-0.10
1319	-0.04
1320	-0.14
1322	0.04
1323	-0.03
1324	0.04
1325	-0.04
1326	0.12
1327	0.05
1329	-0.06
1330	0.01
1332	-0.07
1334	-0.03
1335	0.07
1336	0.00
1339	-0.10
1340	0.21
1341	-0.04
1343	-0.20
1345	0.02
1346	-0.06
1347	0.00
1348	-0.02
1349	0.30
1350	-0.03
1351	0.04
1353	-0.08
1355	0.11
1357	0.13
1358	0.04
1359	0.02
1360	-0.05
1361	0.01
1366	-0.05
1367	0.03
1368	0.07
1369	0.04
1370	0.05
1371	-0.04
1372	0.19
1373	-0.14
1374	-0.01
1375	-0.02
1376	0.09
1377	0.09
1378	0.13
1379	0.00
1382	0.04
1384	0.26
1385	-0.16
1386	0.12
1388	-0.14
1389	0.05
1390	0.02
1391	0.00
1392	0.28
1394	-0.02
1396	-0.01
1397	-0.13
1398	0.15
1401	0.15
1402	-0.13
1403	-0.06
1404	-0.12
1405	0.00
1407	0.00
1408	0.05
1410	-0.05
1412	0.22
1413	-0.06
1414	0.06
1415	0.02
1418	-0.11
1419	0.06
1421	-0.04
1422	0.12
1425	-0.12
1426	-0.15
1428	-0.01
1429	-0.12
1432	0.10
1436	-0.05
1438	0.08
1439	0.10
1440	0.01
1444	-0.04
1446	0.09
1447	-0.10
1448	-0.04
1449	-0.11
1450	0.09
1451	0.34
1452	0.04
1456	-0.22
1457	0.16
1458	-0.01
1460	-0.15
1462	-0.01
1464	0.37
1466	0.04
1467	0.00
1468	0.01
1472	0.16
1474	0.02
1476	0.25
1477	-0.12
1479	0.31
1480	-0.11
1481	-0.05
1482	-0.08
1484	0.16
1486	-0.11
1489	0.13
1492	0.03
1493	-0.06
1495	0.11
1496	0.26
1497	0.00
1500	0.10
1501	-0.10
1502	-0.03
1503	-0.21
1504	-0.03
1505	-0.38
1506	0.01
1507	-0.18
1508	0.24
1509	-0.21
1510	-0.04
1511	-0.08
1512	0.01
1513	0.11
1514	0.20
1515	0.00
1516	-0.13
1517	0.00
1518	0.00
1519	-0.17
1520	0.16
1522	0.07
1523	-0.12
1524	0.36
1525	-0.03
1527	0.06
1528	0.09
1529	0.08
1531	0.01
1532	0.36
1533	-0.13
1534	0.06
1535	0.04
1537	0.14
1538	-0.11
1539	-0.02
1540	-0.08
1541	0.06
1543	0.08
1544	0.08
1546	0.03
1547	0.03
1548	0.04
1549	-0.04
1550	-0.02
1551	-0.06
1552	-0.07
1553	-0.05
1554	0.06
1555	0.10
1556	0.06
1557	0.02
1558	0.08
1559	-0.05
1560	0.16
1561	-0.03
1562	-0.05
1563	0.01
1564	0.25
1565	-0.04
1566	0.03
1567	-0.10
1568	0.08
1569	-0.11
1570	0.11
1571	0.16
1572	-0.07
1573	-0.05
1574	-0.09
1576	0.08
1577	-0.02
1578	-0.10
1579	0.03
1580	-0.06
1582	-0.39
1583	-0.05
1584	-0.06
1585	0.07
1588	0.05
1589	0.08
1590	0.01
1591	0.03
1592	-0.18
1593	0.07
1594	-0.04
1595	-0.07
1596	-0.12
1597	-0.02
1598	-0.05
1599	0.06
1600	0.01
1601	0.15
1602	0.26
1603	0.35
1604	0.13
1605	0.13
1606	-0.10
1607	0.08
1609	0.17
1610	-0.04
1611	0.07
1612	-0.12
1613	0.27
1616	-0.02
1617	0.08
1618	-0.05
1619	-0.16
1620	-0.06
1621	0.34
1622	0.01
1623	0.00
1624	-0.04
1625	-0.16
1626	0.00
1628	0.50
1629	-0.13
1631	0.02
1633	0.03
1634	0.15
1635	-0.02
1636	-0.13
1640	-0.06
1641	0.04
1642	0.11
1643	0.08
1644	-0.01
1645	0.28
1646	0.02
1647	-0.03
1648	-0.06
1649	-0.02
1650	0.48
1652	0.09
1653	0.11
1654	0.12
1655	-0.01
1656	0.10
1657	-0.13
1658	0.00
1660	0.00
1661	-0.01
1662	-0.05
1665	0.01
1666	0.05
1667	0.23
1669	-0.09
1670	0.15
1671	-0.09
1672	0.01
1674	0.09
1675	-0.01
1676	-0.11
1677	0.04
1678	-0.13
1680	-0.11
