# paper: FRC Elo 2008-2016

#21

It seems to work fine if you replace all instances of FullSeriesCollection with SeriesCollection and saving the changes in the debugger.

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#22

Was it because of all the spam going on in the Rumor Mill, Chit-Chat, and Extra Discussion?

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#23

No, it was something to do with the risk of stuff happening with the original paper/picture. This was before the spam influx.

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#24

A couple things, it appears you are just using the raw elo differences in calculating red win likelihood. that is (red1+red2+red3) - (blue1 + blue2 + blue3).

Iām thinking if youāre going to calculate win chance, you want to average out the elo on each side. However, it seems FRC Elo win percentages donāt quite follow chess win percentages based on Elo. I went ahead and generated a cumulative distribution plot based on 2016 match data (and given elo ratings from the spreadsheet). I got what is shown in the plot below. The blue line is the āstandardā chess Elo win probability CDF (a logistic distribution CDF), while the orange is from match data. I fit both a logistic CDF (gray) and Gaussian CDF (yellow).
The modded Logistic Dist had a mean of 0 and st. dev of 55 while the Gaussian dist had a mean of 0 and st. dev of 93.

What does this mean? Well, potentially, difference in Elo rating could potentially be a better predictor of winning FRC matches than chess matches. That is, a small difference in average alliance Elo rating has a larger effect on Win % in FRC (2016) than chess.

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#25

Another thing to consider, however, is the distribution of Elo differences. So itās potentially a bit less useful than I made it out to be in the previous post because a huge amount of matches have a fairly small Elo difference.

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#26

Looking at Elo averages instead of sums should be equivalent to changing the x-scale on the cdf by a factor of 3, and that looks like what you have posted. It doesnāt really change anything, because all you are doing is changing the scale. I used the sums in my calculations, which should provide a cdf similar to those found in things like chess.

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#27

Other methods of combining alliance Elos, such as taking each allianceās max Elo or doing some kind of weighted average would make a difference. I just havenāt investigated these alternatives.

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#28

We played around with TrueSkill last yearā¦

TrueSkill is the natural successor to Elo. It was created at Microsoft for online matchmaking, and as such is able to deal with alliances of players.

A good explanation of the algorithm is here:
http://www.moserware.com/2010/03/computing-your-skill.html

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#29

This is great stuff. I was just introduced to it and I have been using an extended lunch time (the day before kick off) to learn of its intricacies .
My first pass has been pretty impressed so far.

We are thinking of using this in our districts to predict for alliance selection (yet another data point to use with scouts)

Also I opened this on a mac using Numbers, as well as OpenOffice on a mac. It seemed fine in both.

I donāt have excel on this machine but I would prefer it over the other two options.

I look forward to pouring over this with a bigger monitor.

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#30

I have updated to include 2017 data up through St. Louis Einstein. Iāll post another update after FoC.

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#31

Elo was very well calibrated in 2017, as it has been in previous years: http://imgur.com/a/cYBKS

That was all 2017 matches, quals and playoffs. Total Brier score = 0.2114.

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#32

Updated to include FoC.

Basically the only substantial change is that 1676 went down 20 points and 862 went up 20 points.

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#33

I have just published an update to my Elo model titled āFRC_Elo_2005-2017.ā This model incorporates a couple of major changes to the Elo model I used during the 2017 season, and this will be the model I use for my 2018 predictions. The key changes I have made are outlined below, along with the reasoning for the changes. I still have a couple of ideas for things I would have liked to try to add, but Iāll have to get to them next year, because I want to start attempting to improve calculated contributions. My priorities for this model are, in rough order from most important to least important:
Making as few assumptions as possible, I want this model to work for future games, which means I donāt want to assume things that may not be true for those games
Maximizing predictive power for qual matches for the period 2012-2014
Making the ratings easy to understand
Making the ratings from different seasons directly comparable to each other

Here are the key changes I made to the model in comparison to the 2017 version:

1. I have shifted all team Elo ratings up by approximately 70 points relative to my 2017 Elo model. This change in isolation does not actually change any predictions, since only Elo differences are used in predictions, not their absolute values. This does however, both make the ratings easier to interpret as well as make the ratings more comparable to other Elo rating systems. With this change, the long-run average Elo will now be approximately 1500 points, although the average Elo in any season may vary between about 1490 to about 1510.

