Analysis: Coping with the Schedule

More than a gauntlet is needed for schedule balance


The Ontario SchoolReach provincial championship whittles roughly 40 teams down to three national invites. To coordinate the largest field of any SchoolReach event, teams are split into pools that play amongst each other, with the (usually) top two of eight in each group moving on to the playoffs.

The composition of the pool can play a significant role in how far a team can progress in the tournament. There are good-faith efforts to balance the pools, but historically with no other background information, organizers had to use reputation (and geographical separation) to form the pools. Often, this led to strange results, such as two 2013 national invites coming from the same preliminary group. Ideally, and with more information, teams would be sorted so that they earn a final rank appropriate to their performance.

But I can’t solve that for now. What I can do is look back, thanks to collecting data from past tournaments. I occasionally get asked (or hear complaints) about how teams don’t get a fair shot during provincials, either through losing a playoff spot to a “weaker” team or having to deal with a group of death. I took a look at some numbers.

The analysis is based on teams that had at least 10 appearances at Ontario provincials since 1999. Results from 2003-05 are excluded from the averages because I don’t have pool composition for those tournaments (just points and ranks). 18 schools fit the bill, including most of the modern “usual suspects” for national qualifications.

Fig 1. Average rank and PPG of frequent Ontario SchoolReach championship attendees

First up is a team’s average rank against their average round-robin points per game. See figure 1, and excuse the crowded labels in places; some teams are close together. There is an unsurprising relationship – teams that finish well scored more points to get there. There are four teams that are at least a full standard deviation from the linear trend:

  • UTS earns more points than necessary to get their rank. They are also limited by being unable to go below 1, even though they would fit closer to a theoretical rank of “0”.
  • Lisgar gets the round-robin points to justify an average rank in the 1-3 range. However, they have a history of stumbling in the playoffs, especially the televised ones, which gives them a lower final rank than their seed would suggest.
  • I will get back to Leaside in a later graph. In the early years, the team scored UTS-esque point tallies. In their later years, they had schedule benefits. Their mid-years are excluded (2003-05).
  • Assumption earns fewer points than expected. It will be seen later that one of my past assumptions (pun intended) that they get easy draws is false. Instead, they probably earn lots of close wins in the prelims, operating on razor-thin margins of victory to often get on the better side of the playoff bubble.
Fig 2. Average rank and strength of schedule of frequent Ontario provincials attendees

Next is the comparison of rank and strength of schedule. The relationship is not as strong, but teams with better ranks usually have an easier schedule. This is expected for balanced pools – the top teams in the pools face teams weaker than them, while the bottom teams face opponents stronger than them. Unfortunately, we don’t have information-based balance, so we are starting to see some outliers:

  • Leaside is on the low side of this chart. They were getting statistically significantly easier schedules than their rank would suggest. However, I believe I can explain this – Leaside made the provincial final in all (and only) the three excluded years. Leaside was extremely good in the 2003-05 period. They were also a very strong prelim team before that, but would slip in the playoffs. For their remaining active years (consecutively until 2009), they probably benefited from reputation placing them as expected pool winners, but they never made playoffs again after the 2005 run. If the 2003-05 results could be added, they would have a higher average rank with probably not too much change in SOS.
  • Lisgar appears low, but is within a standard deviation. As mentioned before, their average rank is worse than expected because of historical poor playoff performance.
  • The cluster of Oakville-Trafalgar, Waterloo, and Westdale have a right to gripe. They face statistically significantly tougher schedules than their results would justify – Westdale is almost two standard deviations from the trend. OTHS is particularly surprising: they had good results in the missing years (thanks to University Challenge celebrity Eric Monkman), but don’t appear to have been given a “boost” from that reputation; they seem to be put in pools under the assumption they don’t do well. Westdale’s tough luck was also looked at in an earlier post when I posited (incorrectly) that Hamilton teams in general suffered from bad schedules.
Fig 3. Average strength of schedule and PPG of frequent Ontario provincials attendees

The last graph, comparing SOS and PPG, could be summarized as how teams cope with the schedule they’ve been dealt. Strength of schedule loosely represents pool strength and the potential unbalance, so teams getting PPGs above the trend are punching above their weight to overcome a bad draw. A few teams are outliers:

  • Westdale still stands out (OTHS and Waterloo draw closer to the trend in this analysis). Their single greatest mountain to climb was the 2013 pool: they had a 5-2 record, their second-best ever PPG relative to the set, and a final rank of 11th, all while dealing with two nationals-bound teams and a third team that also got into the playoffs. Westdale also incredibly made playoffs in 2009 with a 1.15 SOS. Westdale often got the worst schedules, but they made every effort to try to get something out of it.
  • Assumption is the outlier on the low end. I don’t wish to suggest that they are a low-effort team, though. They get schedules that are roughly fair for what is expected of them, but the first analysis suggested that they just don’t pick up large margins of victory.
  • UTS is also an outlier. They appear to have an easy slate of opponents, but they are still performing better than their schedule would expect. UTS has had a few years with tough pools (including the 2013 one mentioned earlier) while still consistently putting up points – they have qualified for nationals four times with a preliminary SOS greater than 1. Organizers (unintentionally) throw tough teams at UTS, and they still prevail.