1682	0.15
1683	-0.03
1684	0.01
1685	-0.05
1686	0.15
1687	0.02
1688	-0.07
1689	0.04
1690	-0.13
1691	-0.05
1692	0.11
1693	0.14
1694	0.02
1695	0.05
1696	-0.02
1698	0.03
1699	-0.01
1700	0.07
1701	-0.03
1702	0.02
1703	0.08
1704	-0.03
1705	0.08
1706	-0.08
1708	-0.02
1710	-0.05
1711	0.00
1712	-0.06
1713	0.03
1714	-0.04
1715	0.00
1716	0.10
1717	-0.12
1718	-0.15
1719	-0.03
1720	-0.03
1721	-0.03
1722	0.21
1723	0.01
1724	-0.03
1725	0.06
1726	-0.07
1727	-0.06
1728	0.25
1729	0.02
1730	-0.19
1731	-0.16
1732	-0.11
1733	0.11
1734	-0.03
1735	-0.06
1736	-0.09
1737	0.07
1739	0.05
1740	0.07
1741	-0.01
1742	-0.08
1743	0.08
1744	0.04
1745	-0.06
1746	-0.18
1747	-0.06
1748	-0.01
1749	0.12
1750	0.05
1751	0.15
1752	0.15
1753	0.28
1754	0.34
1755	0.06
1756	-0.14
1757	-0.01
1758	-0.07
1759	0.08
1760	-0.03
1761	-0.01
1763	0.13
1764	0.05
1765	0.09
1766	-0.07
1767	0.10
1768	-0.09
1769	0.09
1770	0.03
1771	-0.09
1772	-0.16
1774	0.22
1775	-0.10
1776	0.13
1777	-0.04
1778	0.00
1779	-0.02
1780	0.07
1781	-0.01
1782	0.21
1783	0.06
1784	0.00
1785	-0.01
1786	0.11
1787	-0.02
1788	0.06
1789	0.08
1791	0.10
1792	0.05
1793	0.01
1795	0.09
1796	-0.07
1797	0.27
1798	-0.04
1799	0.13
1800	0.03
1801	-0.01
1802	0.08
1803	0.01
1804	0.21
1805	0.32
1806	-0.18
1807	-0.06
1808	0.18
1810	-0.03
1811	0.02
1813	0.33
1814	0.06
1815	0.01
1816	-0.09
1817	0.04
1818	-0.02
1820	0.01
1823	-0.09
1824	-0.13
1825	-0.11
1826	0.02
1827	0.07
1828	-0.05
1829	0.10
1830	-0.07
1831	0.04
1834	0.02
1835	-0.01
1836	-0.05
1837	0.29
1838	0.18
1839	0.11
1840	-0.22
1841	0.01
1842	0.06
1843	0.48
1845	0.08
1846	0.02
1847	0.02
1848	-0.06
1849	0.04
1850	0.05
1851	0.39
1852	-0.07
1853	-0.20
1855	-0.15
1856	0.08
1858	0.05
1859	0.09
1860	-0.04
1861	0.01
1862	-0.05
1863	-0.06
1864	0.12
1865	-0.10
1867	-0.10
1868	-0.05
1870	-0.14
1871	0.29
1872	0.01
1875	-0.04
1876	-0.07
1877	0.17
1879	0.51
1880	0.09
1881	0.08
1882	0.00
1883	0.00
1884	-0.04
1885	-0.10
1886	0.12
1887	0.06
1888	0.06
1889	0.01
1890	0.15
1891	-0.08
1893	0.04
1894	0.22
1895	0.00
1896	0.10
1897	-0.06
1898	0.10
1899	0.05
1900	0.11
1901	-0.08
1902	-0.03
1904	-0.16
1905	-0.02
1906	-0.02
1907	-0.13
1908	0.15
1909	-0.04
1910	-0.10
1911	0.15
1912	-0.08
1913	-0.05
1915	0.11
1916	0.01
1917	-0.13
1918	-0.16
1919	0.04
1920	0.03
1922	-0.05
1923	-0.08
1925	0.25
1926	0.09
1927	-0.09
1929	-0.02
1930	0.14
1931	0.20
1932	0.29
1933	-0.14
1934	-0.03
1937	-0.04
1938	-0.15
1939	-0.08
1940	0.07
1941	0.01
1942	0.00
1943	-0.03
1944	0.07
1945	0.10
1946	-0.06
1947	-0.25
1948	0.19
1949	0.00
1950	0.04
1951	0.21
1952	0.07
1954	0.13
1955	0.00
1956	0.18
1957	0.13
1959	0.07
1960	0.03
1961	0.34
1962	-0.18
1965	0.05
1966	-0.02
1967	0.05
1970	0.30
1972	0.12
1973	0.14
1974	0.15
1975	-0.18
1976	0.08
1977	-0.01
1978	0.30
1980	0.07
1981	-0.28
1982	-0.06
1983	-0.15
1984	0.08
1985	-0.07
1986	-0.18
1987	-0.11
1988	-0.44
1989	0.03
1990	0.00
1991	0.03
1992	-0.13
1994	0.07