While looking at other Elo rating systems, I noticed that nearly all of them either set 1500 as the long-run average rating (as in 538ās ratings), or set all new entries into the system with a rating of 1500 (as in FIBS ratings). My previous Elo model did neither of these, as the previous rookie starting rating was 1350, and the 2017 average Elo was ~1440. The other advantage to this change is that there is now a (relatively) solid reference point for how good a team is, >1500 = above average, and <1500 = below average. Additionally, I have found that a rating of 1600 is the rating of a 90th (Ā±3%) percentile team in almost every season. One additional reference point for these ratings is that the average Elo rating of rookie teams is 1450.

1. I have extended my Elo ratings back in time to 2005. When I originally built my Elo model, I did not include any years prior to 2008 since some 2007 events contained no match data. After reviewing the years 2005-2007, I have decided to include them in my ratings, although I advise caution when looking at Elo ratings from this period. There are some unfortunate teams that competed in this period but do not have any rating because none of their matches were recorded. I decided to include these years because, even though the data are incomplete, including 2007 does improve 2008 predictions, and likewise for 2006 and 2005. In the future, it is possible that I may extend the ratings back as far as 2002, but that would require some larger changes to my model since these years had 2v2 matches and not 3v3 matches.

2. I set all teamās starting Elos during the first year of the model (2005) to 1500 instead of the normal starting Elo of 1450. This change stabilizes the average Elo rating for future seasons around 1500. This stabilization actually improves predictive power for all future seasons, although this improvement is not drastic for years other than 2006 and 2007. This is likely because this change makes rookie ratings consistently 50 points below the average, instead of varying depending on the year. This change also allows for more direct comparison of Elos between seasons, although Elos above 1600 will need to be interpreted differently depending on the season, since each season has a different distribution of high-level Elos.

3. In my previous model, I would find each teamās start of season Elo by taking their previous seasonās Elo and reverting it 20% toward the mean. I have found though that taking each teamās start of season Elo to be a weighted average of their previous two seasonās end of season Elo ratings provides a much better predictor of their next seasonās performance. Specifically, in this model, a teamās start of season Elo rating is found by taking 70% of their previous seasonās rating plus 30% of their end of season rating from two seasons ago, and then reverting this weighted average by 20% toward the pseudo-mean (1550). This change provides substantial predictive power improvement, particularly at the start of the season.

4. Due to all of the aforementioned changes, some of my modelās other parameters have new optimal values. I have already mentioned that I am now starting rookies with a rating of 1450 instead of 1350 previously, and that the new pseudo-mean will be 1550 instead of 1500. These two changes were mostly due to the shifting up of ratings (change 1), although the other changes may have made a small effect. In addition to these, my new model has lower values for both kQuals and kPlayoffs. kQuals moved from 15 under the previous model to 12 under the current model. This means that team ratings will change 20% more slowly in response to qual match performances. kPlayoffs moved from 5 under the previous model to 3 under the current model. This means that team ratings will change 40% more slowly in response to playoff match performances. I expect that these changes are largely due to the improved start of season Elo ratings. If the start of season Elo ratings are better, it means that the model doesnāt need to respond as quickly to performance at the start of events.

In addition to the above 5 changes to the Elo model itself, I have also made a few aesthetic changes to the workbook.

1. I have added sheets for the years 2005-2007
2. Just for fun, I added in the ability to directly compare teams in the āTeam Lookupā sheet. To do this, enter a team number into cell B2. To view only a single team, leave cell B2 blank. The second team will show up on the graph with ā+ā markers.
3. Since the graph can get difficult to see with two teams over 13 years, I have also added a range setting in the āTeam Lookupā sheet. Just enter your desired year range into cells B3 and B4 and click āUpdate Rangeā after importing your desired teams. I had to work out a few bugs for this macro, and I might not have hit them all, so if you notice anything weird let me know.
4. I have updated the āInstructions and FAQā sheet to cover much of the information above.
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#34

I have added an update which includes 2018 data. I also changed the āTeam Lookupā sheet to no longer import matches which are missing score data. This should make the graphs nicer for teams like 2590. Thanks to AGPapa for identifying this problem.

