Team PP20TUH vs. MPP20TUH

[pblessman]

In judging how strong teams are, tournaments sometimes use PPG (points per game) or PP20TUH (points per twenty tossups heard). Wouldn't it make more sense to use a modified model where the opposing team's point total is factored in? To explain let me give an example:

Team A scores the following in for a record of 4-1 and a PPG of 160:

170-0
170-0
170-0
170-0
120-130

Team B scores the following in for a record of 4-1 and a PPG of 159:

170-160
170-160
170-160
170-160
115-400

I think it's obvious Team B is much stronger than Team A, but if ties are broken by PPG, Team A would advance, or be seeded higher if Playoffs are seeded by W/L then PPG. Doesn't this seem inherently unfair?

I propose using a modified way of calculating PPG and PP20TUH by adding half the opponent's score to each team's point total for any particular game to get the modified point total. The maximum modified points total would be twice the team's score. Example from above:

Team A has an MPPG of 173 from the following individual game totals:

170
170
170
170
185

Team B has a MPPG of 247 from the following individual game totals:

250
250
250
250
230

The idea is that (from my gut feeling) the following scores are "normal" for a team with a 200 MPPG (just a few examples):

200-0
150-100
135-130
130-140
100-200

The advantage to my proposal would be that it would be easier to compare teams across brackets, as current systems do not factor in opponent strength in making decisions about which teams to advance to playoffs or how to seed them for playoffs. I have an anlogous suggestion for calculating individual player PPG and PP20TUH which I will describe in another posting soon... Thanks for your input on this one!

[Tegan]

I have been searching for a better system for breaking ties....

In Illinois, aside from head-to-head, total points is often used, which I have claimed often favors really strong teams (fine), and weaker teams perceiced to be strong (seeded based on reputation). Many tournametns in Illinois are "reputation seeded", meaning a 9-9 team that won a sectional six years ago gets a higher seed than a 20-5 team today that was 3-8 six years ago. Surprisingly, when I question hosts, they often times admit they have no clue how good a team is, and seed strictly on "what they have heard".


Since few tournaments actually seed, maybe this is a better way of breaking ties (a tournament that is truly seeded could use total points, since the better teams are the only ones (hypothetically) facing "weaker oppposition"....

Maybe I will use this next year at my tournament.....just to see how it works.

[solonqb]

That's not a bad idea at all, Mr. Blessman.

I'll try to use it at our tournament this year and see how it works.

[jewtemplar]

The only problem is the fact that low opponent scores are sometimes attributable to the tossup domination of the winning team, rather than the weakness of the losing team. I guess the formula is trying to make playoff tiebreakers between mid to upper level teams more fair, but you never know.

[solonqb]

Well, that would depend on whether there were bouncebacks or not. With bouncebacks, one might have to weight the opponents score differently, perhpas a bit less than a half, in order to deflate them.

[Stained Diviner]

I remember this question coming up here a year or two ago. One person suggested using bonus conversion, which makes sense. If two teams are both 4-1 or 3-2 or something comparable after qualifying rounds, then they have each had a significant number of tossups. Take the number of bonus points they got on their own bonuses, divide it by the number of bonuses they had a shot at, and voila.

This assumes that the tournament is very well organized in order to keep track of such things, and it may not be any fairer than what you have proposed. It's at least an interesting idea.

[Tegan]

Coach Reinstein is, as usual, correct about this. There undoubtedly exists a "perfect" way to break ties, but it is likely so complicated that to do it in so short a period of time....AND to assume that everyone in the tournament is giving you the right information to base it on, is pretty tough to do......you would need some help running the computers.

It is true that a fairly good team can be whomped by a really, really good team. I imagine it is rare, but it does happen. There has to be a way to factor that (in a relatively easy way).

Maybe a team's total own bonus points + total of opponent's own bonus points?

[NoahMinkCHS]

I always have to question how strongly bonus conversion should factor into any formula -- after all, most matches consist of (at least) two parts, tossups and bonuses, and I don't know if it's quite fair to preference one over the other. I know there's the usual "depth vs. speed" argument, but if all that really mattered were depth, we could do quiz bowl on worksheets alone. But (thank goodness) we don't.

I understand jewtemplar's point about domination on tossups, but I think that pblessman's formula doesn't hurt a dominant team. In his example, neither Team A nor Team B really dominated, but if they had, their MPPG would have gone up, rather than down. (For example, if my team wins 200-150, we'd have MPPG of 275, whereas if we won 400-10, we'd be at 405.) Of course, then bonus conversion might (inadvertenly?) factor in, such as if my team scored 200 points on tossups, then (in a non-bounceback format) blew our bonuses. (Maybe compare a 200-150 score with a 200-0 score.)