1995	0.04
1996	-0.12
1997	-0.08
1998	-0.08
1999	-0.10
2000	-0.10
2001	0.10
2002	0.00
2004	0.01
2005	-0.11
2007	-0.06
2008	0.12
2009	-0.19
2010	-0.09
2011	-0.14
2012	0.10
2013	-0.02
2014	-0.10
2015	0.03
2016	-0.10
2017	-0.22
2019	-0.04
2021	0.08
2022	-0.03
2023	0.00
2024	-0.26
2025	-0.20
2026	0.21
2027	0.05
2028	0.09
2029	-0.13
2030	-0.09
2031	-0.02
2032	-0.07
2033	-0.09
2034	0.10
2035	-0.12
2036	0.01
2037	0.18
2038	0.00
2039	-0.09
2040	-0.05
2041	-0.13
2042	-0.14
2043	-0.13
2044	0.09
2045	-0.05
2046	-0.20
2047	-0.14
2048	0.02
2049	0.24
2050	0.12
2051	0.02
2052	-0.14
2053	-0.01
2054	-0.16
2055	0.01
2056	-0.18
2057	0.05
2059	-0.02
2060	-0.14
2061	-0.09
2062	-0.17
2063	-0.08
2064	0.04
2065	-0.17
2066	0.03
2067	-0.08
2068	-0.01
2069	-0.05
2070	0.03
2071	-0.16
2072	-0.03
2073	-0.05
2074	0.11
2075	-0.05
2076	-0.01
2077	0.01
2078	-0.05
2079	0.10
2080	0.02
2081	-0.03
2083	0.09
2084	-0.08
2085	-0.01
2087	0.39
2089	0.22
2090	-0.13
2091	-0.06
2092	0.19
2093	-0.01
2095	0.02
2096	0.09
2099	-0.36
2100	-0.20
2102	-0.04
2103	-0.04
2104	0.05
2105	-0.02
2106	-0.03
2107	0.01
2108	-0.10
2109	-0.22
2110	-0.11
2111	-0.03
2112	0.06
2115	0.14
2116	-0.12
2119	0.06
2120	0.28
2121	0.08
2122	-0.16
2124	0.10
2125	0.04
2126	-0.04
2127	0.16
2128	0.00
2129	0.01
2130	-0.02
2132	0.15
2133	0.06
2134	-0.07
2135	0.07
2136	-0.02
2137	-0.09
2139	-0.03
2140	-0.13
2141	0.08
2142	-0.26
2143	-0.09
2144	-0.06
2145	-0.05
2147	0.01
2148	-0.04
2149	-0.07
2150	0.02
2151	-0.01
2152	-0.01
2153	-0.05
2154	0.17
2156	0.05
2157	-0.07
2158	0.03
2159	-0.02
2161	0.12
2162	0.01
2163	0.02
2164	-0.10
2165	-0.20
2166	0.03
2167	-0.07
2168	-0.14
2169	-0.09
2170	0.04
2171	-0.01
2172	0.03
2173	0.08
2174	-0.04
2175	-0.05
2176	0.06
2177	-0.09
2178	0.24
2180	-0.04
2181	-0.09
2182	-0.05
2183	0.04
2184	-0.15
2185	0.09
2186	0.02
2187	0.10
2188	-0.06
2189	0.15
2190	-0.09
2191	-0.03
2192	-0.04
2193	-0.04
2194	-0.02
2196	0.00
2197	-0.01
2198	0.04
2199	0.03
2200	-0.04
2201	0.06
2202	-0.05
2203	-0.13
2204	0.09
2205	0.04
2206	-0.05
2207	0.02
2208	0.17
2209	0.22
2210	-0.06
2211	-0.15
2212	-0.07
2213	0.00
2214	-0.14
2215	-0.24
2216	-0.05
2217	-0.03
2219	0.09
2220	0.00
2221	0.10
2222	-0.22
2223	-0.03
2224	0.07
2225	0.05
2226	-0.05
2227	-0.05
2228	0.04
2229	0.11
2230	-0.08
2231	-0.10
2232	-0.10
2234	-0.01
2235	-0.06
2236	-0.43
2237	-0.11
2239	-0.13
2240	0.02
2241	-0.26
2242	-0.10
2243	-0.16
2244	0.02
2245	0.01
2246	-0.03
2247	-0.02
2249	-0.06
2250	-0.03
2251	0.16
2252	-0.04
2254	0.24
2257	-0.05
2259	0.09
2260	0.00
2261	0.01
2262	0.09
2264	-0.14
2265	-0.07
2266	-0.17
2272	-0.19
2273	-0.26
2274	-0.09
2275	-0.01
2276	-0.01
2278	-0.16
2279	-0.03
2280	-0.05
2283	-0.03
2285	-0.02
2287	0.09
2330	-0.09
2332	0.01
2333	-0.07
2334	0.04
2335	0.04
2336	0.10
2337	-0.11
2338	-0.07
2339	0.02
2340	0.05
2341	-0.10
2342	-0.03
2343	-0.08
2344	-0.05
2345	-0.05
2346	0.14
2347	0.07
2348	-0.08
