Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [bradley-terry-model]

The Bradley-Terry model is regression type model that estimates the relative abilities of 'players' & predicts the probability player $i$ will beat player $j$ in a competition based on the outcomes of observed matches.

The Bradley-Terry model is regression type model that estimates the relative abilities of 'players'. It can be used to predict the probability that player $i$ will beat player $j$ in a competition based on the outcomes of observed matches, even if they have never played each other before. Bradley-Terry models can be extended to include covariates that specify attributes of players or matches.

40 questions
19
votes
4 answers

How to get started with rating and ranking based on pairwise competition data?

I'm interesting in learning about how to rate and rank individuals in a group who only interact/compete in a pairwise fashion (i.e., systems like the ELO rating system for chess). Are there are any go-to methods or more accurate and advanced…
dcl
  • 2,610
  • 3
  • 19
  • 30
19
votes
4 answers

Measuring individual player effectiveness in 2-player per team sports

I've got a spreadsheet of some team scores. First team to 10 points wins. There are 2 players on each team. The players play with different teammates all the time, although they are not chosen perfectly randomly. No individual scores are kept. So…
Bill Waterson
  • 191
  • 3
13
votes
2 answers

Converting a list of partial rankings into a global ranking

I'm working on something like the following problem. I have a bunch of users and N books. Each user creates an ordered ranking of all the books he's read (which is likely a subset of the N books), e.g., Book 1 > Book 40 > Book 25. Now I want to turn…
raegtin
  • 9,090
  • 12
  • 48
  • 53
9
votes
1 answer

How to fit Bradley–Terry–Luce model in R, without complicated formula?

The Bradley–Terry–Luce(BTL) model states that $p_{ji} = logit^{-1}(\delta_j - \delta_i)$, where $p_{ij}$ is the probability that object $j$ is judged to be "better", heavier, etc, than object $i$, and $\delta_i$, and $\delta_j$ are parameters. This…
Silverfish
  • 213
  • 2
  • 5
8
votes
1 answer

How do I get a group of people to collectively rank a set of objects?

I work for an organization that oversees around 180 schools across the country. We regularly collect outcome data from these schools and rank them. I have been asked to do a survey of the national office (around 100 people) to determine what the…
adharris
  • 181
  • 2
8
votes
1 answer

Multinomial choice with binary observations

Is there a standard name for a multinomial choice model where the observations are in the form of binary questions such as "do you prefer A to B" and "do you prefer B to D"? This seems like a common occurrence, and the likelihood is easy enough to…
Tristan
  • 1,592
  • 10
  • 12
7
votes
1 answer

How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets?

As part of my graduate thesis (area: psychology) I have gathered preference data. The data includes approximately 50000 heads-up comparison between elementX and elementX. I have a total of 15 elements. The participant would be shown 36 comparisons…
ChrisFinland
  • 71
  • 1
  • 4
7
votes
1 answer

How to model pairwise preference with both strong and weak preferences?

I have large comparison data in form In a pairwise comparison data each data point compares two alternatives. For instance: A > B (A is preferred to B, A and B are classes, not numbers) A > B B > A B > C A > C etc ... In short we can write…
Łukasz Lew
  • 1,312
  • 2
  • 14
  • 24
5
votes
1 answer

Inference on and quasi variances in Bradley-Terry-models

Upfront I am not a statistician but a medical doctor. I have a working knowledge of statistical methods in my field, but this is my first time with pairwise comparisons and due to a lack of formal math training I am having a hard time to get into…
Bernhard
  • 7,419
  • 14
  • 36
5
votes
0 answers

Bradley-Terry model for unequal team comparisons

I'm trying to predict the outcome of a sports match between two teams. I have data on wins and losses for all teams in the league. I intend to use a Bradley-Terry model to find the relative rankings of each team and predict the probability of team…
ilanman
  • 4,503
  • 1
  • 22
  • 46
4
votes
0 answers

How many comparisons do I need to rank using Bradley-Terry?

I have recently learned about a method for ranking items based on comparisons called the Bradley-Terry method. I am using it to rank about 500 items. I am wondering how many comparisons do I need to make if I uniformly pick items to compare each…
David Faux
  • 853
  • 2
  • 11
  • 16
4
votes
2 answers

logistic regression for competitive games

I am interested in using logistic regression to model a competitive game. The data looks something like this: winner loser teamA teamB teamB teamC teamA teamD ... ... and each team in the dataset has at least 5 wins…
rcorty
  • 438
  • 4
  • 13
4
votes
1 answer

Decision tree: What is the most important next feature?

Summary: A decision tree (aka identification tree) is trained on a training set with a largish number of features (tens) and a large number of classes (thousands+). It turns out that every feature is important to distinguish some subset of classes,…
Superbest
  • 253
  • 3
  • 10
4
votes
1 answer

I have 12 items to get into a single rank order. Can I get this from having a few hundred people see a set of 10 of the possible pairs of items?

I attempted to run a study where people had to rank order 12 statements from best to worst. However, it was extremely messy and difficult for people to rank that many items. Now, my professor and I have decided instead to show people 2 statements…
Bofstein
  • 61
  • 3
3
votes
0 answers

When should one use Bradley-Terry instead of gradient boosted trees for pairwise ranking

Both the Bradley-Terry model and Gradient boosted trees can be used to learn a ranking from pairwise comparisons (e.g. with libraries choix and XGboost). How do they relate to each other? Is there any situation in which one might be preferable to…
vman
  • 173
  • 5
1
2 3