Miguel Cabrera had a rare bad day at the plate, going one for four with a K and two GDPs. One downside of coming up with lots of men on base is hitting into a high number of GDPs. Those runners make a run at the RBI record possible, however.
After running 10,000 simulations of the rest of Cabrera’s season, his average finish comes out to 159.5 RBI. The low for this set of simulations was 122 RBI, the high 211 RBI. Ninety five percent of the observations fell between 137 RBI and 183 RBI, implying a chance of breaking the AL RBI record (184) of 1.67%. The chance of breaking the MLB record (191 RBI) stands at 0.24%. The Tigers and Cabrera get a day off on Monday, heading home to face the Rays. Since Cabrera has not missed a game this year, he can probably use the time off.
Very interesting stuff.
A few questions:
1. Did you figure HRs and Batting Average projections as well?
2. Did you note the fact that his leadoff batter (Jackson) has been injured? In theory, his RBI chances will go UP when he comes back!
3. Did you factor in more intentional walks as the season goes along? I think it is possible that Cabrera will be walked with the bases loaded as some point this season.
4. My hypothesis is that Comerica Park actually gives him a better chance to get RBIs than a smaller park (more doubles with RBIs more than offsets fewer HRs). Do your simulations take into account this effect?
@Bobbleheadguru » 1. I did not, but those are much easier than RBI, since you can use a binomial distribution to get the probabilities. I was doing a triple crown projection last year, and if he gets close to winning that title again, I’ll fire up those numbers.
2&3. No and no. The simulation is based on his plate appearances since 2011. I figure out the probability of each on-base + RBI situation. I then generate a random number, and see where it lands on the distribution. Cabrera gets whatever number of RBI are associated with the bin. For example, it might land on men on first and third, one RBI, or man on second, zero RBI. So I’m assuming his men on base/RBI rates are the same since the start of 2011. That of course may not be true, but it’s a fair estimate.
4. My simulations do not take parks into account. This is very simple simulation. As Tom Tango showed with his Marcel predictions, however, simple gets you a long way to where you want to go.
David, interesting stuff.
Stupid simple math question: If 95% of the projections are between 137 and 183, doesn’t that imply that his chance of getting 184+ is 2.5% (5% divided by 2), not 1.67%? What am I missing?
bstar » It has to do with my approximation of the normal is not exact, mostly due to the distribution not always symmetrical around the mean. Plus, the normal is continuous.
bstar » I suppose I could just count how many simulations are above the record and not be so fancy.
Gotcha, thanks.