I'd like to do some analysis of shooting efficiency in basketball when a team is leading (AHEAD) or trailing (BEHIND) by less than 8 points and whether they are HOME or AWAY. Here are a few examples of the data:
Ray Allen HOME BEHIND 59.4% 134 Ray Allen HOME AHEAD 57.13% 132 Ray Allen AWAY BEHIND 49.1% 166 Ray Allen AWAY AHEAD 48.03% 126 Jason Terry AWAY BEHIND 56.6% 242 Jason Terry HOME BEHIND 52.0% 193 Jason Terry AWAY AHEAD 50.05% 198 Jason Terry HOME AHEAD 48.73% 207 Jamal Crawford AWAY AHEAD 51.65% 82 Jamal Crawford HOME AHEAD 42.50% 178 Jamal Crawford AWAY BEHIND 35.5% 129 Jamal Crawford HOME BEHIND 33.4% 118 Kevin Durant HOME BEHIND 48.6% 222 Kevin Durant HOME AHEAD 44.05% 248 Kevin Durant AWAY BEHIND 41.4% 325 Kevin Durant AWAY AHEAD 40.07% 213
The 4th column is the FG% (i.e. proportion of made shots) and the 5th column is the number of shots (i.e. trials).
You can see even with these 4 players (and there are roughly 200 in the data set), that there is variation of the mean FG% between players, and for each player, there is not a consistent pattern in whether they are "better" at HOME or AWAY or AHEAD or BEHIND. So there's a lot of variance between groups and within groups as far as I can tell.
I thought about using lmer, but I wasn't sure how to do that for this problem, because if I just use the FG% as the outcome, I lose the information about how many shots were taken. Eventually, I'd like to put this into BUGS, but I thought there might be a more straightforward way for now, because I'm not quite ready for that yet.
I should just add that what I'm really after is a way to determine whether a player is "really" better under one of these conditions, or are the apparent differences just due to noise/variation from small sample sizes.
Thanks for any advice.