I will very likely be making changes to this model before 2019, but here are the 2018 end of season ratings:

``````Team	Elo
254	2032
2056	2015
1678	1995
2046	1955
694	1952
1323	1943
118	1938
1114	1930
2910	1930
148	1929
2481	1928
2590	1924
195	1923
2767	1917
3309	1907
842	1895
3357	1893
4539	1892
125	1886
225	1884
3310	1883
5406	1879
133	1875
27	1874
217	1874
1241	1874
1574	1874
1538	1871
230	1867
1629	1864
1619	1862
4613	1859
1796	1858
624	1856
3707	1856
319	1856
2122	1855
1747	1854
3478	1852
3130	1848
5050	1846
2337	1844
2471	1842
4003	1839
176	1838
85	1838
3538	1837
340	1836
971	1836
2478	1834
5172	1833
1318	1832
141	1830
25	1830
16	1830
399	1829
1690	1826
1325	1821
180	1820
3005	1820
1519	1816
1706	1816
2791	1815
3452	1813
3476	1813
4910	1811
67	1810
291	1810
179	1808
5460	1807
5190	1806
3339	1806
2168	1805
4917	1805
4488	1804
2614	1803
1986	1800
1806	1800
1712	1799
3959	1799
494	1799
1918	1796
1640	1795
868	1795
4028	1794
2642	1792
3646	1792
4362	1791
1756	1790
2059	1788
5818	1788
3512	1787
330	1785
5987	1784
987	1783
177	1781
4237	1781
1533	1779
2403	1779
364	1779
359	1777
56	1775
1425	1771
234	1771
1648	1770
1259	1769
269	1768
1731	1765
2557	1764
910	1764
4618	1763
302	1763
610	1762
4476	1761
2834	1760
865	1760
5895	1759
5883	1759
1102	1759
3539	1759
3937	1758
1876	1756
1024	1755
3098	1755
1506	1754
33	1753
4513	1752
525	1752
233	1752
365	1752
6329	1751
5687	1749
5472	1749
368	1748
1741	1748
341	1747
5985	1747
4564	1747
3641	1745
973	1743
2522	1742
384	1742
5572	1742
5199	1742
1622	1741
1726	1741
1923	1741
2877	1740
2052	1740
95	1739
2630	1738
4522	1736
846	1735
6763	1735
3316	1735
1723	1734
4451	1734
3802	1734
2485	1734
6705	1733
2013	1733
3674	1731
3990	1729
832	1729
2451	1729
4678	1729
870	1728
3128	1728
4265	1727
3250	1727
175	1727
1023	1726
1736	1726
1305	1726
772	1725
4946	1724
4253	1723
744	1723
2130	1723
2659	1723
71	1722
294	1721
687	1721
2976	1721
503	1720
1577	1719
1025	1719
4004	1718
346	1718
957	1718
2502	1717
3015	1717
2992	1717
188	1717
1414	1716
78	1716
4911	1716
5803	1716
1836	1715
379	1715
488	1713
20	1713
1492	1712
604	1712
3546	1711
1339	1711
1684	1711
3616	1711
2410	1710
1391	1710
4855	1710
2771	1710
1983	1709
5012	1709
2996	1708
5817	1707
4635	1706
4188	1706
3255	1706
5505	1706
1197	1704
4146	1704
1156	1704
1100	1704
2175	1704
4944	1703
6090	1702
2706	1701
5254	1701
1730	1701
2655	1701
2054	1701
1262	1701
3683	1701
4272	1701
1218	1701
4776	1700
3663	1700
5046	1700
4405	1700
4655	1699
2826	1699
6579	1699
2383	1699
5584	1699
3656	1698
66	1698
3536	1698
6672	1697
4980	1697
862	1697
1011	1696
3750	1696
2708	1696
639	1695
88	1695
4587	1695
1559	1694
1065	1694
456	1693
4541	1692
4795	1691
876	1691
4063	1690
422	1690
103	1690
5802	1689
2194	1689
4290	1688
1421	1688
3824	1688
1322	1688
6077	1688
1599	1688
3542	1688
649	1687
4143	1687
1073	1687
1477	1687
2075	1687
5501	1686
70	1686
5152	1686
1772	1686
3197	1685
4388	1685
6800	1685
3314	1684
314	1684
303	1683
2556	1683
3620	1682
2974	1682
1746	1682
4533	1682
3328	1681
3547	1681
3534	1681
3276	1681
5567	1680
2200	1680
1744	1679
968	1679
4145	1679
7021	1678
6025	1678
3847	1678
5010	1677
5053	1677
888	1677
597	1677
930	1676
1360	1676
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2202	1675
316	1675
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237	1673
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3940	1672
4550	1672
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3929	1671
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115	1669
6418	1668
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3835	1665
5530	1665
2137	1665
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1987	1664
245	1663
6474	1662
333	1662
238	1662
4189	1662
5842	1662
342	1661
3374	1661
4959	1661
2930	1661
2682	1661
1729	1661
5036	1661
5554	1660
2102	1660
1902	1660
3695	1660
3223	1660
1018	1660
5314	1660
2987	1658
3230	1658
167	1657
386	1657
5889	1657
578	1657
2960	1657
708	1657