2349	-0.09
2350	0.06
2352	-0.07
2353	0.07
2354	-0.05
2357	0.07
2358	-0.02
2359	-0.02
2360	0.06
2361	0.12
2362	0.29
2363	-0.13
2364	-0.15
2365	-0.31
2366	0.04
2367	0.03
2368	0.07
2369	-0.08
2370	0.01
2371	-0.03
2372	0.06
2373	-0.01
2374	-0.04
2375	-0.02
2376	0.06
2377	-0.10
2378	0.02
2380	0.36
2381	0.02
2382	0.10
2383	-0.09
2385	0.24
2386	0.01
2387	0.21
2388	0.05
2389	0.01
2390	0.07
2391	-0.09
2392	0.03
2393	-0.05
2394	-0.25
2395	0.01
2396	-0.09
2397	-0.29
2398	0.03
2399	0.05
2400	-0.03
2401	0.05
2402	0.03
2403	-0.05
2404	0.10
2405	0.05
2406	0.01
2407	0.06
2408	0.08
2409	0.02
2410	-0.09
2411	0.04
2412	0.01
2413	-0.19
2414	0.09
2415	-0.06
2417	0.18
2418	-0.08
2419	0.12
2420	-0.02
2421	0.03
2422	0.10
2423	0.01
2424	-0.01
2425	0.08
2427	-0.33
2428	-0.04
2429	0.00
2430	0.04
2431	0.19
2432	0.28
2433	-0.14
2434	0.07
2435	-0.02
2436	-0.07
2437	0.02
2438	-0.02
2439	-0.10
2440	0.12
2441	0.08
2443	-0.06
2444	0.00
2445	-0.08
2446	0.27
2447	0.19
2448	0.08
2449	-0.02
2450	0.04
2451	-0.09
2453	0.15
2454	0.05
2455	0.03
2456	0.06
2457	0.08
2458	0.09
2459	0.01
2460	0.04
2461	0.00
2462	0.13
2463	-0.23
2465	0.02
2466	0.05
2467	0.18
2468	-0.15
2469	-0.05
2470	0.01
2471	-0.15
2472	0.00
2473	-0.04
2474	-0.12
2475	-0.11
2476	0.33
2477	0.13
2478	0.05
2479	-0.01
2480	-0.13
2481	-0.08
2483	0.10
2484	-0.12
2485	-0.05
2486	-0.10
2487	-0.02
2488	-0.07
2489	0.06
2490	0.13
2491	-0.04
2493	-0.02
2495	0.10
2496	-0.03
2497	0.19
2498	-0.09
2499	0.10
2500	0.06
2501	0.02
2502	-0.04
2503	0.05
2504	0.02
2505	-0.10
2506	-0.05
2508	-0.03
2509	-0.05
2510	0.02
2511	-0.08
2512	-0.14
2513	-0.03
2514	0.15
2515	0.01
2517	0.00
2518	-0.03
2520	0.17
2521	0.03
2522	-0.06
2523	-0.02
2524	0.23
2525	0.01
2526	-0.11
2528	-0.01
2529	-0.10
2530	-0.09
2531	0.14
2532	0.07
2533	0.15
2534	-0.03
2535	0.07
2536	0.25
2537	-0.04
2538	-0.01
2539	0.06
2540	0.02
2542	0.08
2543	-0.04
2544	-0.02
2545	0.03
2546	0.03
2547	0.11
2549	0.03
2550	-0.03
2551	-0.02
2553	0.16
2554	0.06
2555	0.09
2556	0.03
2557	-0.09
2558	0.05
2559	0.04
2560	0.17
2561	0.09
2562	-0.04
2563	0.29
2564	-0.13
2565	0.18
2566	0.17
2567	-0.22
2568	-0.26
2569	0.04
2570	-0.12
2571	0.14
2572	0.03
2573	0.00
2574	-0.01
2575	0.17
2576	0.02
2577	0.02
2579	0.01
2580	0.27
2581	-0.18
2582	0.00
2583	0.04
2584	0.13
2585	-0.02
2586	-0.06
2587	-0.10
2588	0.25
2589	0.27
2590	-0.11
2591	0.04
2592	0.03
2593	0.30
2594	0.04
2595	0.25
2596	-0.02
2597	0.13
2598	0.15
2599	0.00
2600	0.05
2601	0.00
2602	0.14
2603	0.06
2604	0.10
2605	-0.11
2606	-0.13
2607	-0.06
2608	0.00
2609	-0.01
2611	-0.07
2612	-0.12
2613	0.01
2614	-0.11
2617	0.06
2618	0.02
2619	-0.07
2620	0.06
2621	0.01
2622	0.08
2623	0.16
2624	0.18
2625	-0.05
2626	-0.06
2627	0.05
2628	0.15
2629	0.14
2630	-0.07
2632	0.13
2633	0.18
2634	0.04
2635	0.02
2637	-0.08
2638	0.06
2640	-0.10
2641	0.03
2642	-0.08
2643	-0.02
2644	0.03
2645	-0.13
2647	0.01
2648	-0.06
2649	-0.21
2650	0.03
