The Madness of Metrics and Match-ups

Well, I had three ideas for this article. The first idea came to me when I was putting the final touches on the 3-part series on upsets. Needless to say, what I was hoping would happen didn't happen, which means there won't be any follow-up to that series. Either during the weeks after the tournament starts or during the off-season, I will update Part 2 of the upsets article with the remainder of the withheld data. The second idea spent about two weeks off of the drawing board, then went right back on it, and the only reason it went back on the drawing board is because the idea for this article fulfills quite a few needs. First, I promised the implementation of micro-analysis in the blog, yet here we are in March and none to be found. By micro-analysis, I mean the study of the brackets from the perspective of match-ups and team-specific qualities, rather than macro-analysis, which is the study of the brackets from the big picture perspective of tournament quality and predictability. Shame on me.....until now. Second, I like to be a ground-breaker, a pioneer in the science of brackets, an innovator to the tools of the trade. I tried last year with the article on trend analysis, and yes, I am still following, testing and improving that tool. I think this article will be just as intriguing and innovative as that one. Third and final, it uses the same data I have been using all season, just in a different way. I am going to be using efficiency analysis to predict match-ups. In particular, this article will focus on using the Four Factors as a tool to determine how teams win and lose their games.

Background

If you have "never" heard of efficiency analysis, let me explain (If you have, you can probably skip to the italicized end of this section). Efficiency analysis simply looks at a basketball game (and/or team) and examines what results from a possession. A possession can end quite a few ways: A made field goal (usually labelled "FGM"), a made Free Throw ("FTM"), a turnover ("TO"), or a defensive rebound ("DRB"). Only two of those four result in points (which is how wins and losses are determined) and sometimes, those two can happen on the same possession (which is something basketball should seriously consider eliminating). In essence, the team that gets more out of their possessions wins the game. Along the history of efficiency analysis, one pioneer named Dean Oliver introduced the concept of the "Four Factors" that were essential to winning (and for sports data scientists to study) any game. These four factors are Effective Field Goal Percentage ("EFG%"), Turnover Percentage ("TO%"), Offensive Rebound Percentage ("OR%") and Free Throw Rate ("FTR"). There is various literature on the internet that goes into more detail on the four factors and how to calculate them, so I will refrain from redundancy. Then, data scientists like Ken Pomeroy, Jeff Sagarin and Bart Torvik used these four factors to produce efficiency ratings systems to assess the quality of sports teams. PPB uses these efficiency ratings systems to evaluate tournament predictability (QC analysis) and identify tournament victims and Cinderellas (SC analysis and OS/US model). For this article, I'm going to be testing the reliability of the Four Factors in predicting when/how a team wins or loses. If these four factors are essential in winning basketball games as suggested by Dean Oliver, then they should also carry some value in a predictive capacity, which is what I will be testing.

Data and Methodology

All data for this article has been obtained from the T-Rank website, published by Bart Torvik. I would highly encourage you to explore his site (only after you finish reading this article). I have compiled the game-by-game efficiency analysis into a spreadsheet and performed a correlation analysis with the margin of victory/defeat to the Four Factors. Before I get into the analysis part, I need to point out a few significant details.

• All game-by-game data includes all games up to the end of the regular season. Data from games played in conference tournaments is not included in this analysis.
• All efficiency rating data was extracted by 10pm EST on Mar 4 and this data is still subject to change. These ratings include the results of some conference tournament, but in this analysis, it is only used to build a team profile (explained later).
• This analysis only includes the projected 1-4 seeds (16 teams total) at the same timestamp for data extraction.
• This analysis features correlation coefficients, where the strength of the relationship is determined by how close the correlation coefficient value is closer to either +1.0 or -1.0. In the case of correlations involving defensive stats, these will tend to be negative since defensive values are calculated on an ascending scale (lower numbers are better) whereas offensive values are calculated on a descending scale (higher numbers are better).

