Intentional walks or base on balls have been around for a long time in baseball. Early on in baseball, the catcher could set up much further away from the plate than they can do know. They would receive four wide pitches, too far away for the batter to have any chance at hitting the ball.

As the intentional walk became more frequent following the end of the dead ball era, batters such as Babe Ruth complained about the unfairness of it. But they weren’t an officially tracked stat until 1955. As you can see from the graph below, there was an increase in usage in the 1960’s but since then there has been a gradual decline.

Nowadays, there are two main reasons that teams will intentionally walk a batter.

Firstly, to get to a weaker hitter when there is just one out required in a inning. This happens more in the National League than it does the American League due to pitchers hitting, which is why there is nearly double the amount of intentionally walks in the National League.

Secondly and much less frequently, teams will intentionally walk a batter when there is 1 out and a man on 3rd, sometimes 2nd as well, but no-one on 1st. This is in an attempt to pick up a double play off the next batter.

These both make some analytical sense but with pitchers hitting less often now, we are seeing this decline in use. But are there other scenarios when intentionally walking a batter would make sense. Let’s examine one of them.

Imagine this scenario, where you’re the manager of an MLB team. It is the bottom of the 9^{th}, your team is up by 2 runs, you have two outs but the bases are loaded. Up to the plate walks Mike Trout, would you intentionally walk him?

Would you do what the Diamondbacks did against Barry Bonds in 1998 or what the Rays did to Josh Hamilton when they were 4 runs up in 2008 (Rays manager at the time was Joe Maddon) and ‘intentionally walk in a run’.

My base instinct here is yes, but let’s evaluate if we really should. I will be using Trout’s and MLB’s 2018 stats to try and answer this question.

To do this we need to find out what the likely outcomes are for Mike Trout and the league average hitter with the bases loaded. But to do that we need to examine some bases loaded scenarios league-wide.

With the bases loaded, we often hear commentators saying that a single will drive in 2 runs and a double will clear the bases, but that doesn’t happen as often as you might think. In 2018, just over 60% of bases loaded singles scored 2 or more runs and only 37% of bases loaded doubles cleared the bases (I removed walk-offs from these calculations).

Using these base stats we can now project the chance of Trout and MLB average driving in runs.

Mike Trout would score a run 46% of the time and would hit a walk-off (bases clearing double, triple or HR) 8.6% of them time. We can now build what would happen in our scenarios, either the pitching team lets Trout have a normal AB or they intentionally walk him. The following probabilities are based of all other batters following being league average.

So if we let Trout bat, as before we have just over 54% chance of Trout not getting on base and the game ending. But if you include what the hitters after him could do, his team would get the required runs to win the game 18.6% of the time and drive the game to extras 9.6% of the time.

If we intentionally walk him the batting teams chance of winning goes up by 2.7 percentage points and chance of extras by 0.7 points. The pitching team would decrease their chance of winning by 3 percentage points overall from 76.6% to 73.6%.

Analytics says we shouldn’t intentionally walk Trout, which is a bit sad. He isn’t so much better than his peers that we should just give up pitching to him.

But let’s not end on a sad note. I will work out how bad the hitters would have to be for it to be worthwhile to walk Trout and how good Trout would have to be for it to be worthwhile with MLB average hitters up next.

**Worse Hitters**

For it to be worthwhile to intentionally walk Mike Trout in our scenario the two hitters after him need to have a slash line similar or worse to the following , .187/.237/.307. That is a woeful performance level from an MLB player but that being said there was 25-30 players last season who had more than 50 PAs who were in or below this region.

It is highly unlikely that the Angels would have two players this bad playing behind Trout, as he generally bats 2, but they have had one game this season with Justin Bour and Albert Pujols in the 3 and 4 slot behind Trout.

With Bour slashing .169/.275/.303 and Pujols a slightly more respectable .214/.295/.402, if these two were the next two up, the difference for our scenario drops to just under 1 percentage point.

**Better Trout**

For it to be analytically worthwhile for a pitching side to intentionally walk Trout, when MLB average hitters were coming up after him, he would need to slashing something similar to or better than .374/.550/.750. That equates to the best seasons Babe Ruth, Ted Williams and Barry Bonds ever had. Or what Cody Bellinger is doing so far this season.

Bellinger’s monthly performance and the monthly performances of other players the last few years show that we would expect on person per month to perform at this level. Trout, himself, has performed at this level for a month 3 times, once in 2012, 2014 & 2015. But none of them can keep it up over a season.

So, if a hitter is having a top 10 season of all time, over at least a couple of months, then you might want to intentionally walk him. Otherwise you should take them on.