So in some ways, you get the best of both worlds: If two teams scored about the same number of PPG in two very different divisions, we have a way to equate what they did... and, it also prevents a pure tossup team with little depth from getting ranked higher than a team with almost as many tossups but much better bonus conversion.

I don't know if this is a perfect formula -- maybe it over-emphasizes opponent's skill? Take my example above, with scores of 200-150 vs. 200-0. It may be that both the 200 teams knew identical questions and didn't know the rest -- in that case, the first team had the good luck of playing a better opponent, and would get a higher seed based solely on that. (Granted, this would be less likely over a 5 or 10 round tournament, but it's not impossible at all.) So I don't know what the answer to that criticism is. But I do think this idea, in some form, has a lot of potential to make things fairer and more competitive. I think we should keep discussing this and try to come up with something really good.

[snhou]

I'm curious as to why it's obvious that Team B is better than Team A. In fact, I'd say the opposite is true, Team A is better than Team B.

Unless Team B had its wins against, say, DCC, Maggie Walker, Raleigh Charter, Solon and the blowout against TJ, while Team A had its wins against C and D teams, of course. The solution for that would lie in the TD coming up with balanced brackets.

[Stained Diviner]

The reason for doing bonus conversion is that it is unaffected by what team you play. If you control three bonuses against Thomas Jefferson and convert 45 points, that is equivalent to controlling 15 bonuses against Podunk D and converting 225 points. It is very hard to compare tossup conversion against different levels of competition, but bonus conversion should not be affected.

[pakman044]

Well yes, but for teams that have few bonus opportunities, their bonus conversion stat will be inaccurate (they could get one or two bonuses that are right in their area, or a few that really aren't). As a team converts more, their bonus conversion stat will approach the true mean (in theory, even though we're talking about a small size of bonuses anyway, so the law of large numbers doesn't really apply).

I'm not really sure how much in the way of bonus conversion attempts is necessary to assure that the team's B/TU is accurate; I'll leave that up to someone who has more stat than I.

Patrick King

[djayboots]

A high school tournament (untimed) at Stanford actually introduced a similar "Strength of Schedule" statistic for breaking ties. It was defined as the average of your team's PPG and all of your opponents' PPG. Obviously not a perfect system, but it worked out all right for this particular tournament.

Here is the SQBS report.

[STPickrell]

At the tournament I ran in 1997, I used a strength of schedule factor. Sadly, for the life of me I can't remember what I did. :-)

I'd also disagree that Team B is stronger than Team A. We're assuming roughly equal strength of schedule here ...

Team A destroyed its first four opponents, preventing them from getting a single tossup. They then played competitively in their last match. Team B barely squeaked by its first four opponents and got blown out in the final match. Granted, Team A's last opponent was probably not as good, but in the other four matches, Team A proved its skill.

Also, on the low end of the brackets, this could make a difference. Why should a 1-4 or 2-3 team who gets blown out by Jefferson B and Spotswood A be rewarded for letting their opponents hang up 400 on them, as compared to a team who keeps it closer but low-scoring against not as proficient opponents?

I'd rather use % of tossups answered or margin of victory than bonus conversions for the simple fact that at the lower end, there might not be enough bonuses to make an accurate sampling, whereas every single team there has heard the same # of tossups.

A good team can get whomped by a better team but it's rare. I remember once at the St. Anne's tournament in 1993, Lee destroyed a good Charlottesville team by a score of 270-30 or the such.

[pblessman]

The reason Team B is better than Team A can be seen when you look closely at the differences between Quiz Bowl and other "sports::

1. There is no defense in quiz bowl, only offense, i.e. there is no such thing in Quiz Bowl as "holding a team to no toss-ups" unless your own team gets ALL the toss-ups, preventing the other team from getting in. You can't block a team's shot or play a full-court press... your only defense is getting toss-ups.

2. Quiz Bowl is different from any other "sport" in that there is a clearly defined number of points which are available for both teams. In basketball each team gets a posession and can score on their own posession, but quiz bowl is the equivalent of saying "We'll have 20 jump balls at half-court and the team that wins the jump ball gets 10 points and a chance to add mor points through free throws" or something like that. If the other team scores a lot of points it therefore actually means your own scored points should be valued MORE not less, as you've played a stronger team and have converted more of your opportunities.

I could expound more on this, but I hope it makes sense...