# Modeling the probability of winning on a sales site

Let's say that I have a dependent variable, the probability of winning on ebay, and I want to model that on various variables. Let's say I have data on each individual ebay item I am bidding on and whether I won or not. Is there a way to model the probability of winning. Or would it better to think of the dep var as a dichotomous variable which is either won or did not win, and then construct a logit. Basically, I'm wondering if and what strategies to pursue in order to find the probability of winning, while accounting for various independent variables.

The logit plan sounds more logical, but I'm wondering if there's something I could use as an alternative for modeling the probability of an outcome.

Basically, I'm wondering about finding:
When I bid $5, what's the probability of winning When I bid$6, what's the probability of winning
and so forth


EDIT:

Let's say I have data on various products that I won and those that I lose, along with various other variables. Why wouldn't it make sense to predict on whether it was win/loss. I guess 0/1 is still not probability, but hmm... I have the data, I'm just not sure if or how to model the probability of winning.

I'm really interested in a single bid price and whether I won/lost.

So predict win/loss on bid price, use a logit model, then estimate the probability of winning (Which I'm not sure about)

• Game-theoretic methods may provide more insight here than purely statistical methods.
– whuber
Commented Dec 21, 2011 at 17:49
• Let's say I have data on various products that I won and those that I lose, along with various other variables. Why wouldn't it make sense to predict on whether it was win/loss. I guess 0/1 is still not probability, but hmm... Commented Dec 21, 2011 at 17:59

Since probability is bounded by 0 and 1, any predictor that relates to the probability of winning will likely do so in an S-shaped fashion. It is easier to build a model using the logit, which gives one the chance of finding linear relationships. With that done, it's a little bit of work but not terribly hard to convert logits into probabilities associated with different combinations of predictors. I think you'd get a lot out of readings on logistic regression.

Theoretically, there is no possible answer for probability of winning an auction described above. However, if you decide to run the same experiment, only with a small group of users, a answer would be possible. Without the control of the users, there is the random variable of different users. Say if somebody decides that they really want that particular item, they will fight to win it for a while. On the contrary, somebody could say "Well, it would be cool to have this", and they might not try as hard, making your probability in your favor. All in all, with your current situation, a solution isn't possible, due to the abundance of unknown and changing variables.

EDIT:

What I meant by not being able to achieve a solution is that you cannot control who participates in the auction you are focusing on, which is a variable that you cannot control.

• And non-quantifiable variables too!
– nico
Commented Dec 21, 2011 at 19:07
• Yes @nico, you are also correct. Commented Dec 21, 2011 at 19:26
• To say that the outcome cannot be predicted with 100% accuracy based on available variables is not at all the same as saying one cannot model the outcome at all. @CodeAdmiral merely points out that prediction will be less than perfect. Now the task is to see how well one can predict using available data (that for all we know might relate to the outcome), given that individual competitors for an item will have unpredictable/unknown characteristics. Commented Dec 22, 2011 at 0:27
• Oh, I get it. You are saying you aren't trying to necessarily going for the theoretical probability, but more the experimental probability. Basically, @ATMathew is trying to get out of this is some basic guidelines. Commented Dec 22, 2011 at 15:15
• You can include a varying intercept by user to condition on specific effects by user. Commented Dec 28, 2011 at 18:09