So there are some data to ponder. I’m sure there are some less-frequent teams that also struggle or get an easy break, but the teams highlighted here should have enough sample size to stand out. Use your own results to see how your team compares to these provincial regulars.

Reach Scores Audio #19

2018 Lisgar Tournament, Glebe vs UTS A

We’re at the end of the preliminary round-robin. From the 2018 Lisgar Reach-style tournament, this round 9 match has Glebe CI against UTS “A”. Moderating and production by Ben Smith.

Here is the link to the episode.


  • The Rhodesia question was a bit misleading because “Rhodesia” did not have its nationhood well-recognized, and because Mugabe overthrew the briefly-rerecognized colony of “Southern Rhodesia”. I accepted the latter answer and nobody felt the need to protest in this matchup.
  • There is a German performance of “As Slow As Possible” on an organ that is playing its 13th note until September 2020. It still has more than 600 years to go.
  • A team scramble was a repeat. I imagine this was a mess to sort out in closer rooms; I threw it out. Without replacement team scrambles on hand, the only way to resolve it is to awkwardly read the first tiebreaker with team scramble procedure, then continue the three unrelated tiebreakers just to the team that answers.
  • A Mersenne prime is, indeed, of the form of one less than a power of 2 (3, 7, 31, etc).

Thanks for listening!

Reach Scores Audio #15

2018 Lisgar Tournament, KVHS vs UTS C

From the 2018 Lisgar Reach-style tournament, this round 5 match has Kennebecasis Valley HS against UTS “C”. Moderating and production by Ben Smith.

Here is the link to the episode.


  • Disputes were settled on the spot, including that aluminum is not commonly considered a metalloid.
  • An answer of “Henry Tudor” for “Henry VII” could be argued as ambiguous (Henry VIII and his short-lived son Henry would also have had the Tudor name). However, “Henry Tudor” was a name used for a significant portion of Henry VII’s life, and almost never used to refer to the later generations. The response of “Henry Tudor” can be considered acceptable.
  • There was definitely a Welsh theme going on this round. In addition to the above, there was a question about the origin of the term “Prince of Wales”.

Thanks for listening!

Reach Scores Audio #14

2018 Lisgar Tournament, Almonte vs UTS B

From the 2018 Lisgar Reach-style tournament, this round 4 match has Almonte DHS against UTS “B”. Moderating and production by Ben Smith.

Here is the link to the episode.


  • There is a pause due to a noisy gust from a vent. Don’t think it was a gas leak, since we all survived.
  • The exchange after the question about the namesake of two provincial capitals:

Player: “Queen Victoria?”

Me: “Yes, she is the namesake of Regina.”

Player: “…And what’s the other [provincial capital]?”

Me: “…Victoria.”

Thanks for listening!

Reach Scores Audio #13

2018 Lisgar Tournament, UTS C vs Glebe

From the 2018 Lisgar Reach-style tournament, this round 3 match has UTS “C” against Glebe CI. Moderating and production by Ben Smith.

Here is the link to the episode.


  • This was the first match with eight players at the table, requiring the use of a bad buzzer on my system. The light is embedded and out of view on the signaler, so I have to interject every now and then to say the player’s light is on.
  • The Ivy League error in the pack required very on-the-fly judgment. The format of list questions would force the game to stop to resolve the continuation of the list in a more serious tournament (especially for a list with five total entries).
  • Singapore was indeed made independent against its wishes after a vote by the Malaysian government. Usually, a nation’s independence comes from the local population seeking it.

Thanks for listening!

2018 Nationals results

The heat was on.

Fifteen teams from across Canada competed in Toronto last weekend for the Reach for the Top national title. It was a very decorated field, with 16 championships among them going into the competition.

Saturday saw the round-robin portion. The big shake-up in the standings came from London Central SS defeating UTS in their match, which gave Central the head-to-head tiebreak for the top of the leaderboard. Kennebecasis Valley HS gave Central their only loss of the day, while Martingrove CI was the other school in the top four seeds.

Sunday playoff competition ended up playing out mostly as expected by seeding. In the play-in round, Kelvin HS gave a close 360-340 upset over the Renert School, but the eliminations still resulted in the top four seeds in the final four. St. George’s School and Eric Hamber SS, both from BC, gave the biggest scares in the quarterfinals, with St. George’s briefly leading over KVHS and Eric Hamber losing in the closest match (330 to 400 for Martingrove).