Analysis: Part 1 - Ratings Perspective

I think the easiest way to present the findings is to divide the analysis into multiple sections rather than cram it all into one long paragraph. This should make the analysis and the article more aesthetically manageable. The first and obvious starting point is at the very top of the efficiency hierarchy: The ratings component. This is the data point that combines all Four Factors into a value that reflects a team's aptitude on offense and on defense. In the chart, I have listed the team's rank in the T-rank ratings system, the team's cumulative rating (both its adjusted offense rating and its adjusted defense rating) and where this rating ranks among all of the other teams' respective ratings. More importantly, the columns labelled "Correl" are the correlation coefficient value for each game's specific rating (offense and defense) compared to that specific game's margin of victory/defeat (for "Correl" under AdjO and AdjD) and the correlation coefficient value for each game's points per possession (offense and defense) compared to that specific game's margin of victory/defeat (for "Correl under PPPo and PPPd).

How to interpret this chart:

• The PPPo and PPPd correlations are stronger than their AdjO and AdjD counterparts. This is actually expected. After all, PPP stands for points per possession and it is being tested against margin of victory/defeat, which is points for minus points against. There should be strong correlation between those two data points because they are using "approximately" the same input. The AdjO and AdjD components are 'adj'usted for quality of opponent. A team should be more efficient against an weak opponent and less efficient against a strong opponent, and this adjustment to the efficiency metric for opponent quality will weaken the correlation between the two.
• The real enigma comes from the lack of consistency with expectations. I would expect one-dimensional teams -- teams that are strong on one side of the ball -- to have wins and losses more correlated with that particular side of the ball. Its just not the case. NOVA is the top offensive rated team and they are among the teams with high W/L correlations to offense rating, yet PUR is the 2nd highest rated team and they are among the teams with low W/L correlations to offense. The same goes for defense, especially when you see TXTC and CLEM.
• As a result, I have added two additional columns at the end of this table, labeled "I" and "D", which stand for identity and dependency. Identity is determined by the rating balance. If a team has an AdjO ranking 20 or more spots higher than its AdjD ranking, it gets an O for 'offensive team' in its identity. If a team has an AdjO ranking 20 or more spots lower than its AdjD ranking, it gets a D for 'defensive team' in its identity. If a team has an AdjO ranking within 20 or less spots of its AdjD ranking, it gets a B for 'balanced team' in its identity. Dependency is determined by the correlation coefficient - whether its wins and losses correlate more with a particular side of the ball. A lower correlation (both relative to its alternative correlation -- offense to defense and vice-versa -- and relative to the other 16 teams) means that team is less dependent on wins/losses from that side of the ball. Like identity, O means more dependent on offense and D means more dependent on defense. In dependency, B means 'both' offense and defense correlate with wins and losses while no letter means neither offense nor defense correlate with wins and losses. I'll address this aspect more in the conclusion.

Since it seems as though we are left with more questions than answers from the rating perspective, let's move on to the four factors perspective and see what it shows us.

Analysis Part 2: Four Factors (Offense)

This chart shows the correlation coefficient for each of the four offensive factors in a game to the game's outcome. Here are my thoughts on this chart:

• Wins and losses in a game correlate most closely with the EFG% factor. This is no surprise to
  
  me. The majority of points in a game typically come from made field goals, both 2-pointers and 3-pointers. Since games are decided by points (not turnovers or rebounds), it seems fitting that the stat responsible for the majority of points in a game is most correlated with the outcome of the game. It explains why many Hall of Fame coaches say phrases like "Everything looks better when the ball goes through the hoop."
• Since higher correlations mean wins and losses correlate better with the factor in question, teams with relatively higher correlations may be susceptible to losing when that particular factor doesn't hold up to season averages. For example, KU, TENN and TXTC have EFG%-correlations above 0.7000, so a cold-shooting night for these teams could mean their last night shooting the ball for the season. NOVA, UNC, DUKE, and MIST aren't far behind.
• Turnovers should have a negative correlation because of its inverse relationship to wins and losses. Since I am using margin of victory, positive margins of victory (wins) should see lower turnover percentages and negative margins of victory (losses) should see higher turnover percentages. The closer these correlations are to -1.0, then it means a particular team wins when they protect the ball and loses when they cough it up. Case in point: CLEM. Other notables in this category in order are DUKE, KU, CIN, UNC, XAV, and TXTC. The two anomalies in this category are NOVA and PUR, who have positive correlations in a relationship that should have negative.
• Offensive rebounds are a way to generate high points per possession because the only rebound that ends a possession is a defensive rebound. If the offense gets the rebound, they can get another shot on the same possession, and usually a better shot than the first one. More shots means more chances to score points. Teams with high correlations in this factor will win more of their games if they collect more of their misses like UVA, UNC, MIST, PUR, CIN, and WVU. Naturally, I would expect teams with relatively lower correlations in EFG% to have relatively higher correlations in OR%, like UVA, PUR, CIN and WVU.
• Free throw rate may be the most convoluted of the four factors. Since it counts how many free throws a team makes against how many shots a team both makes and misses, it measures two things at once: how many free throws you make and how often you get there. Its also slightly distorted by the existence of "And-1s." It is also the only factor distributed evenly across the zero-bound, as it ranges from -0.2365 for DUKE to +0.2977 for XAV and it hits most of the intervals in between. Since its correlation is the least reliable as a predictive measure, I won't address it (although it would be another good opportunity to bash officiating and bad rules in the college game).

