British Championships Premier Tier – Some Statistics

Today (May 31st) saw the final bouts in the first ever round of Roller Derby’s British Championships Premier Tier.

The British Championships is the development of a new, national, Roller Derby tournament, modelled after other national sporting tournaments, and the Premier Tier is the highest division in it. With teams ranked by the UK Roller Derby Association (UKRDA) rankings (themselves provided by ubiquitous derby ranking site, FlatTrackStats), the Premier tier pit the best 6 teams in the UK against each other (minus London Rollergirls, the best team in the UK, as they are so good that they don’t spend enough time playing in the UK to get a local ranking).

After some exceptionally close and surprising games, the final rankings were:

1 Glasgow Roller Derby GRD
2 Auld Reekie Roller Girls ARRG
3 Middlesbrough Milk Rollers MMR
4 Tiger Bay Brawlers TBB
5 Central City RollerGirls CCR
6 Rainy City Roller Girls RCRG

with Glasgow winning all 5 of their bouts, and Rainy City unfortunately losing all of theirs.

We’re here for statistics, however, so what does our least squares ranking approach say about the teams from their performance in all 15 games?

Well, running the toolkit at https://github.com/aoanla/ranking-chain-inference gives the following ranking tables:

Rank (Score difference) Rank (Score ratio) Rank (FTS-esque)
1. GRD 0.0
2. ARRG -99.58
3. MMR -124.16
4. TBB -139.0
5. CCR -171.083
6. RCRG -178.16
1. GRD 1.0
2. ARRG 0.496
3. MMR 0.430
4. TBB 0.372
5. CCR 0.322
6. RCRG 0.300
1. GRD 1.0
2. ARRG 0.735
3. MMR 0.684
4. TBB 0.650
5. CCR 0.594
6. RCRG 0.578

No matter what ranking approach we choose, we agree with the results of the tournament itself (unsurprisingly, as this is an all-plays-all tournament, which should be very good at ranking participants).

However, there’s more we can do with least squares fits than just ranking. One of the results of any least squares fit to data is a set of “residuals” – the differences between the real scores that happened and the “perfect” scores that our predicted strengths would result in. We can use these residuals as a measure of how good our predictions are, and how well we fit the data – but we can also use them to see which results are the most surprising out of all the games played.

As our prediction is holistic – all of the games contributing equally to the error in our prediction – we can test which game is the most `surprising’ by seeing how the residuals change if we remove 1 game from the list we consider. The game which reduces the residuals the most must be the game which is furthest from the `predicted’ result (and we can measure how surprising each game is by the relative amount by which they change the residuals).

For British Champs Premier Division, if we run over all 15 games, we find that there are precisely two bouts which have a really strong effect on the accuracy of our predictions, both reducing the residuals by a factor of two if they were removed. Those games are: TBB 243  v CCR 114  and GRD 280 v TBB 54.

What’s interesting about this result is that the two are divergent in their effect – the former is one where Tiger Bay Brawlers did much better than they did on average in the tournament (the prediction from all games is that they should have been quite closely matched with Central City), and the latter, one where they did much worse than they might have expected (the prediction would be that they would lose to Glasgow by closer to a 2:5 ratio than the 1:5 they achieved).

So, it appears that the most significant thing about the Premier Tier this time around was that Tiger Bay Brawlers performed in a very inconsistent manner. With no more visible statistics from British Champs on team composition, it is hard to theorise further, but an obvious possibility is that the composition of TBB’s roster was more variable than for the other teams, presenting them with much weaker or stronger formations for each bout.

Another interesting thing we can do with statistics is to combine results from multiple tournaments in order to make predictions. In this case, the author noted that Gent Go-Go Roller Girls’s annual SKOD tournament presented an interesting opportunity – British Champs Premier Tier’s MMR and CCR were both attending, but so was British Champs National Tier (Northern Division)’s Newcastle Roller Girls. The author is of the opinion that NRG are a likely candidate for promotion to Premier Tier in the next year (especially as rankings other than UKRDA’s already place them in the same league as the Premier Tier teams), so seeing them pitted against two current Premier Tier teams was a useful opportunity to gather data.

Running the least squares ranking against the combined set of all of the results from SKOD2015 and British Champs Premier Tier 2015 produces the following ranking (UK teams in Bold):

Rank (Score difference) Rank (Score ratio) Rank (FTS-esque)
1. GRD 0.0
2. ARRG -108.8
3. NRG -119.6
4. MMR -122.8
5. GGGRG -128.9
6. TBB -139.0
7. DRD -150.9
8. CCR -163.1
9. RCRG -178.1
10. PR -184.3
11. NDG -209.6
12. DRRG -215.2
13. NHH -253.1
14. CRD -360.0
1. GRD 1.0
2. ARRG 0.469
3. MMR 0.435
4. NRG 0.432
5. GGGRG 0.406
6. TBB 0.372
7. DRD 0.346
8. CCR 0.336
9. RCRG 0.300
10. PR 0.278
11. NDG 0.241
12. DRRG 0.240
13. NHH 0.193
14. CRD 0.097
1. GRD 1.0
2. ARRG 0.715
3. MMR 0.688
4. NRG 0.686
5. GGGRG 0.667
6. TBB 0.650
7. DRD 0.618
8. CCR 0.607
9. RCRG 0.578
10. PR 0.556
11. NDG 0.519
12. DRRG 0.514
13. NHH 0.465
14. CRD 0.3403

As can be seen, the results suggest very strongly that Newcastle Roller Girls would, if promoted to the Premier Tier, perform very strongly – coming either third or fourth against a very closely matched Middlesbrough Milk Rollers. The author very much hopes that, in 2016, we get a chance to see if this prediction comes to pass…

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About aoanla

Aoanla is a physicist/systems support guy for the UK bit of the LHC experiment at CERN in real life, and therefore already had some experience in looking at high-speed collisions before getting into roller derby. He writes bout reports for the bouts he turns up to on his own blog, but is now planning on writing articles and bugging people for interviews here, too.
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One Response to British Championships Premier Tier – Some Statistics

  1. Pingback: Scotland heads the Premier Tier of British Champs! | scottish roller derby

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