2652	-0.05
2653	0.02
2654	0.02
2655	-0.02
2656	0.05
2657	-0.01
2658	0.12
2659	-0.03
2660	0.13
2662	0.04
2663	-0.21
2664	0.03
2665	0.04
2667	-0.01
2668	0.12
2669	-0.02
2670	0.04
2672	0.02
2673	0.06
2674	0.04
2675	-0.41
2676	0.10
2678	0.12
2679	0.02
2680	-0.06
2681	-0.18
2682	-0.07
2702	0.00
2704	0.11
2705	0.01
2706	-0.05
2707	0.25
2708	-0.17
2709	0.08
2710	-0.02
2711	0.07
2713	0.01
2719	0.16
2721	0.04
2723	0.01
2725	0.21
2729	-0.01
2733	-0.08
2735	-0.04
2737	0.15
2739	0.00
2741	-0.09
2743	-0.05
2745	0.13
2747	0.10
2749	0.09
2751	0.02
2753	-0.03
2757	-0.01
2759	0.29
2761	0.03
2763	-0.17
2765	0.15
2767	-0.18
2769	0.08
2771	-0.09
2773	-0.05
2775	-0.09
2777	0.19
2779	0.09
2781	-0.09
2783	-0.01
2785	0.15
2787	0.00
2789	0.06
2791	-0.12
2793	0.08
2795	0.00
2797	-0.07
2799	0.25
2803	0.19
2805	-0.03
2809	-0.03
2811	-0.05
2813	0.06
2815	0.03
2817	0.15
2819	0.12
2821	0.18
2823	-0.14
2825	0.05
2826	-0.18
2827	-0.02
2829	0.16
2830	0.10
2831	-0.11
2832	-0.01
2833	-0.10
2834	-0.09
2835	0.31
2836	-0.06
2837	0.31
2838	0.01
2839	0.01
2840	-0.03
2841	0.01
2842	-0.07
2843	0.14
2844	0.10
2845	0.15
2846	-0.02
2847	0.02
2848	-0.13
2849	0.05
2850	0.04
2851	-0.04
2852	-0.05
2853	-0.04
2854	0.06
2855	0.12
2856	-0.03
2857	-0.02
2859	0.16
2861	0.08
2862	-0.06
2864	-0.01
2865	0.11
2866	-0.03
2867	0.10
2869	0.00
2871	0.15
2872	0.13
2873	0.02
2874	0.09
2875	-0.10
2876	0.06
2877	-0.04
2879	0.09
2880	-0.16
2881	-0.02
2882	0.07
2883	-0.04
2884	0.34
2885	0.21
2887	0.03
2888	-0.13
2890	0.04
2892	0.17
2893	0.02
2894	-0.14
2895	0.18
2896	0.07
2897	-0.02
2898	0.09
2900	0.00
2901	-0.01
2902	0.15
2903	0.05
2904	-0.02
2905	-0.05
2906	0.04
2907	-0.12
2908	0.18
2909	0.11
2910	-0.03
2911	0.06
2912	0.00
2913	-0.26
2914	0.03
2915	-0.01
2916	0.04
2917	0.16
2918	-0.06
2919	0.14
2920	0.03
2921	-0.15
2922	-0.05
2923	-0.01
2924	0.07
2925	-0.04
2926	0.07
2927	0.04
2928	-0.08
2929	-0.01
2930	-0.07
2932	0.22
2933	0.21
2934	0.02
2935	0.00
2936	-0.08
2938	0.31
2940	0.07
2941	0.09
2942	0.08
2943	-0.01
2944	0.04
2945	0.08
2946	0.01
2947	0.10
2948	-0.02
2949	-0.02
2950	0.00
2951	0.02
2952	-0.02
2953	0.03
2956	-0.05
2957	0.11
2958	-0.03
2959	-0.04
2960	-0.03
2961	0.08
2962	0.12
2963	-0.03
2964	0.00
2965	0.12
2966	0.01
2967	0.00
2969	-0.01
2970	-0.11
2971	0.09
2972	0.05
2973	-0.02
2974	-0.04
2975	-0.03
2976	-0.05
2977	-0.10
2978	0.01
2979	-0.13
2980	0.07
2982	0.08
2983	0.26
2984	0.02
2985	-0.01
2986	0.21
2987	-0.04
2988	0.11
2989	0.02
2990	-0.02
2991	0.12
2992	-0.14
2993	-0.04
2994	0.02
2995	0.08
2996	0.00
2998	0.00
2999	0.46
3000	0.08
3001	0.10
3002	0.11
3003	0.00
3004	0.28
3005	-0.02
3006	0.08
3007	-0.02
3008	-0.01
3009	0.02
3010	0.03
3011	0.06
3012	0.01
3013	0.04
3014	0.07
3015	-0.09
3016	0.00
3017	-0.01
3018	-0.10
3019	0.01
3020	0.05
3021	-0.03
3022	0.03
3023	-0.03
3024	0.04
3025	0.03
3026	0.06
3027	0.03
3028	0.08
3029	0.00
3032	0.34
3034	-0.11
