Interesting +/- for the OSU Game

First of all, just a reminder, the so-called "official" +/- you see in the box score on the KU site is wrong. Pretty much everyone uses the same software and the software calculates it incorrectly. So the numbers I provide are slightly different and absolutely correct.

Also, my proprietary player rating includes the +/-. In fact, the +/- is 1/3rd od the impact on the player rating. So when you see a player rating like the one for Ochai in this game understand that the +/- can have a huge impact. Ocha's player rating was abysmal and that is largely due to the +/-. His stats were so-so so they didn't help too much. +/- is a stat I have been following for years. I started manually doing the +/- in 2005 as soon as the raw data was made available (play-by-play data). It is become more popular in recent years for some reason but to algos like me it has always been an important stat. It is not a comprehensively "tell all" important stat but it is significant. That is why I came up with my player rating, to try to get something closer to a "tell all" type single number stat.

So let's look at a few numbers in the +/- just to help get oriented. You can see the total +/- where Braun, for instance had 16, Harris had 7, etc. You also see the minutes played (calculated down to the second). You can also see the total score for each team while each player was in the game. The right three columns under the "In the Game" columns are the normalized offense, defense and total +/-. In other words, dividing the total KU score by the minutes played. When you do that you see that when Braun was in the game, for instance, KU scored 70 points, OSU scored 54 points and thus KU outscored OSU by 16 points or a +/- of 16. When you divide these by minutes played, while Braun was on the court, KU scored 1.98 points per minute, OSU scored 1.53 points per minute and KU outscored OSU by 0.45 points per minute.

Now lets look at the KU points per minute for several players. In the 22.9 minutes McCormack was on the court, KU scored 47 points for a points per minute of 2.06. That was the best on the team. By contrast in the 30.6 minutes Agbaji played KU scored 45 points for a points per minute of 1.47 for the worst on the team. That is a pretty stark difference between McCormack and Agbaji. The spread is not normally that large. To the extent you want to draw conclusions, you would say that McCormack was about 1/3 more effective at helping the team offensively than Agbaji. This is the general thrust of analyzing the +/- data.

Likewise, Defensively, Wilson seemed to be the most effective allowing OSU to score only 1.23 points per minute in the 25.9 minutes he played. On the other end of the spectrum, OSU scored 2.07 points per minute when Lightfoot was in the game. McCormack had the 2nd lowest defensive +/- at 1.4.

The overall best +/- goes to McCormack at 0.66. In other words, every minute McCormack was in the game KU outscored OSU by 0.66 points per minute. Lightfoot was the worst. When he was in the game KU was actually outscored by OSU by 0.27 points per minute.

Finally the three columns on the for right are a little tougher to understand but in some ways the most valuable. They are in essence the "value over replacement" if you will. It compares the difference between the minutes a player is in the game and the minutes a player is on the bench. So lets look at Braun. You can see his KU/Pts/M delta is 1.12. This is the difference between KU's offensive +/- when Braun is in the game (1.98) to when Braun is on the bench (0.86). This is essentially looking at how much better the team does (or worse) with him versus with his replacement. So basically it is saying that when Braun went to the bench the team dropped off from scoring 1.98 points per minute to 0.86 points per minute. This is a huge drop off. Likewise on defense, when Jalen Wilson was in the game the team allowed OSU to score only 1.23 points per minute but when he was on the bench they scored a whopping 2.2 points per minute. That is a difference of 0.97 points per minute. The team was clearly much better defensively with Wilson in the game.

As I said, 1/3rd of my player rating is from the +/-. Very often the differences discussed above are less stark. This game is an example where there were some pretty stark differences in the +/-. Unfortunately for Ochai, despite his decent stat line, he really didn't help the team that much from a +/- standpoint and that has to be considered.

