# What will produce better model - Modeling the whole plus the variance or just modeling the variance?

I have a set of horse racing data. Specifically distances run by horses in races. For example, for a sample of 1000 horse races at a mile I have data for how far each horse ran during the course of the race. One might say that if it's a mile race, then each horse ran 5,280 feet. That would be incorrect because of ground loss. Ground loss can be attributed to a variety of factors (no pun intended): post position, running style, race distance, track configuration, etc.

Given this, would it be preferable to make total distance run the dependent variable and use race distance (in feet) along with other variables as the explanatory variables? Or

Would it be preferable to use ground loss (actual distance run - stated race distance).

Specifically, My concern is the high covariance between total distance run, say 5350 feet and an explanatory variable (stated distance) of 5280 may create a signal to noise issue and undermines the model's accuracy/validity. Or, is this an ideal situation that will lead to excellent results.

• It would help to explain what ground loss is and how it makes a mile not be 5,280 feet. Also, will your horses be running different distances (ignoring ground loss...so all horses run what most of us would call a mile)?
– Dave
Dec 7, 2019 at 1:10
• @Dave Ground loss is the distance greater than the stated distance of a race. A horse experiences ground loss when it races wide on the turns, or does not run straight in the backstretch or stretch, or has to weave through horses to get a clear running. Dec 7, 2019 at 1:28
• What is the actual objective of your modeling exercise? Dec 7, 2019 at 1:57
• @jbowman the objective is to be able to accurately predict/model the total distance a horse will run given the distance of the race, post position, number of turns, etc. I can get to that directly by modeling total distance or by modeling grounds loss and then adding that to stated distance. Which is better? Dec 7, 2019 at 2:00

Okay, so running a zig-zag around a mile-long track results in a lot more running than just the one mile. That makes sense. Now addressing your question, it sounds like race length will be a major contributor to distance run. If your main goal is to have an accurate predictive model, then I think you have to include that distance.

Even if you want to use the regression to do parameter inference and can accept a noisier model, I'd remain inclined to leave race distance in my regression. Especially if you have some fairly different race lengths, that variable will account for much variability in the dependent variable. (In other words, it's just not fair to compare distance run in a two-mile race to a half-mile race.)

Quick note: I would expect some interaction terms. For instance, having a good starting position is, I assume, likely to become less of an advantage as the race goes on, since competeting horses will have more time to catch up.

• Thanks for the response. So, I'm in agreement that using race distance as an explanatory variable, but what should my independent variable be - ground loss or total race distance or does it matter. Thanks again. Dec 7, 2019 at 1:49
• @Mutuelinvestor I have a suspicion that you would find ground loss more interesting (and it probably has less of a relationship with race distance), though it depends on what you want to predict. So...what do you want to predict? (I'll read your response to jbowman.)
– Dave
Dec 7, 2019 at 1:59
• After reading your response to jbowman that you want to predict total distance covered but don't know if you should predict that or predict ground loss and then add the race distance or go straight to distance covered, I see that you have an empirical question on your hands. Try both and see what happens! My guess is that the ground-loss-only model will give better results, since the other method kind of has to predict both ground loss and race length, giving two places where you could go wrong, not just one.
– Dave
Dec 7, 2019 at 2:07
• race length (in feet) will be one of my inputs in either case. Dec 7, 2019 at 2:11
• I don't mean that you literally have to predict race length, but more conceptually that a model of total distance run will have to understand both and have uncertainty about both, while a model of ground loss only deals with ground loss, and then you know the race length. Anyway, after thinking a few more minutes, I'd be shocked if you got better performance from the total distance model than the ground loss model, though I also think it's worth trying both. Go prove me wrong! (This problem is much more interesting to me if I'm wrong.)
– Dave
Dec 7, 2019 at 2:15