http://tangotiger.com/index.php/site/article/cost-of-a-penalty

Let’s stick to NBA because it’s simplest.  Tango’s argument, as I understand it, is

1) The ratio of HCwin% (over 0.5) to HC point differential, or win% (over 0.5) to point differential, is about 30 (I have it a tad higher, but 30 is fine for the sake of this argument), therefore 1 point is worth ~ 1/30 = .033 WP.

2) A 1.5 pt charge-block swing (as defined in the thread) is worth an expected ~1.5 pts (again, close enough for this argument)

3) Therefore the average 1.5 pt charge-block swing is worth ~0.05 WP.

I have several objections

1) The win/differential ratios are simply empirical properties of average results and average point differentials.  There’s no inherent reason for this to match up to one actual point in one actual NBA game.  Even if you, by fiat, added 1.5 points to every home team’s score once the teams thought the game was completed, this would only flip the winner about 3.4% of the time (adding it to the away team would flip ~3.5% of the time), which is well short of the .05 claimed. 

2) There’s the implicit assumption, to even use the formula in part 1, that a point early in the game (specifically a change in points on that possession) is expected to result in an equal change in points in the final score.  Namely:

1 ingame point * (1 win / 30 final score points) = .033 WP requires that ingame point and final score point cancel, and my contention is that they clearly do not.  It should be common knowledge to anybody who’s ever looked at NBA halftime lines (and enough data to make sure they’re not completely bonkers that way, which they aren’t) that if you are outperforming early, you are expected to do relatively worse in the second half than you were expected to do in the second half before the game.  Point differential early will NOT show up on a 1:1 basis as point differential in the final score because of this effect (there are occasional endgame situations where a game point is worth more than a final score point, like when it triggers fouls or a favorite forces OT at the buzzer, but these are rare and the expected extra point differential can be counted on one hand, often just one finger.. and sometimes the dog forces OT which clearly offsets some or all of the final regulation bucket).

Memphis was a 4.5 pt dog pregame yesterday, and because they got crushed so badly in the first half, they were a 2.5 point FAVORITE in the second half.  The point differential San Antonio built up in the first half was NOT expected to translate 1:1 to final score point differential, not even mentioning missing out on the points they were implicitly favored by in the second half before the game started (for a more even game, Indiana was a 1-point dog at Atlanta on may 3rd, led by 8 at halftime, and were expected to give 2.5 points of it back in the second half).  With relatively rare endgame exceptions of small magnitude, point differential during the game- and therefore a change in point differential during the game- does NOT translate 1:1 to final score differential, and it’s really not even close early in the game or at halftime So the formula can’t be applied at all without an average ingame point differential: final point differential multiplier (which I estimated around 0.7), bringing the value of the call down to 0.035 WP.

Tango doesn’t agree, but I can’t even figure out what part he disagrees with.  Maybe somebody else can explain it better.

Thanks for starting this thread, much appreciated.

I think you’ll like this one from Phil:
http://www.insidethebook.com/ee/index.php/site/comments/common_sense_approach_to_explaining_that_10_runs_is_one_win/

We talk about baseball and hockey first, so you can see how it works.  Someone comes in at post 17 for NBA.  He shows there that it’s 40 points per win (.025 wins per point).  We’re trying to figure out why 40, not 30.

***

As for the fiat-rule: if the standard lines give an average of 3 1/2 point to the home team, and the home team wins around 62% of the time, isn’t that enough to tell you that you have around .033 wins per point?

The 30 points per win comes from correlating team win% to point differential.  It also comes from comparing home win% to home point differential.  This is no different than how we do it in baseball and hockey.

Tangotiger - 20 May 2013 05:13 PM

The 30 points per win comes from correlating team win% to point differential.  It also comes from comparing home win% to home point differential.  This is no different than how we do it in baseball and hockey.

Do you have the study for that 30 points per win?

I spent about 60 seconds on it.

2011-2012 was the NBA strike year with compressed scheduling.  It could be and probably was strange in a bunch of ways, so I wouldn’t worry if various things measure differently.  Knowing the Home win% and home spread tells me something- the approximate combined landing frequencies of the included points, which match up fine in NBA.  Phil’s computation actually has a small error- sometimes the extra run ties it up to extras, which is ~50/50, other times it only ties it up to go to mid 9 which is lower WE.

But none of that really addresses the point I’m trying to make.  Let me ask a question- what effect do you think it has on the final score if you know the home team led 2-0 after each team had one possession compared to the home team trailing 2-0 after 1 possession each?  4 points?

In MLB, if you start the home team down by 1 to start the game, their chance of winning goes down by roughly .090.  And if they start down 2 runs, chance goes down by roughly .180.

http://tangotiger.net/innwin2.html

So, yeah, if the home team starts down roughly3-4 points in an NBA game, and it’s jump ball at that point, both teams now have a 50-50 shot of winning.