Analysis Part 3: Four Factors (Defense)

This chart shows the correlation coefficient for each of the four defensive factors in a game to the game's outcome. Here are my thoughts on this chart:

• Nothing new here: Defensive EFG% is most correlated to wins and losses, just like the
  
  offensive component and for the same reasoning. Keep in mind that defensive numbers should be negative because of their inverse relationship to margin of victory. Teams with strong correlations (closer to -1.0) mean their wins and losses correlate with good (for wins) or bad (for losses) EFG% defense. XAV, TXTC, WVU, KU, and PUR boast correlations -.6000 and stronger. TXTC has lived and died by their defense all year long. WVU's style of defense explains their strong correlation: If they don't force a turnover, an average team can typically score against their half-court defense. XAV is a team that can score consistently, yet their losses come from teams that scored more proficiently than they did (AZST and NOVAx2).
• Defensive turnover percentage is in a close race for 2nd most important factor on the defensive side of the ball. Logically, it is pretty simple: if a team forces a high percentage of turnovers, then their opponent doesn't score on a high percentage of their possessions. Your opponent can't win if they can't get a score, especially if they can't even get a shot attempt. It is no surprise that the team with the highest win/loss correlation to this factor is WVU, or should I say Press Virginia. Not only do they force turnovers, they usually score pretty easily on the ensuing offensive possession. MIST is probably not a surprise on this list. They need a large defensive turnover rate to make up for their own bad offensive turnover rate. The real surprise on this list is UNC with a -0.16, the only team with a negative correlation in this factor. For a program built on Dean Smith's and Roy William's philosophy of defense-to-offensive transition points, UNC's wins and losses do not seem to correlate with their amount of turnovers they force on the defensive side of the ball. As a UNC fan, even I am shocked by this one.
• Defensive rebound percentage, albeit the third most important factor, still boasts some relatively significant W/L correlations. If a team has a high DR%, it means two things: Their opponent just missed a shot and their opponent will not get another chance at points on that possession. Teams with high correlations in this category have a simple recipe for success: They must force a missed shot and collect the resulting rebound. CIN, UNC, KU and DUKE have high correlations in this factor, but only CIN and DUKE boast the defensive identity to force missed shots and collect the defensive rebound on a consistent basis. The anomaly in this group is XAV. This may have something to do with their extremely high correlation to defensive EFG%. If their opponent is scoring effectively, like AZST and NOVA did in three total games, then their EFG% will be bad because of a high percentage of made field goals and their DR% will be low because more made field goals equals fewer defensive rebounds to collect, both of which would be correlated to a negative margin of victory (a loss).
• Defensive FTR is a little bit cleaner than its offensive counterpart. Only four teams boast a positive FTR correlation: UVA, XAV, PUR, and ARI. Again, I'm not sure how to interpret this factor. There is no such thing as Free Throw Defense, and this factor can be diluted by allowing a large number of field goal attempts, but that is contrary to good defensive EFG% and DR%.