3035	0.01
3036	0.14
3037	0.06
3038	0.03
3039	-0.17
3040	0.17
3041	0.12
3042	-0.09
3043	0.11
3044	-0.02
3045	0.08
3046	0.48
3048	0.02
3049	0.12
3052	0.09
3053	0.01
3054	0.09
3055	-0.06
3056	0.02
3057	0.16
3058	0.09
3059	0.01
3060	0.21
3061	-0.06
3062	0.07
3063	0.09
3064	0.04
3065	0.06
3067	-0.07
3069	0.06
3070	-0.01
3071	0.45
3072	0.00
3073	0.06
3074	0.20
3075	-0.05
3076	0.04
3077	0.22
3079	0.14
3080	-0.05
3081	0.08
3082	0.04
3083	-0.02
3084	0.14
3086	0.13
3087	0.13
3088	0.05
3089	0.13
3090	0.09
3091	0.01
3092	0.26
3093	0.12
3094	-0.01
3095	0.06
3096	0.01
3097	0.23
3098	-0.10
3100	0.03
3102	-0.09
3103	-0.03
3104	0.20
3105	0.32
3106	0.01
3107	0.13
3108	0.21
3109	-0.06
3110	0.18
3111	-0.08
3112	0.25
3114	0.20
3115	-0.02
3116	0.08
3117	0.00
3119	0.10
3120	0.03
3121	0.34
3122	-0.08
3123	0.07
3124	0.16
3125	0.05
3126	0.27
3128	0.01
3129	0.11
3130	-0.17
3131	0.00
3132	0.03
3133	0.07
3134	0.20
3135	0.00
3136	0.00
3137	-0.12
3138	-0.04
3139	-0.06
3140	-0.07
3141	0.13
3142	0.06
3143	0.03
3144	0.09
3145	0.01
3146	0.06
3147	0.00
3148	0.33
3149	0.02
3150	0.05
3151	0.16
3152	0.03
3154	-0.01
3155	0.00
3156	0.33
3157	0.09
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3161	0.04
3162	0.09
3163	0.17
3164	0.12
3165	0.31
3166	0.01
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3169	0.06
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3171	-0.05
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3173	0.00
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3179	0.10
3180	0.19
3181	0.05
3182	0.12
3183	0.15
3184	-0.03
3185	-0.07
3186	0.02
3187	0.01
3188	0.34
3189	0.06
3190	0.25
3191	0.08
3192	0.03
3193	0.08
3194	0.14
3195	0.15
3196	-0.01
3197	0.06
3198	0.21
3200	0.02
3201	0.14
3202	-0.01
3203	0.17
3204	-0.01
3205	-0.03
3206	0.02
3207	0.30
3208	0.15
3209	0.07
3210	0.10
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6860	0.11
6861	-0.24
6862	0.36
6863	0.15
6864	0.19
6865	0.15
6866	-0.23
6867	0.12
6868	0.18
6869	0.03
6870	0.08
6871	0.00
6872	-0.02
6873	0.29
6874	0.25
6875	0.03
6877	0.17
6878	0.08
6880	0.25
6881	0.13
6882	-0.04
6883	0.17
6884	0.47
6885	0.12
6886	-0.08
6887	0.04
6888	0.05
6889	0.28
6891	0.16
6892	0.17
6893	0.09
6894	0.14
6895	0.26
6896	0.16
6897	0.15
6898	-0.01
6899	0.06
6900	0.27
6901	0.35
6902	0.23
6904	0.15
6905	0.10
6906	0.00
6907	0.04
6908	0.09
6909	0.25
6910	0.08
6911	0.01
6912	0.32
6913	0.14
6914	0.30
6915	-0.02
6916	0.04
6917	0.08
6918	-0.12
6919	0.01
6920	0.06
6921	0.19
6922	0.25
6923	0.10
6925	0.02
6926	0.31
6927	0.32
6928	0.18
6929	0.21
6931	0.11
6932	0.18
6933	0.05
6934	0.08
6935	0.14
6936	0.22
6937	0.26
6938	-0.17
6940	0.04
6941	0.08
6943	0.22
6944	0.28
6945	0.29
6946	0.22
6947	0.13
6948	0.21
6949	0.00
6950	-0.19
6951	-0.06
6952	0.22
6953	-0.14
6954	0.24
6955	0.33
6956	0.13
6957	0.11
6958	0.11
6959	0.35
6960	0.44
6961	-0.03
6962	0.23
6963	0.14
6964	0.32
6965	0.06
6967	0.14
