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Tuesday, March 17, 2009
Being Behind is a Good Thing (Part II)?
Followup to part 1.
OK, I have halftime stats for all NBA games from 2001/2002 to 2006/2007.
That is not a whole lot of games to be breaking things down by halftime point differential, but here goes:
diff at half time N games final WP
0 203 .500 (of course)
+1 472 .456
+2 413 .557
+3 412 .604
+4 403 .598
+5 390 .664
+6 387 .698
+7 368 .750
+8 314 .717
+9 310 .803
+10 or more 1899 .888
What do you know! The same effect! Assuming that the expected wp is around .525, the sample wp is 6.9 percentages points less, which is over 3 standard deviations for 472 games.
However…
If we look at the same table broken down by the home and road teams, we see a strange effect which puts some doubt on the authors’ conclusions as to the reason for the effect (that when a team is down by a little at half time, they put out more effort in the second half, particularly in the first few minutes of the second half. And they give us a lot of experimental support for that psychologically-based thesis.
diff homegames home WP roadgames road WP
0 203 .562 203 .438
+1 224 .545 248 .375
+2 240 .633 173 .451
+3 226 .668 186 .527
+4 226 .664 177 .514
+5 225 .716 165 .594
+6 216 .741 171 .643
+7 224 .808 144 .660
+8 165 .758 149 .671
+9 192 .813 118 .788
+10+ 1238 .920 661 .828
So what is likely going on, as suggested by the table above? Well, for some reason the road team in the NBA, at least in this sample, tends to be up by 1 at the half far more than they should be. In fact, the road team is up at the half 248 time and the home team is up at the half only 224 times. Obviously since the home team is around 5 point better for the whole game, they should be up at the half more than the road team is for any point differential. That is the case, other than at 1 point. I am not sure why that is, but it probably has something to with the strategies employed by the home and road teams, resting players, etc., especially in a close game.
So what is happening, again, at least according to this limited set of NBA data, is that when a team is up by one point at the half, on the average, they are the worse team!
So of course they will have a losing record for the game, regardless of the energy or effort put in in the second half. I suspect that the same thing is happening in NCAA. Did the authors break down the data by home and road teams?
The same effect could be true when you take into consideration the relative strengths of the two teams, independent of their home/road status. For some reason, the better team, again, independent of home/road status could be behind by one point at the half more often than the worse team. And again, they will tend to win the game more than 50% of the time, even being behind by 1 pt, since they are the better team overall. Or maybe that is not the case, independent of home/road status. Maybe there is something fundamental about being the home team that makes you down by 1 point more often in the first half. Can anyone think of a reason why that might be true?
Let’s look at points scored and allowed for the first and second half for home and road teams as a function of the various point differentials at half time.
It is too much to put in a chart, so I will summarize in words.
Tied at the half, the home team and road teams score 48.4 in the first half. In the second half, the home teams score 49 (includes overtime - that is why it is 1.6 pts more than 1st half) and road team scores 47.7. So home team outscored the road team by 1.3 pts in the second half. You would normally see the home team score around 2 to 2.5 points more in the second half, but when a game is tied at the half, it suggests that the road team is better than the home team, not counting the home/road status of both teams.
With a 2 point lead at the half, the home team scores 49 points in the first (same as in a tie game) and scores only 49.3 in the second half. What happens is that the bigger the lead by the home team in the first half, the less points they score, relative to the first half, in the second half.
For example, with a 5 point lead, the home team scores 49.7 in the first half and only 48.7 in the second. With a 10 or more point lead, they score 55.7 in the first and 47.3 in the second.
The reason for this is two-fold. Teams that have a lead in the first half will have tended to have gotten lucky in scoring and thus will regress in the second half, and teams with a big lead at the half will tend to have a big lead late in the game and will start resting starters and slowing down their offense.
Anyway, with a 2 point lead, when the home team is ahead they score 49.3 in the second half and allow 47.9. With a 2 pt lead at the half by the home team, the teams tend to be about the same strength, not counting home/road status.
In a tied game, the home team scores 49 in the second half and allows 47.7.