Analysis Part 4: Shooting

Since both offensive and defensive EFG% appear to be most correlated with wins and losses, it is only appropriate that this factor is investigated a little bit further. In the chart, EFG% has been dissected into its two components: Two-point field goal percentage and three-point field goal percentage. Here are my thoughts on the chart:

• In all honesty, it may have been wiser to build my identity-dependency construct from this
  
  chart rather than initially with the ratings chart. In fact, this chart would give only two teams -- CIN and AUB -- different ratings for their dependency value. Nonetheless, the correlations in this chart tell a lot about each team. While I won't go over each and every team (my readers are smart enough to discern these things from the chart), I will highlight the obvious ones.
• NOVA winning and losing depending on their offensive 3-point percentage, what a shocker! (sarcasm mine). At .7635 correlation, there is no denying they live by the 3 and die by the 3. The next closest two teams -- KU and UNC -- have also been in love with the 3-point shot, even though it has cheated on them on multiple occasions. Such is March Madness: One cold night and you go home.
• One of the fundamental cores of defense: It is built from the inside out. Two teams whose wins and losses correlate with defensive field goal percentage inside the arc -- KU and XAV -- don't have a strong defensive identity.
• As a corollary to the previous bullet, a strong defense inside should allow a team to defend better on the perimeter. I personally do not believe defense can affect 3P% (as other statistical studies have shown), but the chart shows something interesting. Teams with good defensive identity tend to have little win/loss correlation with opponent's 3P%, as demonstrated by the low correlations of UVA, DUKE, MIST, TENN and CLEM. Yes, there are a few anomalies to this pattern, namely UNC and TXTC. WVU's high dependency on opponent's 3P% makes some sense, considering players could have the mindset to make up for a turnover with a 3-point shot. It is not perfect correlation with defensive identity and low 3P%, which is why I still believe my viewpoint, but the patterns of continuity were interesting.

Conclusions

How does all this play out in March? Before I give you my final thoughts, I want to point out one detail. This is the only year in which I have done this kind of analysis. I haven't tested this method nor my conjectures on previous years to see if they are reliable or even valid. Take them worth a grain of salt, but more importantly, pay attention to the correlations in the charts above and visit Bart Torvik's site to see the raw data with your own eyes. I'm pretty sure you can identify a lot of usable information for bracket picks.

• I think offensive-identity teams have smaller margins for error than defensive-identity teams. It is probably why Pete's F4/Champ rules as well as a few other rule-based methods set the bar lower for Defensive Efficiency than Offensive Efficiency. A defensive-identity team can always make shots or generate shots from turnovers, but an offensive-identity team cannot always get stops or force bad shots. Defensive teams are safer bets than offensive teams.
• Teams that have high correlations in multiple factors suggests victim teams. It says to me that if one of those factors comes us short, they could be heading home before the first weekend. KU and XAV fit this category, but if they don't get matched up against a team that can exploit these vulnerabilities, it will be awfully difficult to pick against them.
• If I had to logically guess, I would say teams whose identity is the same as their dependency are more likely to advance further than teams whose identity is different from their dependency. It's chain-breaking logic: To break a chain, target the weakest link. I think it would be easier to crack/pressure UVA's offense than its defense. I think it would be easier to crack/pressure NOVA's defense than its offense (or its 3-point shot).
• Likewise, I think balanced teams are safer bets than one-dimensional teams. Self-explanatory.
• The lack of a dependency for MIST is NOT an endorsement for MIST as the 2018 National Champion. I've highlighted one of their glaring deficiencies in this article (one that does scare me). They were 9th out of 16 on offensive rating correlation and 6th out of 16 on defensive correlation, so it was hard to call either of those a dependency. The shooting correlations show their wins and losses are highly correlated to 2P%, so a strong 2-point defense could be their vulnerability.

In a phrase, the madness of March comes down to the metrics and the match-ups. Oh my! How do you win? How do you lose? How do you survive and advance? If you know the answers to these questions, tell me because they will be a big help in picking a perfect bracket. I hope this analysis made sense. If not, I hope the idea of it and the data behind it will aid you in bracket-picking or even lead you to producing a better version of this study. As always, thank you for reading my work and if something doesn't make sense, feel free to ask in the comments. I'm going to try to get the next article out on Selection Sunday, hopefully before the bracket is revealed. It will be a foresight article that I have done the last two years as a hindsight article.