My quintessential example of the subtlety of the +/- is the 2008 team. With all the great players on that team like Brandon, Shady, Mario, Sherron, etc, the overall season +/- had RussRob 2nd and Darnell 3rd. Mario was 1st. Darnell and RussRob rarely had gaudy stat lines. But the team was simply better with those two guys in the game. That was for the whole season so a pretty valuable stat at that point.

Without further adieu here is the +/-. Also for the season. Also the player rating charts.

Pretty interesting that we only had 4 players in that game who truly out shined their replacement. Maybe Big Dave is better off coming in off the bench..

HE, ask and you shall receive. I will do my best to give a lucid and understandable explanation. There is a degree of background into the nature of the numbers that time will not allow me to go into lest this become a tome. But I will try to give an understandable synopsis without the gory detail.

1. Expected Player Rating is based on the assumption that the baseline total of all players will sum to 83 points before adjustments. This is chosen to represent a level of performance that would be needed to beat the 7th or 8th best team in the country (varies and fluctuates). In other words, the current 7th best team is Houston and they have a total rating of 83.7. The No. 8 team is Duke and they have a rating of 82.5. To beat these teams KU would have to have a net rating of their total rating plus a fraction. I chose this number just because it seemed like a good level to place an expectation.
2. All individual Expected Player Ratings derive from two factors, the 83 value explained in No. 1 and the minutes played by a player. Each value of minutes played is assigned a proxy value. Without overtime all of the minutes played will equal 200. I sum up the proxy value to get a total proxy value. The reason for this proxy value is that the relationship between minutes played and the proxy value is a non unit slope. That is a fancy way of saying it is a sliding scale. So for instance, if a player plays 40 minutes his proxy value is 56 but if a player plays 20 minutes (half of 40) his proxy value is 24. Or looking at it another way, a player that plays 40 minutes has a 40% proxy premium (56/40=1.4) whereas a player playing 20 minutes has a proxy premium of 1.2 (24/20=1.2). It is critical to understand this concept to understand the meaning and value of the Expected Player Rating. The purpose for this is simply working on the assumption that a player who plays more minutes should produce at a higher rate than a player who player who plays fewer minutes. I derived this proxy (sliding scale) relationship by looking at every season back to 2004 and normalizing the data to a least square fit of sorts. In other words, in some years the slope of this proxy relationship was slightly higher and in some years it was slightly lower. But is was actually amazingly consistent. So this concept that the more minutes a player plays the more he should proportionally contribute. The concept is expressed in Self's words that starters build a lead and bench players hold the lead. All I am doing is putting some statistically meaningful equations to this concept. So when Dajuan or Ochai plays 35 minutes they will have a proxy value of 47.25 or if they play 30 minutes they will have a proxy value of 39 and so on.
3. After calculating the proxy value for all players, these proxy values are summed up. Then each players proxy value is divided by the sum of all proxy values to give the percentage of the total proxy value for the team. Then this percentage is multiplied by 83. This gives the EPR of that player. The total always adds to 83 as explained in No. 1.

This resulting EPR simply says the team needs to play at a total level of 83 (I could use a different number here I simply chose 83 because it seemed reasonable to me). I mean right now Baylor is the top team in the DPPI and they have a rating of 85. I could use this instead of 83 but it seemed reasonable that the Jayhawks should generally play like the top 7th or 8th best team in the country. And I wanted to make this a set number so I could compare it year to year.

No attempt to distill down something as complicated and dynamic as an individuals level of play is going to be perfect. The main argument I would have against my EPR comes from the massive amount of evaluation I did for all the years back to 2004 and it is that just because 2 players both play the same number of minutes they aren't necessarily expected to have the same level of contribution. I thought about finding a meaningful way to differentiate between players based on some criteria, but the data back to 2004 simply did not justify that. Over the course of a season, the total minutes and the resulting proxy value correlated extremely well. It did not always correlate each and every game, but going back to 2004, if two players averaged the same minutes per game they were very close in their total player rating. And it makes perfect sense. A player that is getting more minutes sort of means he is a better and more valuable player. The logic against that is sometimes players play more minutes because he does not have depth at that position and is forced to play more minutes even though he is not necessarily as good or as valuable as other players on the team who play the same number of minutes. But there is a slight modification in the calculation that attempts to address this that is too complicated to go into and is very minor except in exceedingly rare circumstances.