1718	1656
3481	1656
3853	1656
61	1655
2231	1655
6328	1654
3236	1654
2468	1654
343	1654
3461	1653
2658	1653
58	1652
4469	1652
5155	1652
1710	1652
3667	1652
2363	1651
126	1651
4361	1651
2811	1651
2144	1651
1792	1651
6334	1650
2486	1650
1625	1650
2521	1650
5431	1650
1319	1650
5675	1650
5013	1650
5436	1650
2199	1649
1816	1649
670	1649
2377	1649
2710	1649
4967	1648
5420	1648
59	1648
5576	1648
75	1648
6933	1647
3770	1647
2765	1647
418	1646
226	1646
1885	1646
358	1645
1255	1645
3164	1644
135	1644
4391	1644
3711	1644
836	1644
5544	1644
3737	1643
1418	1643
7179	1643
5285	1643
3218	1643
1058	1642
3171	1642
3256	1642
3140	1642
4818	1642
3623	1642
4976	1642
236	1641
1306	1641
383	1641
3244	1641
612	1641
120	1640
4525	1640
4027	1640
3997	1640
3179	1640
4392	1640
829	1639
6117	1639
4531	1639
2851	1639
5114	1638
4039	1638
4198	1638
4026	1638
2601	1638
3010	1638
4786	1638
5614	1637
360	1636
533	1636
447	1636
4276	1636
2152	1635
1071	1635
433	1634
5434	1634
4415	1633
63	1633
2959	1633
7039	1633
1523	1633
287	1633
348	1632
5234	1632
5517	1632
3931	1632
4499	1631
1540	1631
5596	1630
1817	1630
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3260	1630
5528	1630
614	1630
4623	1629
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2537	1628
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2702	1628
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395	1628
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5216	1628
5499	1627
2611	1627
3459	1627
527	1627
4085	1627
3492	1627
3419	1627
3792	1626
3100	1626
5509	1626
2823	1626
3604	1626
6104	1626
5099	1626
1178	1626
159	1625
2164	1625
469	1625
3313	1625
4607	1624
999	1624
2846	1624
4653	1624
6548	1624
4930	1623
8	1623
5407	1623
3196	1623
5546	1623
5945	1623
4557	1623
5846	1622
2977	1622
3970	1622
7225	1622
6406	1622
1251	1622
1778	1622
6193	1622
4216	1622
1317	1621
4472	1621
5823	1621
3360	1621
4586	1621
1596	1621
3986	1621
1592	1621
1683	1620
5193	1620
4020	1620
467	1620
6907	1620
5188	1620
1002	1620
1410	1619
3574	1619
93	1619
997	1619
6378	1619
1939	1619
4450	1618
2170	1618
4061	1618
1626	1618
323	1618
3535	1618
4183	1617
3668	1617
5654	1617
2283	1617
4984	1617
4965	1617
3042	1617
6647	1616
4325	1616
2040	1616
1126	1616
1721	1616
5674	1616
2145	1616
3555	1616
122	1616
4079	1615
4646	1615
222	1615
5427	1615
3184	1615
3603	1615
5437	1615
663	1614
3635	1614
1551	1614
156	1614
1511	1614
181	1614
2342	1614
3277	1614
3928	1614
21	1613
1699	1613
1501	1613
4230	1613
1595	1613
2181	1613
3026	1613
1675	1613
1108	1613
3572	1613
3883	1612
3161	1612
3410	1612
1982	1612
1708	1612
1768	1611
4468	1611
1310	1611
4096	1610
5414	1610
5990	1609
2928	1609
5763	1609
2509	1608
3647	1608
4983	1608
207	1608
4611	1608
991	1608
191	1608
6493	1607
1099	1607
4688	1607
4256	1607
2227	1607
2609	1607
2352	1606
4181	1606
4077	1606
2225	1606
201	1606
1658	1606
354	1605
3137	1605
703	1605
2016	1605
5712	1605
2090	1604
1	1604
4904	1604
1825	1603
558	1603
51	1603
1311	1603
5740	1603
6055	1602
2607	1602
6831	1602
4920	1602
3034	1602
1732	1602
747	1601
5587	1601
3239	1601
4909	1600
23	1600
5030	1600
2579	1600
2491	1600
6508	1600
1208	1600
3039	1599
3838	1599
3072	1599
228	1599
1711	1599
5804	1599
5976	1598
1807	1597
2883	1597
2526	1597
5102	1597
5735	1597
6415	1597
5550	1597
1745	1596
2512	1596
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4159	1596
3472	1596
5618	1596
3284	1596
1657	1595
86	1595
2594	1595
4069	1595
3882	1594
6803	1594
6424	1594
2638	1594
2903	1593
308	1593
5914	1593
3844	1592
907	1592
4192	1592
353	1592
7048	1592
131	1592
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2180	1591
3414	1591
847	1591
2386	1591
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263	1591
4774	1591
1553	1590
1720	1590
948	1590
611	1590
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5910	1589
2657	1589
223	1589
144	1589
2643	1589
3637	1588
6829	1588
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3526	1586