MLB is much better behaved.  I don’t actually have the exact number to the question I asked, but I ran a similar question for halftime results (whoever wins the jump ball gets the ball first in Q1 and Q4, other team gets it first in Q2 and Q3, so 1h and 2h possessions are both balanced).  Using results at halftime, comparing the final score differential to the final score differential when the home team was doing 4 points worse at HT, min 100 games in each, which meant I was comparing home winning by 12 down to home losing by 4, pairwise, to home winning by 8 down to home losing by 8, the average difference in final scores was only 3.1 points (78% of 4) despite the former group being bigger pregame favorites by about a point on average.  When I did the same thing for HT scores 6 apart, the difference was 4.7 points (78% of 6).  2 point differences, 1.5 in final (75% of 2).  So whichever way you chop it, you have two groups of teams where the group with the BETTER teams on average does WORSE in the rest of the game.  And the bigger the difference in halftime differential, the worse they do for the rest of the game.  And the markets completely bear that out.

So a swing early in an NBA game comes with two things- the immediate points and future suck.  Your theory includes the immediate points, but it doesn’t account for the future suck.

TomC: this is very interesting.

In the NHL, we see this effect when a team is up/down by 2 goals.  The next goal is scored something like 52% of the time by the trailing team, in spite of the fact that the team that is leading is likely to be the better team to begin with.

So, this “future suck” is interesting as its own topic.

But, I don’t see why we need to be too concerned with it right now.  A random point at a random point in the game has an effect of on average .033 wins.  If you would like to concede that (rather boring declaration), the “future suck” topic is a much more interesting tangent, and we can talk about that instead.

I don’t concede that.  You haven’t made any coherent argument that it is or should be true, and I don’t think that value is close to correct.  Over my years of data, 27.5% of games were decided by 5 or fewer (in either direction), so adding 5.5 points to a final score would flip the result 27.5/2 = 13.75% of the time, for a value of 2.5% per point.  Here’s the chart for x.5 pt frequencies.

X Land Value
1.5 4.0 1.3
2.5 9.3 1.9
3.5 14.8 2.1
4.5 20.2 2.2
5.5 27.5 2.5
6.5 33.5 2.6
7.5 40.3 2.7
8.5 47.1 2.8
9.5 52.6 2.8
10.5 57.8 2.8
11.5 62.6 2.7
14.5 73.6 2.5

So if you pick a random game during the season, and a random team in that game, and add X points to their final score, you can’t even get a 3%*X WP return.  And that’s completely ignoring the future suck discount.  (And I match your 0.033 by both (HWP-.5)/averageHCA and the slope of the season wins-season ptdiff regression, so it’s not that).

Right, in the thread I linked, using Phil’s method, we are getting 40 points per win (or .025 wins per point).

So, Phil’s method isn’t working compared to NHL and MLB.

I asked Phil to look into the reason.  One possibility is if you can stop the game at half time or at the three-quarter mark, would Phil’s method also match the regression method?

Using halftime and counting ties as half wins, I get 26.5 points by correlation, 26.4 points by HCW%/HCA, and about that with the counting chart method.  For 3q, I get 30.7 on correlation, 30.5 on HCW%/HCA, and about that with the counting chart method. 

Fantastic!

Ok, so, we’ve narrowed it down to something in the 4th quarter, that the scoring changes enough in the 4th quarter that it messes us up.

How far can you take your dataset?  Can you for example look at the score through the 40th minute?  44th?  46th?

Cool!  I bet the 40/30 issue with the counting method is, indeed, something about the last minute.  That’s when you’re not maximizing expected point differential any more, you’re trying to maximize your chance of winning. 

My guess is ... down by 3, seconds to go, you try a desperation three ... and you miss.  Under normal circumstances, you’d have tried a two.  So what “would” be a one-point game is a three-point game instead. 

On the other hand, if you’re *up* by 3, the other team fouls and now you’re up by 5.  So the trend is *away* from games looking close, which means you appear to need 40 pts instead of 30.

In baseball and hockey, there’s no tradeoff where you try for a better chance of winning in exchange for a lower expected score.  Well, empty net goals, and maybe trying for a home run in the bottom of the ninth instead of a single.  But those are small compared to basketball.

Just guessing, and late to the party here.

That’s as far as I can go with my data.  I agree with Phil that it’s probably an endgame effect, but you can see the influence on games that are on the outside edge of competitive before the last minute, where one team stalls and doesn’t go for ORBs and the other team is taking quick 3s in a battle that’s as much over variance as expectancy because only a far-tail result means anything.

We have that in hockey too, but I guess it doesn’t come into play often enough to matter.

Anyway, it would be interesting to see at which point it does matter in NBA.  Is it last minute, last two minutes?  At what point does the model break?