### Rewriting NBA scoring rules to help the underdog

There are far fewer upsets in professional basketball and football than there are in baseball and hockey. On Jan. 11 (tomorrow, as I write this), the Nuggets are favored by 12 points over the Cavaliers. That translates into at least an 85% chance of victory for Denver -- and, in fact, on Betfair, you can get 4.2:1 odds on Cleveland right now, which translates to only a 19% chance.

That's common for the NBA -- but I doubt you'll ever find an MLB game where one team's odds are that high.

Is the low competitive balance in basketball a good thing or a bad thing? It's bad in the sense that you'd like to see both teams have a fighting chance. It's good, I guess, in that the best teams are pretty much guaranteed to rise to the top of the standings.

In an oft-cited post from 2006, Tom Tango calculated how many games you need, in each sport's major league, for the r-squared ~~correlation~~ between talent and standings to reach 0.5. (UPDATE: Tango says r, but I think he means r-squared.) He found those numbers to be:

12 NFL games (75% of the season)

36 NHL games (44% of the season)

69 MLB games (43% of the season)

14 NBA games (17% of the season)

The better team wins so much more often in the NBA, that after 33 games of the NBA season, you have as much information about which teams are the best as after an entire NHL or MLB schedule. That makes it very hard for NBA teams to make the playoffs by just having a lucky season.

And, of course, it explains why there are so few first round upsets in the NBA playoffs. If a 7-game series in basketball is the equivalent of a 34-game series in MLB ... well, you're pretty sure the better baseball team would prevail in that many games.

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So, what I've been thinking is, how can we change the game of basketball to increase competitive balance, to make it easier for the underdog to win?

The easiest way is obvious: just make the game shorter.

Suppose you made an NBA game 24 minutes instead of 48. What would happen? Well, the normal curve of results would stretch by the square root of 2.

Consider a simplified game with 100 possessions per team, and only 2-point shots. In those games, a 14-point favorite is almost exactly 1 standard deviation of results (by binomial luck) above zero. That gives it an 84 percent chance of winning. But in a 50-possession game, a 7-point favorite is only 0.7 standard deviations above zero. So its chance of winning is reduce to just 76 percent. (I hope I've done this right.)

The problem is, who wants to watch a 24 minute game? It would only last an hour. You could have two games a night, but ... I don't know, every night a doubleheader? Plus, splitting a double-header is kind of unfulfilling.

A few years ago, I tried to come up with some other solutions that would make NBA games less predictable. They're not that great. But, last week, after a commenting thread at Tango's site, I thought of one that's reasonable. It's not perfect, and it might not be as entertaining, and there might be lots reasons why it wouldn't work in real life ... but it would definitely give the underdog a better shot.

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Here's what happens. Instead of a single 48-minute game, you play a series of 4-minute games. Whoever wins the most 4-minute games, wins. (If it's a tie, you have one additional tie-breaker game.)

I don't know what to call those mini-games. They have the same thing in tennis, where they're called "games," but that word is taken. We could call them "sets," or "ends" (like in curling), or "innings", or "rounds". Actually, in French, an inning is "une manche", which literally means "sleeve". We could call them "sleeves". OK, maybe not. I'll call them "innings" for now.

So, we play a bunch of four-minute innings.

The problem is: what if you're down four innings at the end of the third quarter? Since there are only three innings per quarter, you'd have no chance to win. To prevent that, we add one more rule: if you go up by 6 points, you win the inning immediately. So, in theory, if you go on a 30-0 run in the fourth quarter, you'd win five innings and have come back from four down.

The "innings" game favors the underdog by adding some luck: even if your opponent scores ten more points overall, they might have bunched those points in one or two innings, so you might still win the game. It's like the 2012 Baltimore Orioles, who scored only 6 more runs than they allowed -- but finished 93-69 on the strength of their 29-9 record in one-run games.

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That's the theory. To test it out in practice, I ran the results of the 2008-09 NBA season, based on play-by-play data provided by Ryan Parker at "Basketball Geek" (much appreciated!). The database has 1176 out of the 1230 games that year, which I figure is complete enough.

I just rescored every game as if it was being played by "innings" rules. I included real overtime, if there was one, even if it wasn't necessary to break an "innings" tie. If a team went past 6 points in an inning, it still got reset to zero for the next inning. But if a team hit 6 on its first of multiple free throws, the following shots counted towards the new inning. I only counted the unfinished inning at the end of the game if it was necessary to break a tie. If that inning was tied, too, I flipped a coin for OT. (In real life, you'd want to finish the last inning if it could win or tie the game. But I couldn't do that, because I had no data.)

Bottom line: that the bad teams did indeed win more often. Before I give you the results, I should mention that you can't consider them perfectly reliable. Team strategies would be different in the "inning" game than in regular games. Garbage time might not be garbage time, or vice-versa. I might be assuming deliberate fouls in games where the fouling team is actually ahead in innings. Teams wouldn't try 3-point shots when up by 4 in an inning. And so on.

But, with those caveats in mind, here are the results. It's the team's actual record, followed by their record in the rejigged "innings" game.