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3506	1586
173	1586
2539	1586
5524	1586
5424	1586
6978	1586
1676	1586
4638	1586
4400	1586
2832	1585
4905	1585
5150	1585
5907	1585
5462	1585
2333	1585
401	1584
5039	1584
5205	1584
123	1584
2584	1584
3044	1584
1257	1583
5496	1583
4103	1583
1369	1583
3863	1583
5843	1583
4	1583
5492	1583
5826	1582
3550	1582
4055	1582
1557	1582
4512	1582
5410	1582
580	1582
5291	1582
949	1582
2147	1582
5006	1582
111	1581
3293	1581
4970	1581
554	1581
3996	1581
4458	1581
6445	1581
3618	1581
4961	1581
5590	1581
3258	1580
3880	1580
1072	1580
5442	1580
1989	1579
102	1579
3581	1579
4819	1579
1014	1579
696	1579
4342	1579
4401	1578
3009	1578
1610	1578
5458	1578
2543	1578
6359	1578
5000	1578
6072	1578
5653	1577
3999	1577
108	1577
4521	1577
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``````
0 Likes

#35

Amazing Job, I have a question in the āEnd of Seasonā Elos there are no team numbers column could you please add it to be able to find teams more easily?

Thaks

0 Likes

#36

I have uploaded a v2 which is scrolled all the way to the left on the āEnd of Season Elosā sheet to show the team numbers. Let me know if that wasnāt the issue you were experiencing.

I also added 2018 to the legend on the graph in the āTeam Lookupā sheet.

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#37

A few questions:

Any thoughts on the increased standard deviation in the last two years? seems like a large jump from the values of the other years (although 2014 is close). I suspect this reflects more on game design than your model, but Iād still be interested in hearing your thoughts.

I assume the 70/30 weighting on the past two yearās elo was chosen due to it having the strongest predictions for future performance, do you think that thereās any value in a different weighting scheme for an All-Time elo rank? If so, how might you weight the previous years? Would you keep the current 70/30 system, have an equal average of all years, weight years by the predictive strength of elo? Have you thought of making a GOAT elo-rank and do you think there would be any value to an elo system that didnāt have such a hard reset after each season?

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#38

I think the standard deviations are almost entirely a function of the game design. I just use them as a rough way to normalize winning margins between years. What I find more interesting is the standard deviation of Elo ratings for each year:

These give a loose upper bound on how ādominantā a team can possibly be for each year. 1114 at the end of 2008 had an Elo nearly 200 points higher (or more than two standard deviations higher) than the next highest team, in a year where it was relatively difficult to be dominant.

2018 in contrast was one of the easiest years to be dominant, likely due to the positive feedback loops for scoring described in other threads. Itās because of years like this that I try to make as few assumptions as possible in my Elo model, since my Elo predictions this year were great at the same time as some other predictive methods were poor because they didnāt know how to deal with a game like this. Iām a little concerned that 254 might have been so good this year that some of the assumptions Elo made broke down and under-rated them. I only gave them a 0.012% chance of going undefeated (if you look at pre-match win probabilities), which might have been low, but itās hard to tell since this is such a rare event, and I might be engaging in hindsight bias.

I assume the 70/30 weighting on the past two yearās elo was chosen due to it having the strongest predictions for future performance

Yes, this is correct.

ā¦do you think that thereās any value in a different weighting scheme for an All-Time elo rank? If so, how might you weight the previous years? Would you keep the current 70/30 system, have an equal average of all years, weight years by the predictive strength of elo?

