## Thursday, September 28, 2023

### All-Time Hoops Updates Complete - Walton's UCLA and 1st All-Black Champs Texas Western

We have gone through and verified accuracy of all 179 all-time great teams, and you will now see a line at the top of each team when you print out the sheet of two teams you want to play from this list:

To go in reverse order, the cards for our all-time champs from our big tournament - Bill Walton's UCLA came out accurate when we ran the Version 2 calculations. We would expect them to score about 1.28 points per trip down the court against other great teams in the game, and allow 0.94 point per game so those AdjO and AdjD at the top of the card let you know about how good each team's office is. That results in an overall rating of +17, meaning against the average great team in the game UCLA would be about 17 points per 100 possessions better than the other great team based on the cards.

Keep in mind the average great team in the game would be about 21 points better than the average team in a given season, so the math then indicates that UCLA would actually be about 38 points better than the average team in a season.

This is accurate. In fact UCLA's average score during their undefeated season was 95-64, and their Strength of schedule was a +7, meaning the average team they played was 7 points better than the average team - so add that to the 31-point margin of victory and if UCLA had played just an average schedule of opponents it is estimated they would have won by 38 points per game.

However, when we did this advanced math with extra weight on tournament games over regular season games, some team cards were a bit better or worse than the original calculation.

Texas Western is in the history books to win a national title starting all black players, even more significant since they won the title game against Adolf Ruff's all-white Kentucky team.

When we recalculated all teams we found we had shortchanged some and overestimated some.

In this case, the Texas Western Cards should have produced about an average 6-point loss against the other great teams in the game - but once we ran the updated math they are actually about four points better than we thought. We have not changed the cards for the teams that are slightly off but the temporary fix for all of them is to adjust the dunk range, so if you were to play Texas Western in the game right now you would use the same cards but simply change their dunk range from 51-52 to a 51-56 range.

Even at the new -2, Texas Western would still be 19 points worse than UCLA's +17. That actually means they would be about a 12-point underdog because games do not last 100 possessions unless you play Loyola Marymount in our game.

Math Detail only for Fellow Stat Nerds

With around 2/3rds as many possessions (66 or a few more depending on fouls or steals and fast breaks in the last five minutes of a Value Add Basketball Game) so if dice rolls were completely average for a whole game, UCLA would have a 12-point lead at the end of a Value Add Basketball Game, but if you continued another 30 possessions or so to get to 100 total possessions between the two teams, then on average UCLA would win by 19.

The reason the dunk range and defensive "adj dunk range" is the perfect tool for adjusting precisely for strength of schedule and different eras, as well as for home court advantage, is that every die roll from 11-66 should come up just more than one time per game for each team in a game.

Therefore before this adjustment, the 53, 54, 55 and 56 when Texas Western would not be a dunk, but after the adjustment they would be a dunk. So that is an average of just over four times a game Texas Western gets two points. At first this sounds like we have improved them by 8 points per game rather than four.

However, before the adjustment those die rolls just mean nothing happens and you look at the 20-sided die roll which could be a 3-pointer, 2 pointer, two shots at the line or a missed shot. The average of those combinations would give Texas Western more than 1 point per time, so the dunk range guarantees at least 2-points but sometimes they would have gotten 2 anyway, or sometimes they will hit a 3-pointer on the 20-sided die and the offense has the option of choosing a dunk OR the result of the 20-sided die. In the end, it comes out to one point per number in the dunk range.

Without this adjustment, the cards for Merrimack that went 12-4 to win the Northeast Conference would likely have player cards as good as Kansas, that went 13-5 in the Big 12. However, the level of competition that factors into the dunk range adjusts for the fact that Kansas average opponent was 17 points better than the average team last year while Merrimack's opponent was 17 points worse than average.

Therefore www.kenpom.com calculates Kansas was +23 points better than average while Merrimack was -11 worse than average.

Therefore after we calculate Kansas cards based on stats that were held down by facing such tough opponents, if the numbers on the card would add up to an average +12, then they have 11 dunk numbers to make them as good as they really were based on competition.