Best Wins, Worst Losses, Seedings

[OFID]

Here's something that might inform our discussions of seedings ...

For some time, I've been trying to wrap my head around a situation where, say, Team A's best win is better than Team B's, but Team B's second, third and fourth wins are better than Team A's. I thought that a visualization might be helpful.

For this visualization,

• A team's best win is the win against the team with the highest rating score, the second best win is the one against the team with the second highest rating score, and so on.
• A teams worst loss is the loss to a team with the lowest ratings score, the second worst loss is to the team with second lowest rating score, and so on.
• The ratings for the opponents are plotted against integers indicating how bad the win/loss was, i.e., 1 for the best/worst, 2 for second best/worst, and so on.
• The team's wins are connected by a line, as are the team's losses. Each team has its own line color and plotting symbol for the wins (or losses).
• The size of the plotting symbol corresponds to the margin of victory (or margin of loss).
• The color of the plotting symbol indicates the venue (home is green, away is red, neutral is black).
• Wins are connected by solid lines. Since the best win is the one with the highest rating score and subsequent wins have lower rating scores, the win lines go down.
• Losses are connected by dashed lines. Since the worst loss is the one with lowest rating score and subsequent loses have higher rating scores, the loss lines go up (assuming there is more than one loss, otherwise a single point is plotted).

The plot for best wins and worst losses according to the Massey rating score for the three elite teams (South Carolina, Baylor and Oregon) appears on the first page of the attached pdf. The table supporting this plot is on the second page.

Observations:

• The eye is immediately drawn to the solid red win line which is nearly always below the other two solid lines. This is Baylor's win line. Those huge green triangles in the lower right are Baylor's overwhelming victories at home versus the cream puffs they scheduled in their out-of-conference schedule. Had they not forgone the opportunity to schedule some decent teams, their wins in the middle of the plot would have been as good as South Carolina's and Oregon's.
• The solid black win line is South Carolina's. Their best two wins are better than Baylor's and Oregon's best win. SC's third win is the same as Baylor's and Oregon's best win (all against UConn). SC does not play in as strong a conference as Oregon, so after the SC line dips below the Oregon line.
• So if Baylor's wins are inferior to SC's and Oregon's, how is Baylor's rating score (2.655) virtually indistinguishable from SC's (2.656) and better than Oregon's (2.641)? The answer is that Baylor has no bad losses. Their only loss was to SC (the red triangle in the upper left corner). Oregon's rating score lags behind the other two because they have two bad losses (Arizona St and Louisville).

The plot for the Massey power score (which measures potential, as opposed to the ratings score, which measures accomplishment) appears on page 3 of the pdf, and the supporting table appears on page 4. These look pretty much the same as the Massey rating score plot and table, with Oregon's wins looking a little better. Note that for the Massey power scores, the rankings for the three elite teams is reversed: Oregon first (84.1), Baylor second (81.9) and SC third (81.2).

The plot for the RPI scores appears on page 5, and the supporting table appears on page 6. These look a little different. The Baylor wins look better in the middle of the graph, as do the SC wins. Since RPI is 50% opponents SoS and 25% opponents opponents SoS, RPI hates Baylor because of the out-of-conference cream puffs. SC (0.694) and Oregon (0.692) are almost right on top of one another at #1 and #2, but Baylor (0.665) lags behind at #4.


UConn fans are probably more interested in the the rest of the AP top 10. The plot for the Massing ratings score is on page 7 of the pdf, and the supporting table is on page 8.

Observations:

• The UConn lines are green with 'x' for the plotting symbol. Our best 9 wins are worst or second worst of the seven team, then middle of the pack through the 19th best win, and then among the best. Despite this, we're fifth in the Massey ratings score because, like Baylor, we have no bad losses. Our only losses were to Oregon, Baylor and SC.
• Through 11 wins, Maryland's wins (solid blue line with diamonds) look best. They have four losses, one of which wasn't a bad loss (SC) and another wasn't too bad (Northwestern). They're fourth in the Massey rating rankings.
• Looking only at the first 5 wins, UCLA's look best (solid magenta line with squares). However, loss line (dashed magenta with squares) looks the worst with two really bad ones (Washington and USC [Southern California, not South Carolina]) among their four losses. These losses sink them to 11th in the Massey rating rankings.
• North Carolina St's wins (solid aqua line with downward pointing triangles) are middle-of-the pack until the 13th, after which they're the worst, or among the worst. The also have two awful losses (North Carolina and Georgia Tech) among their three losses. They're 12th in the Massey rating rankings.
• Louisville (red line with upward pointing triangles) has the best win (Oregon) and have some of the better wins after the 15th, but in between the wins don't stand out at all. The have two pretty bad losses (Syracuse and Ohio St) among their 3 losses. They're 9th in the Massey rating rankings.
• Stanford (black line with circles) is fourth in the AP poll. Their first eleven wins are middle of the pack, and after that, they bubble up to the top. Their only really bad loss was Texas. However, they were blown out by Oregon. They're 7th in the Massey ratings rankings.
• Mississippi State (gray line with asterisks) has possibly the least impressive collection of wins and the most losses, two of which were really bad (West Virginia and Alabama). They don't look like they belong with the rest of these teams. They're 16th in the Massey ratings rankings.

UConn is clearly below the Elite Three teams, but where do we stand with respect to the next 7 in the AP poll? The only one of these 7 teams to beat one of the Elite Three was Louisville, who was discussed above. They don't appear to be better than UConn.

The problem is there's no evidence that UConn is better than any team that is better then DePaul. How did the other 7 teams fare against teams better than DePaul, but worse than the Elite 3?

• Stanford has 4 wins (Mississippi St, Gonzaga, Oregon St twice) and 1 loss (UCLA).
• Louisville has 1 win (NC State) and 0 losses.
• Maryland has 4 wins (Northwestern, Iowa, Indiana twice) and 4 losses (Iowa, NC State, Northwestern, SC)
• NC State has 1 win (Maryland) and 1 loss (Louisville)
• UCLA has 4 wins (Stanford, Arizona, Indiana, Oregon St) and 1 loss (Arizona)
• For the sake of completeness, Mississippi St has 0 wins and 1 loss (Stanford)

Stanford and UCLA can both make strong cases that they're better than DePaul. Louisville has a much weaker case. There's no evidence that Maryland or NC State (or Mississippi St) is better than DePaul.

That argument puts us at overall #6, a solid #2 seed within a regional.


The plot for the Massey power score is on page 9 and the supporting table is on page 10 of the pdf. They're pretty similar to the Massey rating score plot and table, and the 'better than DePaul' argument is similar.

The RPI score plot and table are on pages 11 and 12, respectively. They're also pretty similar, with most noticeable differences being several of NC St wins looking worse, some of Louisville's worse wins looking better, many of Stanford's better losses looking worse and Mississippi St's wins looking better. The 'better than DePaul' argument looks a little different:

• Stanford has 4 wins (Mississippi St, Gonzaga, Oregon St twice) and 1 loss (UCLA).
• Louisville has 1 wins (NC State) and 1 loss (Florida St).
• Maryland has 4 wins (Northwestern, Iowa, Indiana twice) and 4 losses (Iowa, NC State, Northwestern, SC)
• NC State has 2 wins (Maryland, Florida St) and 1 loss (Louisville)
• UCLA has 4 wins (Stanford, Arizona, Indiana, Oregon St) and 1 loss (Arizona)
• Mississippi St has 1 win (Texas A&M) and 1 loss (Stanford)

However, the conclusion remains the same.