Monday was for the final four. In the first semifinal, KVHS jumped out to a quick lead over Central, hoping for a repeat of the win they pulled off in the round-robin. Central, however, picked up most of the points in the middle round of the game and finished with a 440-300 victory, sending them to their fifth national final. In the other semifinal, UTS repeated what they did in the Ontario final and took a strong 550-280 win over Martingrove to head to their ninth final. The final, a rematch from 2012, had the reverse outcome of the round-robin game and gave UTS a 520-280 victory over Central.

Congratulations to UTS for their unprecedented fifth title, and also congratulations to all the participating teams representing their provinces. The database link to the results is found here.

The top four teams (UTS, Central, Martingrove, KVHS) have been well-documented on this site, and they are no strangers to the high end of the competition. They are all perennial challengers to the title, and will be in the future. Some top players will graduate, but their clubs are so deep and well-organized that they will return with other players vying for the trophy.

The next four teams (alphabetical order of Eric Hamber, Kelvin, Old Scona, and St. George’s) demonstrate a divide in the field. While the BC teams gave close quarterfinals, there is a gap that keep the top four in the top four; 3 Ontario teams and KVHS have been the semis in three of the last four years. I believe the difference comes from those teams being able to play multiple tournaments throughout the year; it keeps them in competition mode all year and exposes them to more topics. I hope that other regions look to this model as a productive way of boosting teams.

On a side note, I often get concerns about the order of teams on my tournament pages. In the Ontario and national tournaments, there are no published ranks for several teams that are eliminated part-way through the playoffs (for example, 5-8 at Nationals). I list those teams in order of R-value; it stems from my original intention of using the R-value as a way to determine teams that deserve progression to higher tournaments, though for Nationals it is moot.

The bottom half of the field got consolation matches. As has been noticed in the comments of the last post, the consolation tournament can end up as the most productive use of your tournament fee: most consolation teams played at least as many matches as the champion, UTS! The consolation model is a good way to get more playing time in, but as has also been noted, it is a shame the eliminated quarterfinalists can’t find a way to get more matches.

The Renert School finished as the consolation champion for the second year in a row, beating fellow Albertans from Webber Academy. Both teams matched their best-ever Nationals result. Cobequid EC earned consolation third place over Fredericton HS.

Fort Richmond Collegiate from Manitoba was the only new team in the field. It is always good to see teams earn a nationals experience, and hopefully they can continue to challenge the regular front-runners in the province.

Marianopolis College was the Quebec representative. They did not have as good a result as some other years, but as I have said before, the Quebec system has inherent difficulties in developing consistent clubs. Next year will be an entirely different lineup, and they could have entirely different results.

Auburn Drive HS rounded out the field. While I suspect it is only a minority opinion, I feel the need to address the idea that they didn’t deserve to be there. In short, they did. The Reach national model is based on fair representation across all the provinces, which includes Nova Scotia. Up until the early 2000s, most provinces only sent one representative. With only one representative, it was difficult to tell if the provincial runners-up could have been one of the top teams in the nation as well (eg: Lisgar CI has three national titles despite no provincial titles). The Nationals field began expanding to include more runners-up, including from the maritime provinces. In 2010, the final was two maritime teams. In 2008, both New Brunswick teams made the semifinals. Regions go through ebbs and flows of relative strength, and the second qualification spots do help give representation if any provinces have resurgences. It is true that Nova Scotia competition and participation is at a low point right now, but there is nothing stopping them from being stronger in the future, so the runner-up slot should still remain as a route to Nationals. There is merit to discussing alternative qualification methods, but it should not come with dismissive attitudes to regions of Canada.

I’d like to finish on a more pleasant note, so I’m glad to hear of all the camaraderie and good spirits the teams had. Ultimately, everyone is there for the enjoyment of the same activity, and it displays true character to takes wins or losses in stride. Good luck to all the teams next year, and once again, congratulations to UTS this year!

2018 mid-Nationals update

The elusive UTS-KV final is still possible…

The 2018 Reach for the Top national championship is now deep into the playoffs, with only three games remaining.

London Central SS faces Kennebecasis Valley HS in the first semifinal tomorrow. Central enjoys a surprise top seed after beating UTS in the round-robin, while KVHS will be hoping to repeat their own upset of Central that happened in the round-robin. There is not too much statistical difference between the two teams, but Central will have a slight edge on a longer and balanced pack.

UTS meets Martingrove CI in the other semifinal. This is a rematch of the provincial final, where UTS handily took victory. Martingrove is going to have a very tough challenge in this match – a victory would have to be the biggest playoff upset since the 2013 Bellerose run. UTS’ raw R-value of 157% smashes the Nationals record; before this, seven teams were clustered in the 140-145% range to top the all-time charts. Interestingly, Martingrove has been very consistent these last three years: 135%, 136%, and 136%.

The preliminary results table is found here. It will need to be updated to include playoffs and rankings that come from those games. I will have a fuller write-up for all the other teams once I get some time later this week.

Good luck to the semifinalists!