6968	0.21
6969	0.00
6970	0.26
6971	0.03
6974	0.20
6975	0.25
6976	0.00
6977	0.05
6978	0.00
6979	0.26
6981	0.02
6982	0.32
6983	0.16
6985	-0.07
6986	0.29
6987	0.21
6988	0.15
6989	-0.11
6990	0.11
6991	-0.08
6992	-0.12
6993	0.34
6995	0.25
6996	0.17
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6998	-0.12
6999	0.17
7000	0.12
7001	-0.01
7002	0.10
7004	0.19
7006	-0.02
7009	0.25
7010	-0.16
7013	0.16
7016	0.12
7017	0.44
7018	0.17
7019	-0.06
7020	0.00
7021	0.07
7022	0.05
7023	-0.05
7024	0.42
7025	0.37
7026	0.19
7027	0.16
7028	0.01
7029	0.22
7030	-0.03
7031	0.43
7032	0.27
7033	0.02
7034	0.07
7035	0.07
7036	0.14
7037	0.19
7038	0.10
7039	0.06
7040	0.16
7041	0.17
7042	-0.04
7043	0.01
7045	0.32
7046	0.13
7047	0.09
7048	-0.02
7050	0.44
7051	0.23
7052	-0.02
7053	0.16
7054	0.10
7055	0.13
7056	0.13
7057	0.25
7058	0.18
7059	0.06
7060	0.21
7063	0.36
7064	0.30
7065	0.17
7066	0.35
7067	0.15
7068	0.26
7069	0.16
7070	-0.29
7071	0.10
7072	0.12
7073	0.19
7074	0.01
7075	0.37
7076	0.32
7077	0.05
7079	0.17
7080	0.29
7081	0.11
7083	0.24
7084	-0.03
7085	0.05
7086	0.13
7088	0.21
7091	0.12
7093	0.26
7094	-0.03
7095	0.10
7096	0.23
7097	0.24
7101	0.07
7102	0.11
7103	0.09
7104	0.21
7106	0.07
7107	0.27
7108	0.33
7109	0.02
7110	0.05
7111	0.24
7112	0.24
7113	0.31
7115	0.17
7116	0.34
7117	0.15
7118	0.15
7119	0.22
7120	0.18
7121	0.37
7122	-0.04
7123	0.07
7124	0.29
7125	0.45
7126	0.01
7127	0.02
7128	0.28
7130	0.34
7133	0.27
7134	0.08
7135	0.17
7136	0.04
7137	0.15
7138	0.15
7140	-0.04
7141	0.11
7142	0.22
7143	-0.06
7144	0.09
7145	0.24
7146	0.27
7147	0.02
7148	0.05
7149	0.34
7150	0.28
7151	0.24
7152	0.26
7153	0.18
7154	0.09
7155	0.16
7156	0.09
7157	0.09
7158	0.37
7160	0.15
7161	-0.11
7162	-0.09
7163	0.02
7164	0.07
7165	0.16
7166	0.19
7167	0.02
7168	0.11
7169	0.02
7170	0.00
7171	0.11
7172	0.07
7173	0.25
7174	0.15
7175	0.21
7176	0.20
7177	0.16
7178	0.09
7179	-0.04
7180	0.39
7183	0.22
7184	0.34
7185	0.20
7187	0.11
7188	0.11
7189	0.11
7190	0.11
7191	0.12
7192	0.19
7193	0.03
7194	0.30
7195	-0.06
7196	0.21
7197	0.24
7198	0.10
7200	-0.01
7201	0.39
7202	0.07
7203	0.32
7204	0.09
7205	0.32
7206	0.00
7208	0.17
7209	-0.07
7210	0.17
7211	0.22
7212	0.23
7213	0.26
7214	0.31
7215	0.12
7216	0.20
7217	0.22
7218	0.32
7219	0.13
7220	0.05
7221	0.22
7222	0.14
7223	0.11
7224	0.16
7225	0.02
7226	0.04
7227	0.14
7228	0.05
7229	0.24
7230	-0.23
7231	0.20
7232	0.17
7234	0.13
7235	0.24
7237	-0.05
7238	0.22
7239	0.25
7240	0.15
7242	0.14
7243	0.24
7244	0.10
7245	0.02
7246	0.21
7247	0.11
7248	0.11
7249	0.33
7250	0.20
7251	0.07
7254	0.03
7255	0.03
7256	0.15
7257	0.06
7258	0.14
7259	0.15
7260	0.41
7262	0.36
7263	0.28
7264	-0.13
7265	0.08
7266	0.14
7267	0.23
7268	0.29
7269	0.12
7270	0.21
7271	0.23
7272	0.07
7273	0.16
7274	-0.18
7275	0.29
7277	-0.05
7278	0.13
7286	0.09
7287	0.13
7288	0.05
7289	0.06
7290	-0.08
7291	0.10
7292	0.03
7293	0.08
7294	0.05
7295	0.39
7296	0.24