ATL 45-32 42-35

BOS 57-20 53-24

CHA 34-44 37-41

CHI 40-39 42-37

CLE 63-15 56-22

DAL 47-30 48-29

DEN 54-28 52-30

DET 37-39 31-45

GSW 28-49 32-45

HOU 45-27 45-27

IND 36-43 31-48

LAC 19-59 24-54

LAL 63-15 58-20

MEM 24-57 21-60

MIA 39-38 37-40

MIL 32-47 37-42

MIN 24-57 29-52

NJN 33-47 35-45

NOH 46-31 45-32

NYK 30-47 34-43

OKC 23-57 26-54

ORL 59-22 54-27

PHI 41-41 47-35

PHX 44-35 46-33

POR 53-26 48-31

SAC 15-64 22-57

SAS 50-27 43-34

TOR 32-48 31-49

UTA 44-31 44-31

WAS 19-61 26-54

You'll notice that most of the bad teams improved, and most of the good teams declined. The SD of the actual records was 13.1 wins; the SD of the "innings" records was 10.4 wins. That's a big difference. To me, it makes the standings look more "normal", compared to other sports, with no team in the teens in either wins or losses. (Of course, to an NBA fan, they might look too compressed; it's a matter of taste.)

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Here's some details of what individual games looked like.

-- Overall, 38 percent of innings were what I'll call "big innings," ended because of a 6-point lead. Probably, with teams changing strategies, that would increase somewhat. To, maybe, 50%? That seems reasonable to me, half ending early, and half ending by the clock.

-- The chance of a major comeback seems to be about the same. In regular basketball, teams down by 8+ points at the start of the fourth quarter, won 8 percent of the time (8 wins in 100 tries). In "innings" basketball, teams down by 2+ innings at the start of the fourth quarter, won 6.7 percent of the time (7 out of 104).

-- There were 213 games out of 1176 where the outcome was different between the two rules. Some of them were surprising. On December 19, 2008, the Nets beat the Mavericks 121-97. But, in the "innings" replay of the game, Dallas won 7-6!

-- The next most extreme reversals were 21, 18, 16, and 14 point games. There were 26 games total where a team that won by 10+ points, would have lost the "innings" game.

-- One thing about these rules is that you have to be willing to put up with a lot of similar-looking scores. There are a LOT of 7-6 and 7-5 victories. Most games have between 12 and 16 innings.

-- One of the things Tango wanted to see were occasional shutouts. With these rules, it never happened. But there was a "oneout." It was November 21, where New Orleans beat Oklahoma City 10-1 (105-80). There were only 11 "twoouts," games where the losing team won only two innings. They were all blowouts by normal standards -- 19 points was the closest.

-- There were three games where the winning team scored 12 or more innings. Those winning teams scored 129, 121, and 140 points, respectively. (The last one was a triple-overtime game in real life: Miami 140, Utah 129 (12-8).)

-- The most "big innings" was 13, on March 28. Denver beat Golden State 10-7 (129-116). There were two games with 12 big innings, and six with 11. Some of them look like (real-life) overtimes.

-- There were seven games with no big innings at all -- where neither team ever took a 6-point lead within an inning.

-- You can download a spreadsheet of game results here (.csv).

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I'm not really advocating that the NBA change to this new format. It's more an experiment, just to prove that there *is* a way to increase competitive balance, without shortening the game or changing the rules too much.

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UPDATE, Jan. 12:

One thing I just thought of: "big innings" don't help competitive balance much. Only innings than end by the clock do.

Suppose you had a rule of ONLY "big innings". The first team to get a six-point lead scores the inning. Most innings wins. (And, if you go over six points, you carry the extras over to the next inning.)

That wouldn't do at all. Because, suppose you take six times the winning team's innings, minus six times the losing team's innings. That's just the overall point differential, and it has to be positive. So the team that wins the innings game is also the team that would have won the regular game!

It seems like the thing that gives the underdog a chance is innings that end by the clock. So, maybe you want to have more of those.

Suppose we go to 7 points for a big inning, instead of 6. Hang on ... OK. With 7 points required instead of 6, the SD of wins drops even further, to 9.5. Now, only 24.5% of innings are "big". Nicer!

There sure are a lot of 7-5 and 7-6 and 8-4 scores, though. That might get tiresome.

Labels: basketball, distribution of talent, luck, NBA

## 6 Comments:

It's first one to win 6 innings, right? So, it wouldn't end 10-1, it might have been 6-0?

Which is probably when they won't go for it, if the game can end in under an hour.

Love that you went into the actual data.

No, it goes 48 minutes. An inning is 4 minutes or 6 point lead, whichever comes first.

Actually, assuming the last inning gets completed if it matters, the game could go 51 minutes 59 seconds before OT. Unless you want to consider the last inning's time overage to be OT.

Unlimited innings, is what I was trying to say, but failing.

What if you just lengthened the shot clock?

Sure, lengthening the shot clock would help. But it might make the game less interesting, no?

Interesting idea, to play "innings". It could increase the underdog's chances. Increasing (or removing) the shot clock could do the same. I recall that the NCAA introduced a shot clock in the early 80s after weaker teams seeking upsets intentionally would slow the tempo down greatly if they ever got a small lead.

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