precision recall breakeven point There are two popular measures that aggregate $Precision$ and $Recall$, there are $F1$ and $\text{Precision Recall Breakeven point}$. 
$F1$ can be calculated easily by formula, but how to calculate $\text{breakeven point}$?
I have some experiment and get all four values: true positive, false positive, true negative, false negative, so now I can calculate Precision and Recall but how to find breakeven point in this case.
 A: There is an excellent post (Obtaining predicted values (Y=1 or 0) from a logistic regression model fit) about the break-even point of precision (or sensitivity) and specificity. The latter is not the same as recall, but it should be easy to generalize from there.
If you look at the plot you will see a point where the metrics cross, this is your optimal cutoff point. 
EDIT  I have updated the code to include precision, recall, and F1
perf = function(cut, mod, y)
{
     yhat = (mod$fit>cut)
     w = which(y==1)
     sensitivity = mean( yhat[w] == 1 ) 
     specificity = mean( yhat[-w] == 0 ) 
     c.rate = mean( y==yhat ) 
     d = cbind(sensitivity,specificity)-c(1,1)
     d = sqrt( d[1]^2 + d[2]^2 ) 

     # F-score
     retrieved <- sum(yhat)
     precision <- sum(yhat & y) / retrieved
     recall <- sum(yhat & y) / sum(y)
     Fmeasure <- 2 * precision * recall / (precision + recall)
     out = t(as.matrix(c(sensitivity, specificity, c.rate,d, Fmeasure)))
     colnames(out) = c("sensitivity", "specificity", "c.rate", "distance", "F-score")
     return(out)
} 

y3.mod <- glm(y3 ~ x1 + x2 + x3 + x4 + x5 + x6, family=binomial()) 

par(mfrow=c(1,1))
s = seq(.01,.99,length=100)
OUT = matrix(0,100,5)
for(i in 1:100) OUT[i,]=perf(s[i],y3.mod,y3)   
      plot(s,OUT[,1],xlab="Cutoff",ylab="Value",cex.lab=1.5,cex.axis=1.5,ylim=c(0,1),type="l",lwd=2,axes=FALSE,col=2)
axis(1,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.)
axis(2,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.)
lines(s,OUT[,2],col="darkgreen",lwd=2)
lines(s,OUT[,3],col=4,lwd=2)
lines(s,OUT[,4],col="darkred",lwd=2)
lines(s,OUT[,5],col="black",lwd=2)
grid()
box()
legend("topleft",col=c(2,"darkgreen",4,"darkred","black"),lwd=c(2,2,2,2,2),c("Sensitivity","Specificity","Classification Rate","Distance","F-score"))

A: Precision and recall measure the performance of a set of items which are predicted to be positive.
The break-even point measures the performance of a ranking of items which puts the items most likely to be positive at the top. You can take the top k items from this ranking and calculate the precision and recall of that set. Different values of k will give you different values of precision and recall. It is a fact that for some value of k, precision will equal recall, and this value of precision (and recall) is the break-even point.
So you need more information. You can't get the answer from just the precision and recall of the set of items which are predicted positive. You need to know the order of the items.
Once you have this, the break-even point is in fact equivalent to the measure called R-precision. This is the precision of the top R items in the ranking, where R is the number of relevant items. That's the way to calculate it.