I mean, sure, I think there are alternative systems out there that have value, and parameters in my current model could be tweaked to maximize performance in regards to something other than predictive power. I donāt know how Iād weight previous years if building a system like this. I canāt think of any metric to try to optimize like I do with predictive power, so Iād probably just pick values that āfeel rightā to me, which I am loathe to do since I canāt really objectively justify why I made the decisions I did.

Have you thought of making a GOAT elo-rank and do you think there would be any value to an elo system that didnāt have such a hard reset after each season?

Yeah, Iāve certainly thought about trying to get more into the GOAT conversation, but I think when you get down to it, these conversations rest more on personal preference than anything objective. You can certainly use statistics to back up your claims, but unless you have a single statistic which encapsulates everything about a team and everyone agrees this is the best metric, people will pick and choose which metrics to use to decide who is the GOAT.

Personally, I donāt put much weight in 254ās undefeated season. I donāt think they have many great wins in quals, and they had some awesome playoff partners who provided a lot of help to them when they faced tough opponents in the playoffs. It kind of stinks for them, but it may not have even been possible for them to win the GOAT position in my mind this year just because it was so easy for other teams to also be dominant. All of this is just my opinion though, other people value other things in the GOAT conversation and thatās fine.

If I had to make a GOAT list, I would probably use the Elo standard deviations above to find out which teams were the most dominant relative to the rest of the field in their year. It would probably look something like this, with the top 3 or so in serious contention:

Sometime Iāll probably extend Elos back to 2002, which would be cool because then we could include the legendary 71 in 2002.

All in all, Iām much more interested in maximizing predictive power than almost anything else. Anyone can choose to rank teams however they would like, and thatās totally fine. However, at some point I would encourage people to put their ideas to the test and actually take a shot at predicting things. Otherwise you are very likely getting caught up in hindsight bias.

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#39

Just for fun, I went and found what kind of scores 254 would have needed to end the season as strong as 1114 did in 2008 relative to the next best team. To do this, 254 would have needed an ending Elo of 2293, which they could have achieved if they had won all of their matches by around 100 more points than they did. Obviously, there are other ways they could have gotten their Elo this high, but this gives a sense of how much better they would have needed to be to get my GOAT title.

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#40

I love the idea of using standard deviation of ELO to gauge the dominance of proformances accross the years. I donāt like the idea of comparing to the next best team though, because the ability of the second team seems fairly arbitrary and two extremely outlier robots could easily be built in the same year. I think it would be much better to to use the standard deviations above the average to compare across years.

I also personally see more recent achievements in a brighter light, (This what you were talking about with persal opinions) because all teams are getting much better at building robots over the years. For example, 1114 was incredibly dominant at the time in 2008, but if FRC gave us the 2008 game again next year, I believe their would be hundreds of similarly capable teams.

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