I am purposely leaving out the 1 point lead for a minute.
With a 3 point lead, the home team scores 49.1 and allow 48.4. So they score a little less and allow a little more than with a 2-pt lead, as we would expect.
So nothing unusual so far in tied games and when the home team is up 2 or 3 pts.
What about the road team? Obviously in a tie game, the stats exactly mirror the home team.
With a 2 pt lead (now the road team is a bit better than the home team, not counting home/road status - but still worse of course if you include home/road status), the road team scores 46.5 in the second half and allow 49.2. In the first half, the road team scored 49.1 and allowed 47.1.
With a 3 pt lead, the road team scored 48.5 and allowed 45.5. In the second half, they scored 47.0 and allowed 49.5. Around the same second half differential as with a 2 pt lead.
So to summarize so far:
In a tie game, the differential in the second half is 1.3 pts in favor of the home team.
Then the home team is up by 2 points, they outscore the road team by 1.4 pts in the second half. When up by 3, they outscore them in the 2nd half by .7. When up by 4, it is only .3.
Again, we see a diminishing point differential in the second half as the differential increases at the half, because of the fact that they will rest their starters if they have a big lead at the end.
The road team when up by 2 at the half will score 46.5 and allow 49.2 in the second half for a differential of -2.7. So, interestingly, the road team will do worse in the second half, when leading by 2 as opposed to a tied game. You would expect the opposite as a road team that was ahead at the half by 2 pts should be a better team than a road team that is tied. But then again, maybe it is because they will also tend to have a large lead at the end more often than if the game were tied at the half, but I would think that that effect would be very small.
Anyway, if the road team has a 3pt lead, they are outscored in the second half by 2.5 points.
With a 4 pt lead at the half, it is -3.3.
OK, so what about with a 1 point lead? The $64,000 question.
The home team with a 1 pt lead scores 48.3 in the first half and of course allows 47.3. That is around the same number of pts scored as in a tie first half game (that was 48.4). In the second half, the home team scores 49.3 and allows 48.1 for a differential of 1.2. That is almost exactly the same as in a tie game (1.3 differential in a tie game)! They score and allow a little more for some reason with a 1 pt lead than in a tie.
So when the home team has a 1 pt lead, there is no discontinuity between the tie game and a 2 or 3 pt lead.
What about the road team? With a 1 pt lead, they score 47.7 in the 1st half and allow 46.7 of course. That is a little less than in a tie game or a 1 point game for some reason (or no reason at all - remember we are working with relatively small samples of games). In the second half, they score 46.9 and allow 50.5, a differential of 3.6 pts.
Remember that in a tie game, they score 47.7 and allow 49.0 in the second half.
So it looks like everything is good except that they allow an inordinately high number of points in the second half - that is, the road team with a 1 pt lead at the half.
With a 2 pt lead, remember they (road team) score 49.1 in the first and then score 46.5 and allow 49.2, for a differential of 2.7. With a 3 pt lead, the second half differential is 2.5. 4 pts, 3.3.
So, to really summarize:
Road team
Pts 2nd half diff
tie game -1.3
1 pt lead -3.6
2 pt lead -2.7
3 pt -2.5
4 pt -3.3
5 pt -2.5
6 pt -2.3
7 pt -3.8
8 pt -3.8
9 pt -2.8
10+ pt -4.4
Home team
Pts 2nd half diff
tie game 1.3
1 pt lead 1.2
2 pt lead 1.4
3 pt .7
4 pt .3
5 pt .7
6 pt -.3
7 pt 1.0
8 pt -.9
9 pt -.5
10+ pt -.9
So, you can see an effect (disconnect) only when the road team is up by 1 point and if you look at the points scored and allowed, you can see that is in in the points allowed by the road team when they are up by 1 at the half. They allow an inordinately high number of pts in the second half. That could be because of more effort by the home team, less effort by the home team, or some complex strategy thing (where “strategy” includes things like personnel on or off the court).
In addition, the whole effect is magnified because, again for some reason that I am not aware of, the home team tends to be down by a point at half time more than one would expect.