Barry Salt: Speeding Up And Slowing Down

The sample of 20 American feature films from 1959 that I have added to the Cinemetrics database has revealed a feature that I did not expect. (Sort the database on year to quickly find them clumped together.) My belief had been that the cutting rate nearly always speeded up over the whole length of most ordinary commercial American features, and that any rare exceptions to this would be failures at the box office. However, I also believed that in art films (usually called “independent films” nowadays) and also in foreign films, the cutting rate very frequently slowed down over the course of the film. But the first degree trendline for my sample of American films shows that nearly half of them have slower cutting in the second half of the shots compared to that in the first half of the shots. The first degree trendline actually represents graphically the degree of difference between the ASL (Average Shot Length) for the first half of the shots in a film and the ASL for the second half of the shots in that film.

The films in my sample in which the cutting rate decreases over the length of the film are Compulsion, The Five Pennies, Gidget, Go, Johnny, Go!, Heller in Pink Tights, Never So Few, The Nun’s Story, Ride Lonesome, and Some Like it Hot. Of these, Some Like it Hot and Gidget certainly did very well at the box office, though I seem to remember that Heller in Pink Tights did not. The others were reasonably successful, I think. As you can see from the Cinemetrics graph, Darby O’Gill and the Little People has a flat cutting rate over its length.

Of course, down the lengths of all these films, as in all films, there are alternating stretches of slower and faster cutting, which can sometimes be a bit difficult to make out on the Cinemetrics graphs. The higher degree trendlines highlight these fluctuations to some extent, but are not always completely successful in doing this. I can illustrate this problem with the graph for Ride Lonesome, using the sixth degree and twelfth degree trendlines.

Figure 1

The sixth degree trendline very approximately picks out the stretches of faster cutting from the beginning to 3 minutes, that from 25 minutes to 27 minutes, and the final stretch from 62 minutes to near the end of the film. But it completely misses the section of overall fast cutting from 7 minutes to 12 minutes, and from 38 minutes to 42 minutes. This is inevitable, as a sixth degree trendline can only have 3 maxima at the most, whereas there are at least 5 fairly clear stretches of faster cutting in the film. So let us see how the twelfth degree trendline, which can have six maxima, and five minima (or vice versa), does in this situation.

Figure 2

This looks a lot worse to me.

Now there is an alternative to trendlines for picking out the changes in cutting speed throughout the length of a film, and this is the moving average. This statistic was considered by Gunars Civjans and Yuri Tsivian in the early days of Cinemetrics, but they did not develop it. I think it should be reconsidered.

The usual moving average is taken over a fixed number of quantities (shot lengths in our case) prior to the point in question, but the appropriate form of moving average in the case of Cinemetrics is the “centred moving average”. This takes the average shot length for a range starting a certain number of shots before the point under consideration, and ending the same number of shots after the point. Some tests suggest that a range of 20 shots works best; ten before, and ten after the point for which you want the average. Applying this to the shot length record for Ride Lonesome produces the following graph:

Figure 3

The graph is inverted from the Cinemetric perspective, because that is the easy way for me to do it with the graphing tools in spreadsheets. Here, the shot lengths are indicated by black lines, and the moving average is in green. The horizontal x-axis is calibrated in shots, not minutes and seconds. This graph can be given a smoother profile by taking a second centred moving average from it. In fact, the best result seems to come from taking a 10 shot centred moving average first, before then applying the 20 shot centred moving average. This procedure produces the graph below.

Figure 4

You can see that this new curve also has no problem in following the major ups and downs in the original shot length plot, and has extra smoothing as well.

So why might we be interested in these cutting rate variations?

I hold the position that variation in cutting rate is ordinarily used as an expressive device of a conventional kind – more cuts for sections where there is more dramatic tension or action, and less for less of the same. And I also believe that in general there is a conventional idea about alternating scenes with different dramatic character in plays and films, so that things like cutting rate and closeness of shot which are used expressively should change on the average from scene to scene. Hence the next step is to check out the results of this idea for this film.

Ride Lonesome has 18 scenes from a dramatic viewpoint, and they are clearly marked out by dissolves between them, in the conventional way of the period when it was made. In the graph below, the shot lengths are still given by black lines, but the ASL for each scene is indicated by the red bars, and the centred moving average by a green line.

Figure 5

The shot lengths are given in deciseconds, not seconds, and the maximum value shown is 20 seconds, so that the lines for some shots, and indeed some mean ASLs for the scenes, go off the top of the graph, just as they do in the Cinemetrics graphs. The first scene runs from Shot No. 1 to Shot 55, the second scene comprises Shot 56 alone, the third scene runs from Shot 57 to Shot 141, and so on. The green line still represents a plot of two successive centred averages.

For comparison, below is the graph with the sixth order trendline plotted in instead of the centred moving average.

Figure 6

So the moving average has a better correspondence with the mean ASL for the scenes than the trendlines, as well as identifying the sections of faster and slower cutting better.

Incidentally, my graphs plotting the mean ASLs for all the scenes in the film are the visual equivalent of the verbal discussion of this variation of cutting rate from scene to scene in The Adventures of Robin Hood at the beginning of my piece The Numbers Speak from Moving Into Pictures. This piece is also in the “Current Movie Measurement Articles” section of the Cinemetrics website.

Ride Lonesome is unusual in that it only has 18 scenes in it. This is at the lower end of the range of the numbers of scenes occurring in ordinary commercial films. This range seems to run from about 20 scenes to about 50 scenes, with most films having somewhere around 30 scenes. (I shouldn’t be surprised if the number of scenes in an ordinary film follows a Normal (Gaussian) distribution.) An example of a film with a more usual number of scenes is given by Darby O’Gill and the Little People. The Cinemetrics graph for this, with a 12th. degree trendline, is reproduced here in inverted form, for comparison with my “moving average” treatment.

Figure 7

And here is my moving centred average graph for this film, with the ASL for scenes marked in as well. Some of the lines indicating each shot’s length are shifted a bit relative to the previous Cinemetrics graph, because my x-axis is a linear scale in ordinal shot number, rather than the time to the shot in question, as is the case with the elastic scale of the x-axis of a Cinemetric plot. This does not affect the point being made.

Figure 8

The correspondence between the general shape of the moving average plot and the “mean ASL for scenes” plot is not quite so good as in the case of Ride Lonesome, but there is a rough resemblance between the two, which is not the case for the trendline.

Darby O’Gill has 37 scenes, and to be certain of getting all the ups and downs resulting from the cutting rate changes from one to the next with a trendline, one would have to use a 38th. degree (or order) trendline, not a 12th. degree one.

Barry Salt, 2010