7297	0.41
7298	0.31
7299	0.12
7301	-0.13
7302	0.04
7303	0.04
7308	0.34
7309	0.09
7311	0.53
7312	-0.01
7313	0.27
7314	0.21
7315	0.19
7316	0.33
7317	0.03
7318	0.42
7319	0.27
7321	0.39
7322	-0.09
7323	0.05
7324	0.09
7326	0.19
7327	0.21
7329	0.12
7330	0.16
7331	0.29

``````

Best schedules: 1031, 1988, 2236, 616, 3742
Worst schedules: 4323, 3326, 4621, 5296, 4812

I decided to take another look at the hypothetical “serpentine valley” I investigated last year. Back then, I was more interested in if teams going into an event had an incentive to perform worse than their ability. I found that if there was a so-called serpentine valley, it was very small and centered around rank 10.

Here, I did a similar investigation using end of event rank instead of start of event Elo. A serpentine valley here might indicate that teams in matches near the end of the quals might be incentivized to get fewer RPs if they want to maximize their chances of winning the event. Here is a book with that data as well as a summary sheet: serpentine_valley_v2.xlsx (1.4 MB)

I pulled rankings and results from all events since 2008. Which gave me a sample size of about a thousand events. I found how many event wins and how many wildcards were achieved from each ranking position, and dividing those by the number of events where a team got this rank gives us a win and win/wildcard probability from each rank. Below are graphs summarizing that data:

These graphs actually look remarkably similar to the pre-event Elo graphs from my earlier work. The “serpentine valley”, if it exists at all, is centered around rank 8 or 9. For reference, the gap between rank 8 (bottom of the valley) and 10 (top of the valley) is 1.1%, jumping from 3.8% to 4.9%, or about 12 out of 1000 events. This is much smaller than I probably would have expected, and that is the lowest point compared against the highest point. Comparing rank 7 or rank 9 to rank 10 is nearly identical. The “valley” that we are seeing could feasibly be largely noise, as there are larger “valleys” at ranks 15 and 23, and I have no reasonable explanation for why there would be dips around those ranks.

My takeaway is that this methodology really doesn’t provide evidence that any reasonable number of teams are incentivized to throw matches. That doesn’t mean those incentives don’t exist, just that you’d really have to dive much deeper into the data to prove that they actually do. Maybe someday when I add alliance selections into my event simulator I’ll revisit.

Fun fact, the lowest any team has ever ranked and still won the event was 62nd. Which happened twice, once at the 2015 LS Regional and once at the 2010 Michigan State Champs.

Caleb, since you have the data… Instead of win probability, what about probability of being on X alliance? I’m wondering if that would show any difference.