So I place a lot of value in the EPR but it is extremely important to understand this next concept in evaluating the EPR on the graphs. Since a good portion of the data that goes into the player rating is team based (i.e. +/-) you have to be very cautious in dinging a player too much if the actual rating is a little below the EPR. This is "Team Total Concept". On any given night, one player is going to have a "go to" type performance. Think David in the Oklahoma State game. So when a player is riding a wave, a smart team tends to hop on and ride the wave with him. So the other 4 players could conceivably have total player ratings below the EPR, not because they played poorly but because they deferred to the hot hand. DaJuan often falls into this category. He is rarely the "hot hand" and his player rating could be a little below the EPR because he deferred. But there is a limit to this. Actually there is a pretty severe limit to this by the nature of how the player rating is calculated. So if a player's rating is slightly below the expected it can be attributed the "Team Total Concept". But that will only apply for a small cushion. Any time a player's total rating is too far below the EPR, it is an indication they were a weak link in that game.

Okay, remember, you asked for this. I hope this gives you some insight. You see the tip of the iceberg, but since I have the motivation and time to spend countless hours evaluating and deriving these things, I take for granted the great complexity and nuance of the numbers. I don't look at this data like most others because I see both the strengths and weaknesses of every thing I do and thus, I can derive a meaningful evolution due to that. I get that it is black box stuff to most people. The main reason I did the player rating was really for others because mot normal humans aren't going to look at the plethora of metrics. I wanted to come up with a simple value that would be pretty meaningful that would be something anyone could look at and understand. And I assure you, when it comes to these evaluations it is clinical and objective. There is zero subjectivity of any kind in any of these formulaic and algorithmic evaluations. When I express my opinions, I make it clear I am expressing my opinions. When I provide these evaluations they are pure algorithm. I completely understand that everyone has favorite players and there is a natural tendency to discount anything that doesn't fit the narrative that uplifts the favorite. That is all fine and good and that opinion space is the dominate space where most fans live and the lifeblood of most chat boards and so forth. I try to bring a completely different space when I do these evaluations hoping that someone finds value in them. I do not think that this objective data and algorithm space is better nor am I thinking the opinion space is wrong or lesser. It is simply two different ways of manifesting fandom and one that guys like myself and asteroid have a proclivity and talent for and desire to share in the hope it will bring value and enjoyment to others fandom.

On your last question, I have not updated the DPPI online for sometime. Quite frankly, I wasn't sure that anyone ever looked at it and it takes time. Normally I have the time, I am currently in the throes or remodeling two of my rent houses right now. I try to budget 5 hours per day for that. With my other teaching commitments which is a couple hours per day, my wife and I are learning Spanish and we try to average an hour a day, and the normal chores and things that is the stuff of life added onto all the Jayhawk stuff which during basketball season probably averages 4-5 hours per day on game days and an1-2 on other days, time sort of gets away from me. And of course, my morning reading time is sacrosanct. Some people have to have their morning coffee almost as a religion. I don't drink coffee but I have to have my 2 hours every morning to read. That is my sanity. So luxuries like updating the link to my website sometimes falls down the priority list. I will try to find time in the next couple days. I am hoping to finish one of my houses this week so we can get it back on the market. New floors, every surface in the house repainted, new bathroom and kitchen counters and sinks and some other basic repair and maintenance. I love that stuff also. We rarely have empty houses but it is always a joy when we do because there is nothing quite so satisfying as doing upgrades and remodels and seeing the fruits of your labors. Plus, you can charge a little more because everything is pretty new and shiny.